The quadratic form are a) ′ = ᵢⱼ∑ ᵢⱼᵢ, b) ′()=′, c) ((+)/2)=′, d) 2−3²−².
The question is asking for an expression of the quadratic form with coefficient matrix A for 2c-3rjt2-z2.
For (a): The quadratic form of the vector x with coefficient matrix A is expressed as ′ = ᵢⱼ∑ ᵢⱼᵢ, where is an × matrix and is an -vector.
For (b): Taking the transpose of the triple product ′ we get ′()=′, which shows that the quadratic form with the transposed coefficient matrix has the same value for any a.
For (c): The quadratic form with coefficient matrix equal to the symmetric part of a matrix (i.e., (A+AT)/2) is expressed as ((+)/2)=′, which shows that the quadratic form with coefficient matrix equal to the symmetric part of a matrix has the same value as the original quadratic form.
For (d): The expression 2c-3rjt2-z2 as a quadratic form, with symmetric coefficient matrix A, is expressed as ((+)/2)= 2−3²−², where is a symmetric matrix.
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NEED THIS ANSWERED ASAP!!
The line of site to the horizon would be tangent to the Earth’s surface. What kind of angle is formed between the radius of the Earth and the line of site?
Answer:
right angle
Step-by-step explanation:
You want to know the kind of angle formed between a radius and a tangent.
TangentA tangent to a circle is always perpendicular to the radius at the point of tangency.
The angle is a right angle.
is every point of every open set e c r2 a limit point of e? answer the same question for closed sets in r2
All points belonging to any closed set in R2 are limit points of that set.
What is a limit point?A limit point is a point in a metric space that can be approached arbitrarily closely by points of a sequence or a set. The definition is different from that of an isolated point, which has an open ball around it that does not include any other points of the set.
According to the definition of a limit point, every point in every open set in R2 is a limit point of the set. This is because there is always at least one other point in the open set that is within a specified distance of the point in question.
As a result, every point in every open set in R2 is a limit point of the set. We can answer the same question for closed sets in R2. A closed set in R2 contains all of its limit points. A closed set, by definition, includes its boundary.
As a result, every point in every closed set in R2 is a limit point of the set.
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The cost of a gallon of gas is $3.50. What is the maximum number of of gallons you can buy for $20?
Answer:
5 gallons
Step-by-step explanation:
20÷3.50=5.714...
so the answer is 5 gallons
Write a formula for f(t) as a sum of Heaviside functions. Type uc for the Heaviside function that jumps at c (don't type uc(t) ). F(t) = t, 0 ≤ t ≤ 3 2t−3, 3 < t ≤ 4 5, 4 < t
The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).
To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.
f(t) = t, 0 ≤ t ≤ 3
f(t) = 2t - 3, 3 < t ≤ 4
f(t) = 5, 4 < t
Using the Heaviside function uc for the jump at c, we can represent each interval as follows:
f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3
f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4
f(t) = 5uc(t-4), 4 < t
Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)
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Solve for x. Simplify your answer.
Therefore, the length of the larger part is 9 units.
What is ratio?A ratio is a comparison of two quantities that measures how many times one quantity is contained within the other. It is expressed using the symbol ":" or as a fraction. For example, a ratio of 2:3 (or 2/3) means that one quantity is two-thirds the size of the other quantity. Ratios can be used to compare various quantities, such as length, area, volume, weight, or even numbers of objects. They are commonly used in mathematics, finance, and many other fields.
Here,
If the line segments are divided in the ratio of 2:3, this means that the smaller part is 2 units and the larger part is 3 units. We know that the length of the smaller part is 6 units, so we can set up a proportion:
2/3 = 6/x
where x is the length of the larger part. We can solve for x by cross-multiplying:
2x = 3*6
2x = 18
x = 9
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what is the angle of x when the other is 51
Answer:
I'm sorry, your question is not clear. Please provide more information or context so I can better understand what you are asking.
Step-by-step explanation:
The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with radius 83,000,000 mi. Find the linear speed of XYZ in miles per hour. The linear speed is approximately ______ miles per hour. (Round to the nearest integer as needed.)
The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with a radius of 83,000,000 mi. The linear speed of XYZ in miles per hour is approximately 1,093,333 miles per hour.
What is the orbit and what is the linear speed?
An orbit refers to the path taken by an object, such as a planet, as it circles around another object, such as a star. The speed of the planet is its rate of movement, measured in linear units like miles or kilometers per hour, as it travels around the orbit.
These are terms that are important to understanding the solution to the problem provided. The linear speed of XYZ in miles per hour is approximate _____ miles per hour. (Round to the nearest integer as needed.)
The planet XYZ travels around the star ABC in a circular orbit that takes 24 hours to complete. The orbit is a circle with a radius of 83,000,000 miles.
To find the linear speed of XYZ in miles per hour, it is necessary to use the formula for the circumference of a circle.
Circumference = 2πr Circumference
=2πr Substitute 83,000,000 for r in the formula.
Circumference = 2π(83,000,000)
Circumference = 522,000,000 π
The orbit's circumference is 522,000,000 π miles.
The distance traveled by XYZ in one hour is the linear speed. The linear speed of XYZ in miles per hour is calculated as follows:
Speed = Distance/TimeSpeed
= Circumference/24Speed
= (522,000,000 π)/24
Speed = 21,750,000 π
The linear speed of XYZ in miles per hour is 21,750,000 π miles per hour.
To get an approximate answer, π is equal to 3.14.
Speed ≈ 21,750,000 (3.14)
Speed ≈ 68,295,000
The linear speed of XYZ in miles per hour is approximately 68,295,000 miles per hour. Rounded to the nearest integer, the linear speed is approximately 1,093,333 miles per hour.
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Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b
The upper bound of a + b can be found by adding the upper bounds of a and b.
For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.
For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.
So the upper bound of a + b is:
5.5 + 3.5 = 9
Therefore, the upper bound of a + b is 9cm.
A rectangular plate of sides a and b is subjected to a force that is perpendicular to the plate. The plate is located on the xy-plane as shown. The pressure, p, at point (x, y) on the plate is proportional to the square of the distance of that point from the origin. (a) Find a formula for the pressure at point (x, y). Use k as the constant of proportionality. Use a lower case k. P(x,y) = (b) If pressure is force per unit area, set up the integral needed to find the total force on the plate. (c) Evaluate the integral in part (b). Your answer will be in terms of a, b, and k. Use all lower case letters.
In calculus, integration is the process of finding the integral of a function. The integral is a mathematical concept that represents the area under a curve or the net accumulation of a quantity over a given interval.
(a) The pressure, p, at point (x, y) on the plate is proportional to the square of the distance of that point from the origin, so we have:
p(x,y) = k(x^2 + y^2)
where k is the constant of proportionality.
(b) To find the total force on the plate, we need to integrate the pressure over the entire surface of the plate. The surface area of the plate is given by A = ab, so the total force on the plate is:
F = ∬p(x,y) dA
where the double integral is taken over the surface of the plate.
(c) We can evaluate the integral by expressing the pressure as a function of either x or y and integrating it over the other variable. Since the pressure is symmetric in x and y, we can integrate over an either variable. Let's integrate over x first:
F = ∫[0,b] ∫[0, a] k(x^2 + y^2) dx dy
= k ∫[0,b] (a^3/3 + ab^2/2) dy
= kab^2/2 + k(a^3/3) ∫[0,b] dy
= kab^2/2 + k(a^3/3) b
= (kab^2/2 + ka^3b/3)
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Qual o resultado do problema 3528÷98?
Answer:
36
Step-by-step explanation:
Patty para sus maquetas representadas en las figuras 1 y 2 planea colocar árboles en los puntos rojos que están separados una distancia de 5 cm uno de otro ¿cuanto miden los lados de cada maqueta ?¿Cuántos árboles colocará en cada una por favor ayuda
The total length of the rope in feet required by Patty to make a ladder is equal to 17.5 feet.
length of each piece of rope = 18 inches
Convert the length of the pieces of rope into feet.
One foot is equal to 12 inches
⇒ 18 inches = 18/12 feet
⇒ 18 inches = 1.5 feet.
Since Patty needs five of these pieces of rope.
The total length of rope needed for the steps is equal to,
5 x 1.5 = 7.5 feet
Patty also needs two pieces of rope that are each 5 feet long for the sides of the ladder.
Total length of rope needed for the ladder is,
2 x 5 = 10 feet
Add up the total length of all the pieces of rope required for the ladder,
7.5 + 10 = 17.5 feet
Therefore, Patty needs 17.5 feet of rope to make the ladder.
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The given question is incomplete, I answer the question in general according to my knowledge:
Patty is building a rope ladder for a tree house. She needs two 5-foot pieces of rope for the sides of the ladder. She needs 5 pieces of rope, each 18 inches long, for the steps. How many feet of rope does Patty need to make the ladder?
The function h is defined by the following rule.
h(x) = 4x-2
Complete the function table.
-3
0
2
4
5
X
h(x)
0
0
0
Answer:
h(-3) = -14
h(0) = -2
h(2) = 6
h(4) = 14
h(5) = 18
Step-by-step explanation:
h(x) = 4x - 2
x=-3
h(-3) = 4(-3) - 2
h(-3) = -12 - 2
h(-3) = -14
x=0
h(0) = 4(0) - 2
h(0) = 0 - 2
h(0) = -2
x=2
h(2) = 4(2) - 2
h(2) = 8 - 2
h(2) = 6
x=4
h(4) = 4(4) - 2
h(4) = 16 - 2
h(4) = 14
x=5
h(5) = 4(5) - 2
h(5) = 20 - 2
h(5) = 18
Simplify these radicals (ASAP!!!)
Answer:
[tex]3.\quad 2\sqrt{7}\\\\4.\quad \dfrac{2}{\sqrt{5}}[/tex]
[tex]5.\quad \dfrac{1}{\sqrt{2}}[/tex]
[tex]6.\quad\dfrac{5}{7}[/tex]
Step-by-step explanation:
To simplify radicals find the factors and simplify the square roots of the factors
#3 : √28
28 = 4 x 7
√28 = √(4 x 7) = √4 x √7 = 2 x √7 = 2√7
========================================================
[tex]\#4:\quad \sqrt{ \dfrac{4}{5}}\\\\\sqrt{ \dfrac{4}{5}} = \dfrac{\sqrt{4}}{\sqrt{5}} = \dfrac{2}{\sqrt{5}}[/tex]
========================================================
[tex]\#5\quad \dfrac{3}{\sqrt{18}}\\\text{Denominator } \sqrt{18 }= \sqrt{9 \times 2} = 3\sqrt{2}\\\\ \dfrac{3}{\sqrt{18}}= \dfrac{3}{3\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]
========================================================
[tex]\# 6 \quad \sqrt{\dfrac{25}{49}}\\\\\sqrt{25} = 5\\\\\\\sqrt{49} = 7\\\\[/tex]
[tex]\sqrt{\dfrac{25}{49}}= \dfrac{5}{7}[/tex]
2. Oil is leaking from an uncapped well and polluting a lake. Ten days after the leak is discovered, environmental engineers measure the amount of oil in the water to be 200 gallons with a current inflow rate of 30 gallons per day. The leak is slowing so that on the tenth day, the inflow rate is decreasing by 5 gallons/day each day. Suppose Q(t) is the amount of oil (in gallons) t days after the leak is discovered. (a) Find the second degree Taylor polynomial for Q(t) centered at t=10. (b) Use your answer in the previous part to estimate the amount of oil in the lake at t=12
As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).
what is polynomial ?A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and is made up of variables and coefficients. To put it another way, a polynomial is an algebraic expression made up of terms that are sums, products, and/or products of variables and coefficients. The leading coefficient is the coefficient of the term with the highest degree, while the degree of a polynomial is the maximum power of the variable in the expression.
given
(a) We need to determine Q(10), Q'(10), and Q" in order to determine the second degree Taylor polynomial for Q(t) with a center at t=10 (10).
As we are aware, Q(10) = 200. (given in the problem statement).
We must take the derivative of Q(t) with respect to t in order to determine Q'(10):
Q'(t) = -5t + 250
Q'(10) = -5(10) + 250 = 200
We must take the derivative of Q'(t) with respect to t in order to determine Q"(10):
Q''(t) = -5
Q''(10) = -5
The second degree Taylor polynomial can now be calculated using the following formula: P2(t) = Q(10) + Q'(10)(t-10) + (1/2)Q"(10)(t-10)2.
With the numbers we discovered, we can calculate P2(t) as 200 + 200(t-10) + (1/2)(-5)(t-10)2.
[tex]P2(t) = 200 + 200(t-10) - (5/2)(t-10)^2[/tex]
(b) We must assess the second degree Taylor polynomial at t=12 in order to determine how much oil is in the lake at that time.
P2(12) = 210 gallons because P2(12) = 200 + 200(12-10) - (5/2)(12-10)2. (rounded to the nearest gallon)
As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).
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Kevin made a down payment of $1,500 for his car lease. His monthly payment amount is $200 for 36 months. What is the total cost of the lease if Kevin purchases the car. The residual value at the end of the lease is $8,000?
Kevin made a down payment of $1500 for his automobile leasing. Kevin's monthly payment for a 36-month rental with an overall cost of $4,200 will be $200 if he opts to buy the vehicle outright for $16,700.
What kind of down payment is this, exactly?A deposit on a property is a typical illustration of a down payment. The down payment for a property can range from 5% to 25%, with the remaining amount being covered by a mortgage obtained from a bank or another financial institution.
A down payment or a deposit is it?A commitment is retained by a 3rd person in trust, only until date of completion when it constitutes a component of the deposit.
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The complete question is:
Kevin made a down payment of $1,500 for his car lease. His monthly payment amount is $200 for 36 months. What is the total cost of the lease if Kevin purchases the car. The residual value at the end of the lease is $8,000?
a. $14,500
b. $15,200
c. $16,700
Answer: 16,700
Step-by-step explanation:
....
PLEASE HELP NOW!!! What would be the experimental probability of drawing a white marble?
Ryan asks 80 people to choose a marble, note the color, and replace the marble in Brianna's bag. Of all random marble selections in this experiment, 34 red, 18 white, 9 black, and 19 green marbles are selected. How does the theoretical probability compare with the experimental probability of drawing a white marble? Lesson 9-3
Answer: 18/80 for theoretical and then 18/80=.225 = 22.5% for experimental
Step-by-step explanation: theoretical: theres 18 white marbles, and then add up 34 + 18+9+19 to get 80. to get theoretical its number of favorable outcomes over total size of sample space, therefore 18 over 80
Experimental: divide 18/80 to get .225 then move decimal over by 2 to get 22.5%
HELP. I'm really struggling on this one. My calculus teacher claimed this to be the easiest math problem ever but I still can't understand. Is anyone smart enough to figure this one out. Whats 1 + 1?
Answer:
The answer to 1 + 1 is 2.
Very complicated problem, please mark brainliest!
Answer:
1+1 = 2
Or, 1=2-1
1=1
we know value of one is one
so,
1+1=11
HELP PLS ILL GIVE U POINTS
Answer:
i think 16 im not sure
Step-by-step explanation:
A plan for a house is drawn on a 1:40 scale. If the length of the living room on the plan measures 4.5 inches, what is the actual length of the built living room? 45 feet 25 feet 15 feet 12 feet
Answer:
actual length = 15 feet
Step-by-step explanation:
using the conversion
12 inches = 1 foot
the actual length = 40 × scale length = 40 × 4.5 = 180 inches = 180 ÷ 12 = 15 feet
Can someone give me the answer please and the other one
Answer:
58 degrees
Step-by-step explanation:
51+27=58 degrees
second one is 56 degrees
132-76=56 degrees
The Jones family has two dogs whose ages add up to 15 and multiply to 44. How old is each dog?
Hi!
Your answer is 11 and 4.
11 x 4 = 44
11 + 4 = 15
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Which of the following is equivalent to the inequality 2x + 13 < 5x - 20?
F. x >-11
G. x<?
H. x>;
J. x < 11
K. x > 11
Answer:
k
Step-by-step explanation:
2x+13<5x−20
Subtract 5x from both sides.
Combine 2x and −5x to get −3x.
Subtract 13 from both sides.
Subtract 13 from −20 to get −33.
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x>11
Use the image below to get the measure of ∠w
Answer:49
Step-by-step explanation:
Past studies indicate that about 60 percent of the trees in a forested region are classified assoftwood. A botanist studying the region suspects that the proportion might be greater than 0.60.The botanist obtained a random sample of trees from the region and conducted a test ofB:p=0.6 versus H, :p>0.6. The P-value of the test was 0.015. Which of the following is acorrect interpretation of the P-value?a. if it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is theprobability of obtaining a population proportion greater than 0.6.b. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the8 probability of obtaining a sample proportion as small as or smaller than the one obtained by thebotanistc. If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is theprobability of obtaining a sample proportion as large as or larger than the one obtained by thebotanistd. If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 isthe probability of obtaining a sample proportion as large as or larger than the one obtained by thebotaniste. If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 isthe probability of obtaining a population proportion greater than 0.6.
If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.The correct answer is option C
The P-value is the probability of obtaining an outcome as extreme or more extreme than the one actually observed given that the null hypothesis is true. In this case, the null hypothesis is that the proportion of trees classified as softwood is 0.60. The P-value of 0.015 indicates that the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist is 0.015 if the null hypothesis is true.
Therefore, the P-value is an indicator of how well the sample data supports the null hypothesis. In this case, the P-value of 0.015 is lower than the commonly accepted significance level of 0.05, which indicates that the sample data does not support the null hypothesis and suggests that the proportion of trees classified as softwood is actually greater than 0.60.
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17. The sum of the interior angles of a pentagon is6x + 6y. Find y in term of x
Answer:
We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰
For a pentagon, n=5
so,
[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]
[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]
[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]
[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]
[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]
[tex] \rm \implies \: x + y = 90[/tex]
[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]
Pentagon FormulasThere are many formulas related to a pentagon. A few basic ones are given below.
Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5Sum of interior angles of a pentagon: = 180° × (n − 2) = 180° × (5 − 2) = 540°Each exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°Each interior angle of regular pentagon: = 540° ÷ n = 540° ÷ 5 = 108°Area of a regular Pentagon = 1/2 × Perimeter × ApothemPerimeter of Pentagon = (side 1 + side 2 +side 3 + side 4 + side 5)11. How much time will it take for ₹5000
5618 at 6% per annum
annually?
to become
compounded
Answer:
2.31 Years
Step-by-step explanation:
To calculate the time it will take for ₹5000 to grow to ₹5618 with a 6% annual interest rate when compounded annually, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (₹5618)
P = the principal amount (₹5000)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (1, since it's compounded annually)
t = the time period in years
Plugging in the values, we get:
5618 = 5000(1 + 0.06/1)^(1t)
Simplifying:
1.1236 = 1.06^t
Taking the natural logarithm of both sides:
ln(1.1236) = ln(1.06^t)
Using the power rule of logarithms:
ln(1.1236) = t ln(1.06)
Solving for t:
t = ln(1.1236) / ln(1.06)
t ≈ 2.31 years
Therefore, it will take approximately 2.31 years for ₹5000 to grow to ₹5618 at a 6% annual interest rate when compounded annually.
Find the volume of the washer. Round to the nearest whole millimeter
The volume of the washer as per the given dimensions is calculated to be 7,854 mm³.
In order to calculate the volume of the washer, we are required to subtract the volume of the hole in the center from the volume of the solid cylinder with the outer radius. The volume of the solid cylinder with the outer radius can be calculated using the formula:
V1 = πr1²h (Here, r1 is the outer radius and h is the thickness)
Substituting the given values, we have:
V1 = π(30mm)²(5mm) = 14,137.17 mm³
The volume of the hole in the center can be calculated using the same formula, but with the inner radius,
V2 = πr2²h (Here r2 is the inner radius and h is the thickness)
Substituting the given values, we have:
V2 = π(20mm)²(5mm) = 6,283.19 mm³
Therefore, the volume of the washer is:
V = V1 - V2 = 14,137.17 mm³ - 6,283.19 mm³ = 7,853.98 mm³
Therefore, on rounding the obtained result to the nearest whole millimeter, the final volume is calculated to be 7,854 mm³.
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The complete question is :
What is the volume of a washer with an outer radius of 30 mm, an inner radius of 20 mm, and a thickness of 5 mm? (Round your answer to the nearest whole millimeter)
The table contains data on the number of people visiting a historical landmark over a period of one week.
Which type of function best models the relationship between the day and the number of visitors?
A. A quadratic function with a negative value of a.
B. A quadratic function with a positive value of a.
C. A square root function.
D. A linear function with a positive slope.
Hence , it is to be quadratic function where a has to be less than zero or
A quadratic function with a negative value of a.
Given that ,
The table contains data on the number of people visiting a historical landmark over a period of one week.
We have to find,
The relationship between the day and the number of visitors.
According to the question,
y = a√x +b
And where x = no. of days = 1
y = no. of visitors = 45
45 = a √1 + b
45 = a + b
And When x = 2 and y = 86
86 = a √2 +b
Solving the equation for the values of a and b.
From equation 1
45 - a = b
Put the value of b in equation 2
⇒ 86 = + 45 - a
⇒ 86 - 45 = a √2 - a
⇒ 41 = a (√2 - 1 )
⇒ a = [tex]\frac{41}{\sqrt{2}- 1 }[/tex]
⇒ a = 41/0.41
⇒ a = 100
Put the value of a = 100
45 = 100 + b
45 - 100 = b
b = -55
Now,
The required equation is y = 100 -55.
When x = 4
y = 100√2 - 55
⇒ y = 100(1.4) - 55
⇒ y = 140 - 55
⇒ y = 85
And,
when x = 5
y = 100√5 - 55
⇒ y = 223.5 - 55
⇒ y = 168.60
⇒ y = 168 ( approx. )
Therefore, 168 ≠ 158
Since the function rises less and less in later stage , it can not be a first order function.
So, it is to be quadratic function where a has to be less than zero.
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Solve the system of equations
n=2d+5
0. 05n+0. 10d=2. 25
Answer: THIS IS THE ANSWER
Point C is 3/4 of the way from point A(-4,-2) to point B(8, 6). What are the coordinates of C?
The coordinates of point C are: C = (2 + (3/2) * √(13), 2 + (3/2) *√ ((13))
How to find coordinates of point?
To find the coordinates of point C, we can use the midpoint formula, which gives the coordinates of the midpoint of a line segment. We know that point C is 3/4 of the way from point A to point B, so it is closer to B than to A. Therefore, we can find the coordinates of C by finding the midpoint of the line segment AB and then moving 3/4 of the distance from the midpoint to B.
The midpoint of AB can be found by averaging the x-coordinates and the y-coordinates of A and B, respectively:
Midpoint M = ((-4 + 8)/2 , (-2 + 6)/2) = (2, 2)
Now, we need to find the distance from M to B and move 3/4 of that distance in the direction of B. We can use the distance formula to find the distance between two points:
distance MB = √((8 - 2)² + (6 - 2)²) = √(36 + 16) = √(52)
So, the distance from M to C is 3/4 of √(52), which is:
distance MC = (3/4) * √(52) = (3/4) * 2 * √(13) = (3/2) * √(13)
To move in the direction of B, we need to add the x-component and y-component of the distance MC to the x-coordinate and y-coordinate of M, respectively:
x-coordinate of C = 2 + (3/2) * √(13)
y-coordinate of C = 2 + (3/2) * √(13)
Therefore, the coordinates of point C are:
C = (2 + (3/2) * √(13), 2 + (3/2) * √(13))
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