(a) False; A subspace is formed by the set of vectors that do not belong to the column space.
(b) True; If the matrix contains solely the zero vector, then it is the zero matrix.
(c) True; The column space of a particular matrix is equivalent to the column space of another specified matrix.
(d) False; The column space of one matrix is identical to the column space of another matrix.
(a) False; if A = [1 0; 0 0], then the column space of A is { e1 }, where e1 is the standard unit vector in the plane. If v is not in the column space of A, but w is not in the column space of A, then v + w is not in the column space of A.
Therefore, the set of vectors that are not in the column space of A does not form a subspace.
(b) True; if every vector in Rn is in the null space of A, then in particular, every standard unit vector is in the null space of A. Thus, the ith column of A is zero for i = 1, . . . , n, so A is the zero matrix.
(c) True; the column space of A is generated by the columns of A, while the column space of AB is generated by linear combinations of the columns of AB. By definition of matrix multiplication, the columns of AB are linear combinations of the columns of A, so the column space of AB is a subspace of the column space of A. Conversely, let b be in the column space of A. Then there is an x in Rm such that Ax = b. Thus, ABx = A(Bx), so b is in the column space of AB. Therefore, the column space of A is a subspace of the column space of AB. Hence the two column spaces are equal.
(d) False; if A = [1 0; 0 0] and B = [0 0; 0 1], then the column space of A is { e1 }, while the column space of B is { e2 }. The column space of AB is { 0 }, so it is not equal to either column space.
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if log a = 0.05 , what is log (100a)?
0.6990 is value of logarithm .
A logarithm is defined simply.
The logarithm represents the power to which a number must be raised to obtain another number (see Section 3 of this Math Review for more about exponents).
As an illustration, the base ten logarithm of 100 is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100. Binary logarithms, which have a base of 2, natural logarithms, which have a base of e 2.71828, and common logarithms with a base of 10 are the four most popular varieties of logarithms.
Now, log0.1= log(1/10) =log (10^-1) =-1 log10
Here log 10= 1 .
log a = 0.05
log (100a) = log (100 * 0.05)
= log( 5.00)
= log(5)
= 0.6990
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Can you help please? Thanks
The hypοtenuse's length is c = 17.
Hοw dο yοu figure οut hοw lοng the hypοtenuse is?Add the square rοοts οf the οther sides tο find the hypοtenuse. Tο find the shοrter side, subtract the squares οf the οther sides, then take the square rοοt.
Using the Pythagοrean theοrem, we can calculate the length οf the right triangle's missing side:
[tex]a^2 + b^2 = c^2[/tex]
where a, b, and c are the lengths οf the triangle's legs, and c is the length οf the hypοtenuse.
The lengths οf the twο legs are given in this case: a = 8 and b = 15. Sο we can plug the fοllοwing values intο the equatiοn:
[tex]8^2 + 15^2 = c^2[/tex]
[tex]64 + 225 = c^2[/tex]
[tex]289 = c^2[/tex]
When we take the square rοοt οf bοth sides, we get:
[tex]c = \sqrt{(289)} = 17[/tex]
As a result, the hypοtenuse length is c = 17.
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The vertex of the parabola below is at the point (5, -3). Which of the equations
below could be the one for this parabola?-ہے
A. y=-3(x-5)^2-3
B. x=3(y-5)^2-3
C. x=3(y+3)^2+5
D. x=-3(y+3)^2+5
None of the available options match the parabola's equation.
Which might be the parabola's equation?To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.
A parabola's vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the parabola's vertex.
[tex]y = a(x-5)^2 - 3[/tex]
These values are substituted into the equation to produce:
[tex]-15 = a(2-5)^2 - 3[/tex]
[tex]-15 = 9a - 3[/tex]
[tex]-12 = 9a[/tex]
[tex]a = -4/3[/tex]
[tex]y = (-4/3)(x-5)^2 - 3[/tex]
This equation is expanded and simplified to produce:
[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]
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-3(-4x + 5) = [?]x - [ ]
(Using the distributive property)
The answer to the distributive property-based problem -3(-4x + 5) = [?]x - [] is 12x - 15.
what is equation ?A mathematical assertion proving the equality of two expressions is known as an equation. Variables, constants, and mathematical processes like addition, subtraction, multiplication, and division are frequently included. Finding the value of the variable that makes an equation correct is the aim of equation solving. Linear equations, quadratic equations, and exponential equations are just a few of the different ways that equations can be expressed.
given
-3(-4x + 5) = [?]x - [ ]
12x - 15
by distributive property
The answer to the distributive property-based problem -3(-4x + 5) = [?]x - [] is 12x - 15.
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The rate of depreciation dV/dt of a machine is inversely proportional to the square of t + 1, where V is the value of the machine t years after it was purchased. The initial value of the machine was $500,000, and its value decreased $100,000 in the first year. Estimate its value after 4 years.
The estimated value of the machine after 4 years when the rate of depreciation dV/dt is inversely proportional to the square of t + 1 is $234,375.
Since the rate of depreciation is inversely proportional to the square of t + 1, we can write:
dV/dt = k / (t + 1)²
where k is the constant of proportionality. We can find k by using the initial value of the machine:
dV/dt = k / (t + 1)² = -100,000 / year when t = 0 (the first year)
Therefore, k = -100,000 * (1²) = -100,000.
To find the value of the machine after 4 years, we need to solve the differential equation:
dV/dt = -100,000 / (t + 1)
We can do this by separating variables and integrating:
∫dV / (V - 500,000) = ∫-100,000 dt / (t + 1)²
ln|V - 500,000| = 100,000 / (t + 1) + C
where C is the constant of integration.
We can find C by using the initial value of the machine:
ln|500,000 - 500,000| = 0 = 100,000 / (0 + 1) + C
Therefore, C = -100,000.
Substituting this value of C, we get:
ln|V - 500,000| = 100,000 / (t + 1) - 100,000
ln|V - 500,000| = -100,000 / (t + 1) + ln|e¹⁰|
ln|V - 500,000| = ln|e¹⁰ / (t + 1)²|
V - 500,000 = [tex]e^{10/(t + 1)²)}[/tex]
V = [tex]e^{10/(t + 1)²)}[/tex] + 500,000
Finally, we can estimate the value of the machine after 4 years by substituting t = 3:
V = [tex]e^{10/(3 + 1)²}[/tex] + 500,000
V ≈ $234,375
Therefore, the correct answer is $234,375.
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Select all numbers that are solutions to the inequality w < 1
In the case of the inequality w < 1, we found that the set of solutions is (-∞, 1), which represents all real numbers less than 1.
The inequality w < 1 means that w is less than 1. To identify all the numbers that satisfy this inequality, we need to look for values of w that are less than 1.
We can continue this process and substitute different values of w in the inequality w < 1 to find more solutions. For instance, if we substitute w = -1, we get -1 < 1, which is also true.
Therefore, -1 is a solution to the inequality w < 1. However, if we substitute w = 2, we get 2 < 1, which is false. This means that 2 is not a solution to the inequality w < 1.
Therefore, the set of all numbers that are solutions to the inequality w < 1 is the set of all real numbers that are less than 1. We can represent this set using interval notation as (-∞, 1), where (-∞) represents all numbers less than negative infinity and 1 represents the upper bound of the interval.
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listed are 29 ages for academy award winning best actors in order from smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. (5pts) find the score at the 20th percentile
The score at the 20th percentile is 27.
To find the score at the 20th percentile of the 29 ages for Academy Award winning best actors, follow the steps below:
Arrange the given ages from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
Determine the total number of data points
n = 29
Find the rank of the percentile
20th percentile = (20/100) * 29 = 5.8 = 6 (rounded to the nearest whole number).The rank of the percentile is 6.
Use the rank to determine the corresponding data value. The corresponding data value is the value at the 6th position when the data is arranged in ascending order. The score at the 20th percentile is 27.
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10) A rectangle has a width of 2m+3. The length
is twice as long as the width. What is the length
of the rectangle?
Answer:
4m + 6
Step-by-step explanation:
Since the length is twice as long your equation should look like this
2(2m + 3) = L
which would be 4m + 6 as the length of the rectangle
suppose that 6 j of work is needed to stretch a spring from its natural length of 26 cm to a length of 36 cm. (a) how much work is needed to stretch the spring from 30 cm to 32 cm? (round your answer to two decimal places.) 0.6 incorrect: your answer is incorrect. j (b) how far beyond its natural length will a force of 20 n keep the spring stretched? (round your answer one decimal place.)
(a)The amount of work needed to stretch the spring from 30 cm to 32 cm is 0.6 J. (b) The distance the spring will be stretched by a 20 N force is 0.03 m.
The formula for the force needed to keep a spring stretched beyond its natural length is F = kx where F is the force, k is the spring constant, and x is the distance from the spring's natural length. The spring constant k is given by the formula: k = (Wd)/x² where W is the work done, d is the distance the spring is stretched from its natural length, and x is the distance from the spring's natural length.
Substituting the values for W, d, and x gives: k = (6 J)/(0.10 m)²
k = 600 N/m
Using the formula F = kx and substituting the values for F and k gives: 20 N = (600 N/m)x
Solving for x gives: x = (20 N)/(600 N/m)
x = 0.0333 m.
Hence, the correct answer is 0.03 m.
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in new york city at rush hour, the chance that a taxicab passes someone and is available is 15%. what is the probability that at least 10 cabs pass you before you find one that is free (before: success on 11th attempt or later).
The probability that at least 10 cabs pass you before you find one that is free is 0.00528665 or approximately 0.53%.
How to determine the probabilityThe solution to the problem is explained below:
Let, P(passes someone) = 0.15 or 15%
P(available taxi cab) = 0.85 or 85%
Let X be the number of cabs that pass before you find an available taxi cab. In order to find the probability that you see at least 10 cabs pass before you find a free one, we have to use the cumulative distribution function (CDF).
The probability that X is greater than or equal to 10 is equivalent to 1 - (the probability that X is less than 10). That is,P(X >= 10) = 1 - P(X < 10)
The probability that X is less than 10 is the probability of seeing 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 taxis pass you by.
Hence,P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)P(X = 0) = P(find an available taxi cab on the 1st attempt) = P(available taxi cab) = 0.85
P(X = 1) = P(find an available taxi cab on the 2nd attempt) = P(passed by the 1st taxi cab) x P(available taxi cab on the 2nd attempt) = (1 - P(available taxi cab)) x P(available taxi cab) = 0.15 x 0.85 = 0.1275
P(X = 2) = P(passed by the 1st taxi cab) x P(passed by the 2nd taxi cab) x P(available taxi cab on the 3rd attempt) = (1 - P(available taxi cab))² x P(available taxi cab) = 0.15² x 0.85 = 0.01817
P(X = 3) = (1 - P(available taxi cab))³ x P(available taxi cab) = 0.15³ x 0.85 = 0.002585
P(X = 4) = (1 - P(available taxi cab))⁴ x P(available taxi cab) = 0.15⁴ x 0.85 = 0.0003704
P(X = 5) = (1 - P(available taxi cab))⁵ x P(available taxi cab) = 0.15⁵ x 0.85 = 0.00005287
P(X = 6) = (1 - P(available taxi cab))⁶ x P(available taxi cab) = 0.15⁶ x 0.85 = 0.000007550
P(X = 7) = (1 - P(available taxi cab))⁷ x P(available taxi cab) = 0.15⁷ x 0.85 = 0.0000010825
P(X = 8) = (1 - P(available taxi cab))⁸ x P(available taxi cab) = 0.15⁸ x 0.85 = 0.000000154
P(X = 9) = (1 - P(available taxi cab))⁹ x P(available taxi cab) = 0.15⁹ x 0.85 = 0.0000000221
Hence,P(X < 10) = 0.85 + 0.1275 + 0.01817 + 0.002585 + 0.0003704 + 0.00005287 + 0.000007550 + 0.0000010825 + 0.000000154 + 0.0000000221 = 0.99471335
P(X >= 10) = 1 - P(X < 10) = 1 - 0.99471335 = 0.00528665
Therefore, the probability that at least 10 cabs pass you before you find one that is free is 0.00528665 or approximately 0.53%.
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could someone help me with 7 and 8 i don’t really understand this..
By answering the presented question, we may conclude that from the given graph we can say that zeros are = (-3,-1 ) and (--5,-9) ; y - intercept is, y = -2x/3 + 15 and vertex are = (-0-1)
What exactly are graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
from the given graph we can say that
zeros are = (-3,-1 ) and (--5,-9)
y - intercept is, y = -2x/3 + 15
vertex are = (-0-1)
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If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11
True. If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11.
When a two-digit number is reversed, it becomes a new number with the digits swapped, e.g., 12 becomes 21. The difference between the original number and the reversed number is obtained by subtracting one from the other. For example, the difference between 12 and 21 is 9. It can be observed that the difference between any two-digit number and its reverse is always a multiple of 9.
Now, let's consider the three-digit number ABC. When this number is reversed, it becomes CBA. The difference between the two is
(100C + 10B + A) - (100A + 10B + C) = 99(C - A),which is a multiple of 11.
Therefore, if a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11.
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Complete Question:
If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11. True/ False.
change the denominator of the fraction a+3/6-2a to 2(a^2-9)
The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
What is Formula?In mathematics, formula is mathematical expression or equation that describes relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.
Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.
To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.
First, we can factor the denominator of the original fraction as follows:
6 - 2a = 2(3 - a)
Next, we can rewrite the denominator using the difference of squares formula:
2(a² - 9) = 2(a + 3)(a - 3)
Now, we can use the factored form of the denominator to rewrite the original fraction:
(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))
Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
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Please help me with my math!!
Answer:
The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.
Since a = -3 < 0, the parabola opens downwards and has a maximum point.
To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:
x = -3
y = -3(-3+3)^2 + 4 = 4
Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.
Hence, the answer is option C
Answer:
C) Maximum point; 4
Step-by-step explanation:
Given parabola:
[tex]y=-3(x+3)^2+4[/tex]
The given parabola is in vertex form:
[tex]\boxed{y = a(x - h)^2 + k}[/tex]
where:
(h, k) is the vertex of the parabola.a is the leading coefficient.By comparing the given equation with the vertex form, we can see that:
a = -3h = -3k = 4As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.
The vertex of the parabola is (h, k) = (-3, 4).
Therefore, the maximum value of y is 4, which occurs at x = -3.
expand and simplify 4(2x-1)+3(2x+5)
Answer:
Step-by-step explanation: 4(2x-1)+3(2x+5)
Expand the expression to eliminate the brackets
8x-4+6x+15.....Expansion
Now simplify by grouping like terms
8x+6x-4+15
8x+6x=14x
-4+15=11
Therefore simplification=14x+11
PLS HELPPPP
A group of friends go to a basketball game. The function b(x) represents the amount of money spent, where x is the number of friends at the game. Does a possible solution of (4.5, $107.75) make sense for this function? Explain your answer.
• Yes. The input and output are both possible.
• No. The input is not possible.
• No. The output is not possible.
• No. Neither the input nor output is possible.
Part B: During what interval(s) of the domain is the baseball's height staying the same? (2 points)
Your answer
Part C: During what interval(s) of the domain is the baseball's height decreasing the fastest? Use complete sentences to support your answer.
• 6 -x ‹ 8; the slope is the steepest for this interval
• 8-x < 10; the slope is the steepest for this interval
• 6
• 6
Part A: During what interval(s) of the domain is the baseball's height increasing?
Answer:
This is not my own answer it is a copied one.
If h (x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h (x)) Then the pair given is (6.5, $92.25) Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)
The circumference of a circle is 23π cm. What is the area, in square centimeters? Express your answer in terms of π .
Answer:
132.25 π
Step-by-step explanation:
The formula for circumference is 2πr. 2πr = 23π, so r = 11.5
Formula for area is πr^2
11.5^2 * π = 132.25 π
Hope this helps!
Suppose a product's revenue function is given by R(q) = - 7q + 600qr. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q) =
The expression for the marginal revenue function is MR(q) = 600r - 7.
The given product's revenue function is R(q) = - 7q + 600qr.
To find an expression for the marginal revenue function, we can use the following steps:
Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).
Step 2: Simplify the expression for MR(q) to record the final result.
In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.
So, we have to differentiate R(q) with respect to q to get MR(q).
The derivative of - 7q with respect to q is - 7.
The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.
MR(q) = dR(q) / dq
= (d/dq)(- 7q + 600r)
= (- 7) + (600r)
= 600r - 7
The equation that represents the marginal revenue function is MR(q) = 600r - 7.
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Which of the following statements is about CD and CE is true? A. CD is longer than CE B. CE is longer than CD C. CD and CE are the same length D. CE is 5 units long
From the given graph, CE is longer than CD.
What is the distance between two coordinates?The length of the line segment bridging two locations in a plane is known as the distance between the points. d=√((x₂ - x₁)²+ (y₂ - y₁)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Coordinates of E(8,6)
Coordinates of C(6,1)
Coordinates of D(3,-3)
x=8, y=6
x=6, y=1
x=3, y=-3
Distance CE=√{(8-6)² +(6-1)²} = √29
Distance CD=√{(6-3)² +(1+3)²}= √25=5
Therefore, CE is longer than CD.
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Find the value of the expression x+|x| if x≥0
Step 1: x is a positive number, so the absolute value of x will be equal to x.
Step 2: The expression x+|x| simplifies to 2x
Step 3: Therefore, the expression x+|x| = 2x if x≥0
Translate Into a equation!
The sum of 7 times a number and 6 is 3
Step-by-step explanation:
x is the number.
the equation is
7x + 6 = 3
you decide to record the hair colors of people leaving a lecture at your school. what is the probability that the next person who leaves the lecture will have gray hair? express your answer as a simplified fraction or a decimal rounded to four decimal places. counting people blonde red brown black gray 50 40 39 33 43
The probability is a fraction of 43/205 which is approximately 0.2098.
What is the probability that the next person who leaves the lecture will have grey hair?To calculate the probability of the next person who leaves the lecture having gray hair, we need to know the total number of people who left the lecture, as well as the number of people who have gray hair.
From the given data, we can see that there were a total of 50+40+39+33+43 = 205 people who left the lecture. We also know that there were 43 people who had gray hair.
Therefore, the probability of the next person who leaves the lecture having gray hair is:
P(gray hair) = (number of people with gray hair) / (total number of people who left the lecture)
P(gray hair) = 43/205
P(gray hair) ≈ 0.2098
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a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
We have,
To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.
First, let's calculate the weight of the water in the pool.
The weight of an object is given by the formula:
Weight = mass x gravitational acceleration
Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.
The volume of the pool is given by the formula:
Volume = length x width x depth
Volume = 50 ft x 30 ft x 6 ft = 9000 ft³
Now, let's calculate the weight of the water:
Weight = density x volume x gravitational acceleration
Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb
To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.
The work required to pump the water out is given by the formula:
Work = weight x height
Work = 290,400 lb x 8 ft = 2,323,200 ft-lb
Therefore,
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
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Use the shell method to write and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. x + y2 = 4 y 2 1 X 2 4
In the following question, among the conditions given, The volume of the solid generated by revolving the plane region about the x-axis is (128/3)π.
To find the volume of the solid generated by revolving the plane region about the x-axis, we can use the shell method. The given region is bounded by the lines x=2, y=1 and x+y^2=4.
The integral to evaluate is:
V = 2π ∫r2h dx,
where r = x+y^2 = 4, h = y = 1, and x varies from 2 to 4.
Therefore, V = 2π ∫4^2*1 dx, from x = 2 to x = 4.
Evaluating the integral, we have:
V = 2π[4x^3/3]24
V = 2π(64/3 - 8/3)
V = (128/3)π
Therefore, the volume of the solid generated by revolving the plane region about the x-axis is (128/3)π.
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Pizza burger taco shake
Answer:
Is there supposed to be a joke in this?
Answer:
bro what
Step-by-step explanation:
Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 12. What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?
A. -3
B. -1.5
C. 1.5
D. 3
Audrey and Harper are selling fruit for a band fundraiser. Customers can buy small crates of apples and large containers of peaches. Audrey sold 3 small crates of apples and 10 large containers of peaches for a total of $116. Harper sold 11 small crates of apples and 20 large containers of peaches for a total of $292. Find the cost each of one small crate of apples and one large container of peaches. A) Define your variables. Write a system of equations to represent the situation. Solve using any method. Show all of your work. Andrew decides he wants to help the band as well. He sells 7 small crates of apples and 5 larges containers of peaches. How much money does he raise for the band?
The cost of one small crate of apples is $12 and the cost of one large crate of peaches is $8. The cost of 7 small cates of apples and 5 large containers of peach is $126.
What is the cost of 7 small crates and 5 large containers?The system of equations that describe the question is:
3s + 10l = 116 equation 1
11s + 20l = 292 equation 2
Where:
s = cost of one small crate of apples
l = cost of one large crate of peaches
The elimination method would be used to determine the values of s and l.
Multiply equation 1 by 2
6s + 20l = 232 equation 3
Subtract equation 3 from equation 2:
5s = 60
Divide both sides of the equation by 5
s = 60 / 5
s = $12
Substitute for s in equation 1:
3(12) + 10l = 116
36 + 10l = 116
10l = 116 - 36
10l = 80
l = 80 / 10
l = 8
Cost of 7 small crates of apples and 5 large containers of peaches = (7 x 12) + (8 x 5) = $124
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PLEASE HELP ME WITH THISSS!!!
Answer:
x = 1
Step-by-step explanation:
x + x + x + 30 = 33
3x + 30 = 33
3x + 30 - 30 = 33 - 30
3x = 3
x = 3/3 = 1
Find a basis for the vector space of polynomialsp(t)of degree at most two which satisfy the constraintp(2)=0. How to enter your basis: if your basis is1+2t+3t2,4+5t+6t2then enter[[1,2,3],[4,5,6]]
In the following question, among the conditions given, {q1, q2} is a basis for the vector space of polynomials p(t) of degree at most two that satisfy the constraint p(2) = 0. In this particular case, we must enter our basis as [[1,0,-4],[0,1,-2]], since q1(t) = t^2 - 4 and q2(t) = t - 2.
To find a basis for the vector space of polynomials p(t) of degree at most two which satisfy the constraint p(2)=0, we can take the following steps:
1. Rewrite the polynomials as linear combinations of the form a + bt + ct^2
2. Use the constraint p(2) = 0 to eliminate one of the coefficients a, b, or c
3. Normalize the polynomials so that they are unit vectors
For example, if your basis is 1 + 2t + 3t^2, 4 + 5t + 6t2 then you can enter it as [[1,2,3],[4,5,6]].
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The velocity of a particle. P. moving along the x-axis is given by the differentiable function v, where (t) is measured in meters per hour and r is measured in hours. V() is a continuous and decreasing function Selected values of v(f) are shown in the table above. Particle P is at the t= 30 at time t = 0. T(hours) 0 2 4 7 10 V(t) (meters/hour) 20.3 14.4 10 7.3 5 (a) Use a Right Riemann sum with the four subintervals indicated by the data in the table to approximate the displacement of the particle between 0 hr to 10 hr. What is the estimated position of particle Pat t=10? Indicate units of measure. (b) Does the approximation in part (a) overestimate or underestimate the displacement? Explain your reasoning (c) A second particle, Q. also moves along the x-axis so that its velocity for O<=T<= 10 is given by VQ(t) = 35✓t cos( 0.06t^2) meters per hour. Find the time interval during which the velocity of particle vo(t) is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is at least 40 meters per hour. (d) At time t = 0, particle Q is at position x = -90. Using the result from part (a) and the function vo(t) from part (c), approximate the distance between particles P and Q at time t = 10.
The velocity of a particle. P. moving along the x-axis is given by the differentiable function v, where (t) is measured is given by:
A differential function v gives the velocity of a particle P travelling down the x-axis, where v(t) is measured in metres per hour and t is measured in hours. v(t) is a declining function that is continuous. The table below shows several examples of v(t) values.
T [hours] 0 2 4 7 10
v(t) [meters/hour] 20.3 14.4 10 7.3 5
a) We know that the particle's displacement is the area under the curve v(t). We can calculate the particle's displacement by integrating v(t). Because v(t) is a monotonous (constantly declining) differentiable function, it is also Riemann Integrable. There are now five non-uniform subdivisions:
Partition t0 t1 t2 t3 t4
T [hours] 0 2 4 7 10
v(t) [meters/hour] 20.3 14.4 10 7.3 5
Using Right Riemann sum to approximate the displacement of particle between 0 hr and 10 hr is given by:
[tex]\sum_{n=1}^{4}v(t_n)\Delta t_n=v(t_1)(t_1-t_0)+v(t_2)(t_2-t_1)+v(t_3)(t_3-t_2)+v(t_4)(t_4-t_3) \\=(14.4)(2)+(10)(2)+(7.3)(3)+(5)(3) \\=28.8+20+21.9+15 \\=85.7[/tex]
Therefore, the total displacement between 0 hr and 10 hr is is 85.7 meters.
The estimated position of particle P at time t = 10 hour is 115.7 (= 30 +85.7) meters.
b) Because the function v(t) is decreasing and we are estimating the integral using the Right Riemann sum, the approximation in part(a) underestimates the displacement.
c) A second particle Q also moves along the x-axis so that its velocity is given by :
[tex]V_Q(t)=35\sqrt{t}\cos(0.06t^2)\text{ meters per hour for }0\leq t\leq 10.[/tex]
Hence, the time interval during which the velocity of a particle is atleast 60 meters per hour is [9.404, 10].
Now, the time periods during which a particle's velocity is at least 40 metres per hour are [1.321,4.006] and [9.218, 10]. The distance travelled by the particle Q when its velocity is at least 40 metres per hour is then calculated. :
[tex]\int_{1.321}^{4.006}v_Q(t)dt+\int_{9.218}^{10}v_Q(t)dt\\\\=\int_{1.321}^{4.006}35\sqrt{t}\cos(0.06t^2)dt+\int_{9.218}^{10}35\sqrt{t}\cos(0.06t^2)dt[/tex]
d) At time t = 0, particle Q is is at position x = -90.
We know that P is at xp = 115.7 meters.
Now, The position of Q at t = 10 hr is xq:
[tex]x_q=-90+\int_{0}^{10}v_Q(t)dt=-90+\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt[/tex]
And the distance between Q and P is given by :
[tex]|x_p-x_q|=|115.7-(-90+\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt)|[/tex]
[tex]\\=|205.7-\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt|[/tex]
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