The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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assuming that the p-value to test that the population mean number of errors for the ethanol group (e) is greater than the population mean number of errors for the placebo group (p) is 0.0106 and using a 1% significance level, what is the best conclusion from this hypothesis test in the context of the problem?
The best conclusion from this hypothesis test in the context of the problem is that we can reject the null hypothesis. The null hypothesis for this problem is that the errors is not greater than the population mean.
What is the best conclusion?The null hypothesis for this problem is that the population mean number of errors for the ethanol group is not greater than the population mean number of errors for the placebo group.
In other words, the null hypothesis is: H₀: μe ≤ μp. The alternative hypothesis is that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group. In other words, the alternative hypothesis is: H₁: μe > μp.
The p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. In this case, the p-value is 0.0106, which is less than the significance level of 0.01. This means that the observed test statistic is significant at the 1% level, and we reject the null hypothesis.
Therefore, we conclude that there is evidence to suggest that the population mean number of errors for the ethanol group is greater than the population mean number of errors for the placebo group.
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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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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
suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similarly-sized house. how long would it take the two painters together to paint the house?
It would take the two painters together eight hours to paint the house
Step-by-step explanation: Given that, One painter can paint the entire house in twelve hours. The second painter takes eight hours to paint a similarly-sized house. To find, How long would it take the two painters together to paint the house? Suppose one painter takes x hours to paint the house.
Therefore, the other painter will take x-4 hours to paint the same house. According to the question, [tex]1/x+1/(x-4)=1/12+1/8[/tex] Multiply by LCM, [tex]8(x-4)=12x+12(x-4)8x-32=6x+484x=80x=20[/tex]Therefore, the first painter will take 20 hours to paint the house. The second painter will take 16 hours (20-4). Together they will take, [tex]1/20+1/16=0.1+0.0625=0.1625[/tex] Thus, they will take 6.1538 hours which can be rounded to 4.8 hours.
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4 1/2 divided by 3 (fraction problem)
Answer: 9/6 or 1 1/2
Step-by-step explanation:
9/2 ÷ 3
KCF (keep, change, flip)
9/2 × 1/3
Solve.
Final answer: 9/6
hope i helped :)
the whole problem is in the pic below
Answer:
301.733% increase
Step-by-step explanation:
Help me please I need to show my work
Answer:
x=33
Step-by-step explanation:
all angles in a triangle sum to 180 degrees
x+2x+(2x+15) = 180 <---- simplify this
5x+15 = 180
5x=165
x = 33
solve for x using a tangent and a secant line
Check the picture below.
[tex]11^2=(x+3)(3)\implies 121=3x+9\implies 112=3x \\\\\\ \cfrac{112}{3}=x\implies 37.3\approx x[/tex]
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 somebody help me, please
Answer:
uh I don't even know what this is
Answer: x = 500
Step-by-step explanation:
Use the Pythagorean Theorem
a²+b²=c²
300² + 400² = x²
90000 + 160000 = x²
250000 = x²
√250000 = √x²
500 = x
hope i explained it :)
machines at a factory produce circular washers with a specified diameter. the quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. the null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. the alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. which of the following describes a type i error that could result from the test? responses the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. a type i error is not possible for this hypothesis test.
Answer:
the test does not provide convincing evidence that the proportion is greater than 90%
the product of 2 rational numbers is 16/3.If one of the rational number is -26/3,find the other rational number
Answer:
- [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
let n be the other rational number , then
- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]
[a number × its reciprocal = 1 ]
multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]
n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex] ( cancel the 3 on numerator/ denominator )
n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]
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
Calculate the amount of interest on $4,000. 00 for 4 years, compounding daily at 4. 5 % APR. From the Monthly Interest Table use $1. 197204 in interest for each $1. 00 invested
The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.
To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:
A = $4,000.00(1 + 0.045/365)^(365*4)
A = $4,000.00(1.0001234)^1460
A = $4,889.68
The final amount is $4,889.68, which means that the interest earned is:
Interest = $4,889.68 - $4,000.00 = $889.68
We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:
$1.197204 / $1.00 = 1.197204
Interest earned = $889.68 x 1.197204 = $1,064.08
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With respect to the average cost curves, the marginal cost curve: Intersects average total cost, average fixed cost, and average variable cost at their minimum point b. Intersects both average total cost and average variable cost at their minimum points Intersects average total cost where it is increasing and average variable cost where it is decreasing d. Intersects only average total cost at its minimum point
With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.
The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.
The marginal cost is the cost added to the overall cost of producing one extra unit of output. MC initially falls until it hits a minimum and then increases. When both AVC and ATC are at their minimal points, MC equals both. Also, when AVC and ATC are dropping, MC is lower; when they are growing, it is higher.Initially, the marginal cost of manufacturing is lower than the average cost of preceding units. When MC falls below AVC, the average falls. The average cost will reduce as long as the marginal cost is smaller than the average cost.When MC surpasses ATC, the marginal cost of manufacturing one more extra unit exceeds the average cost.Learn more about Marginal cost curve:
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Complete question:
With respect to the average cost curves, the marginal cost curve:
A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point
B) Intersects both average total cost and average variable cost at their minimum points
C) Intersects average total cost where it is increasing and average variable cost where it is decreasing
D) Intersects only average total cost at its minimum point
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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The function f represents the 1000 revenue in dollars the school can 800 expect to receive if it sells 220 – 12x coffee mugs for x dollars 600 each. 400 200 Here is the graph of ƒ. 2 4 6 8 10 12 14 16 18 20 price (dollars) Select all the statements that describe this situation. a. At $2 per coffee mug, the revenue will be $96. b. The school expects to sell 160 mugs if the price is $5 each. c. The school will lose money if it sells the mugs for more than $10 each. d. The school will earn about $1000 if it sells the mugs for $10 each. e. The revenue will be more than $70o if the price is between $4 and $14. f. The expected revenue will increase if the price per mug is greater than $10. g. The domain for this situation is about 0 - 9. h. The domain for this situation is about 0 - 18.25. revenue (dollars)
The function f represents the 1000 revenue in dollars the school can 800 expect to receive if it sells 220 – 12x coffee mugs for x dollars 600 each.
The statements that accurately describe this situation are:
False. The revenue at $2 per mug is $336, not $96.True. The school expects to sell 160 mugs if the price is $5 each.False. The revenue is maximized when the price per mug is around $9, so selling mugs for more than $10 does not necessarily result in a net loss.True. The revenue at $10 per mug is approximately $1000.True. The revenue is always above $700 if the price is between $4 and $14.False. The revenue is maximized when the price per mug is around $9, so the expected revenue will not increase if the price per mug is greater than $10.The domain for this situation is about 0-18.25. This is the set of all possible values for x, the price per mug. From the graph, we can see that the maximum price per mug that yields a positive revenue is around $18.25. Therefore, any value of x between 0 and 18.25 is in the domain.To learn more about the functions:
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If a car runs at a constant speed and takes 3 hrs to run a distance of 180 km, what time it
will take to run 100 km?
Answer:
100 minutes
Step-by-step explanation:
We know
It takes 3 hrs to run a distance of 180 km.
180 / 3 = 60 km / h
60 minutes = 60 km
40 minutes = 40 km
What time it will take to run 100 km?
60 + 40 = 100 minutes
So, it takes 100 minutes to run 100 km.
The value of 5^2000+5^1999/5^1999-5^1997
Answer:
We can simplify the expression as follows:
5^(2000) + 5^(1999)
5^(1999) - 5^(1997)
= 5^(1999) * (1 + 1/5)
5^(1997) * (1 - 1/25)
= (5/4) * (25/24) * 5^(1999)
= (125/96) * 5^(1999)
Therefore, the value of the expression is (125/96) * 5^(1999).
Step-by-step explanation:
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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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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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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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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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
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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Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block
The true statement is, Parameter values can be used within the method code block. (option e).
In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.
Parameter values can be used within the method code block.
This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.
In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.
Hence the option (e) is correct.
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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.
For more such questions on plane region
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#SPJ11
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!
If y varies inversely with x and y is = to 100 x = 25 what is the value of y when x=10
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=25\\ y=100 \end{cases} \\\\\\ 100=\cfrac{k}{25}\implies 2500=k\hspace{12em}\boxed{y=\cfrac{2500}{x}} \\\\\\ \textit{when x = 10, what's "y"?}\qquad y=\cfrac{2500}{10}\implies y=250[/tex]
Write the equation of a line perpendicular to `y=3` that goes through the point (-5, 3).
Answer:
The equation of a line perpendicular to y=3 that goes through the point (-5, 3) is: x = -5.
Step-by-step explanation:
To find the equation of a line perpendicular to y=3 that goes through the point (-5, 3), we need to remember that the slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The equation y=3 is a horizontal line that goes through the point (0,3), and its slope is zero. The negative reciprocal of zero is undefined, which means that the line perpendicular to y=3 is a vertical line.
To find the equation of this vertical line that goes through the point (-5, 3), we can start with the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line. Since the line we want is vertical, its slope is undefined, so we can't use the point-slope form directly. However, we can still write the equation of the line using the point (x1, y1) that it passes through. In this case, (x1, y1) = (-5, 3).
The equation of the vertical line passing through the point (-5, 3) is:
x = -5
This equation tells us that the line is vertical (since it doesn't have any y term) and that it goes through the point (-5, 3) (since it has x=-5).
So, the equation of a line perpendicular to y=3 that goes through the point (-5, 3) is x = -5.
Answer:
x= -5
Step-by-step explanation:
The perpendicular line is anything with x= __.
x= -5 however, will go through the point (-5, 3) and that is our answer.