hii
Step-by-step explanation:
length-10x
width-x
perimeter-2(l+b)
66=2(10x+x)
66-2=10x+x
64=11x
x=11/64
lenght-11
width-64
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence interval for mu is:______.
Answer:
The 90% confidence interval for population mean is [tex]14.7 < \mu < 19.1[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 16.9[/tex]
The confidence level is [tex]C = 0.90[/tex]
The sample size is [tex]n = 45[/tex]
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as
[tex]\alpha = 1-0.90[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table. The values is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of that of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]
[tex]MOE = 2.207[/tex]
The 90% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
substituting values
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]14.7 < \mu < 19.1[/tex]
About 9% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
Answer:
The mean for all such groups randomly selected is 0.09*800=72.
Step-by-step explanation:
The value of the standard deviation is 7.
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The standard deviation is calculated by using the formula,
[tex]\sigma = \sqrt{Npq}[/tex]
N = 600
p = 9%= 0.09
q = 1 - p= 1 - 0.09= 0.91
Put the values in the formulas.
[tex]\sigma = \sqrt{Npq}[/tex]
[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]
[tex]\sigma[/tex] = 7
Therefore, the value of the standard deviation is 7.
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Find the value of a A.130 B.86 C.58 D.65
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
In a certain state, license plates each consist of 2 letters followed by either 3 or 4 digits. How many differen license plates are there that have no repeated letters or digits?
Answer:
26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities
Step-by-step explanation:
There is nothing stating that the letters and numbers can't be repeated, so all 26 letters of the alphabet and all 10
digits can be used again.
If the first is A, we have 26 possibilities:
AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.
If the first is B, we have 26 possibilities:
BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ
And so on for every letter of the alphabet. There are 26 choices for the first letter and 26 choices for the second letter. The number of different combinations of 2 letters is: 26 × 26 = 676
The same applies for the three digits. There are 10 choices for the first, 10
for the second and 10 for the third:
10 × 10 × 10 = 1000
So for a license plate which has 2 letters and 3 digits, there are: 26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities.
Hope this helps.
W varies inversely as the square root of x when x=4 w=4 find when x=25
Answer:
8/5
Step-by-step explanation:
w = k / √x
4 = k / √4
k = 8
w = 8 / √x
w = 8 / √25
w = 8/5
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
Which of the following is a rational function?
F(x)=8x^2-21x+45
F(x)= 3 root of X +17
F(x)= 16x
F(x)= 5x/x^2-25
PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.
6(x+8) ≥ ‒43+4x
Answer:
[tex]x \geq -91/2[/tex]
Step-by-step explanation:
[tex]6(x+8) \geq -43 + 4x[/tex]
Resolving Parenthesis
[tex]6x+48 \geq -43 + 4x[/tex]
Collecting like terms
[tex]6x - 4 x \geq -43-48[/tex]
[tex]2x \geq -91[/tex]
Dividing both sides by 2
[tex]x \geq -91/2[/tex]
Answer:
x ≥ - 91 / 2
Step-by-step explanation:
In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.
Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]
[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,
[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,
[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,
[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.
help plsssssssssssss
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?
Answer:-95 1/7 feet
Step-by-step explanation:
-120 4/7+25 3/7=-95 1/7 feet
When the input is 4, the output of f(x) = x + 21 is
Answer:
25Step-by-step explanation:
When the input is 4, the output of f(x) = x + 21 is f(4).
Substitute x = 4 to f(x):
f(4) = 4 + 21 = 25
Answer:
25
Step-by-step explanation:
We can find the output by plugging in 4 as x into the function:
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
50 points + brainliest!
Answer:
( x+2) ^2 = 11
x =1.32,-5.32
Step-by-step explanation:
x^2 + 4x -7 = 0
Add the constant to each side
x^2 + 4x -7+7 = 0+7
x^2 + 4x = 7
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 = 4
Add this to each side
x^2 + 4x +4 = 7+4
Take the 4/2 as the term inside the parentheses
( x+2) ^2 = 11
Take the square root of each side
sqrt( ( x+2) ^2) =±sqrt( 11)
x+2 = ±sqrt( 11)
Subtract 2 from each side
x = -2 ±sqrt( 11)
To the nearest hundredth
x =1.32
x=-5.32
Answer:
[tex](x+2)^2=11[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2+4x-7=0[/tex]
[tex]x^2+4x=7[/tex]
[tex]x^2+4x+4=7+4[/tex]
[tex](x+2)^2=11[/tex]
[tex]x+2=\pm\sqrt{11}[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
In △ABC,a=11 , b=20 , and c=28 . Find m∠A .
Answer:
18.4°
Step-by-step explanation:
Use law of cosine.
a² = b² + c² − 2bc cos A
11² = 20² + 28² − 2(20)(28) cos A
121 = 1184 − 1120 cos A
cos A = 0.949
A = 18.4°
For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}
(1) Number of terms
(2) Value of Sum
Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
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A crew clears brush at a rate 2/3 acre in 2 days. How long will it take the same crew to clear the entire plot of 4 acres?
Answer:
It takes the crew 12 days to clear the bush.
Step-by-step explanation:
Given clears 2/3 acres / 2 days, or 1/3 acre per day
Time to clear 4 acres
= 4 / (1/3)
= 4 * (3/1)
= 12 days
A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400
Help ASAP it’s Math I need this rightnow 31 points
Answer:
AC (b)
Step-by-step explanation:
Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)
Answer:
[tex]\boxed{\sf C}[/tex]
Step-by-step explanation:
The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.
[tex]75\%*\sqrt{20} = 3.354102[/tex]
[tex]\sqrt{10}= 3.162278[/tex]
AC is almost half of AE.
[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]
[tex]\sqrt{10} = 3.16227766017[/tex]
It isn’t close to the option C.
For the claim that is given symbolically below, determine whether it is part of a left-tailed, right-tailed, or two-tailed hypothesis test.
p > 0.50
a. a right-tailed hypothesis test
b. a two-tailed hypothesis test
c. impossible to determine from the information given
d. a left-tailed hypothesis test
Answer:
Option A a right tailed hypothesis test
Step-by-step explanation:
A claim given symbolically is most of the time derived from the alternative hypothesis usually tested against the null hypothesis.
A symbolic claim with the option of a less than indicates a left tailed test, while one with the option of greatest than indicate a right tail test and one with the option of both (not equal to; either less or greater) indicates a two tailed test.
In this case study, the sample proportion for the claim was greater than 0.50 thus, the test is a right tailed hypothesis test
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
A similar problem is given at https://brainly.com/question/14683936
Help!! It’s much appreciated in this time
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
please answer asap. there are two pics :)
Answer:
[tex]\boxed{\sf A. \ 0.34}[/tex]
Step-by-step explanation:
The first triangle is a right triangle and it has one acute angle of 70 degrees.
We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.
The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.
The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.
[tex]\sf \frac{3.4}{10} =0.34[/tex]
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high
Answer:
0.0526ft/minStep-by-step explanation:
Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.
Volume of a cone V = πr²h/3
If the diameter and the height are equal, then r = h
V = πh²h/3
V = πh³/3
If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min
Using chain rule to get the expression for dV/dt;
dV/dt = dV/dh * dh/dt
From the formula above, dV/dh = 3πh²/3
dV/dh = πh²
dV/dt = πh²dh/dt
20 = πh²dh/dt
To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.
20 = π(11)²dh/dt
20 = 121πdh/dt
dh/dt = 20/121π
dh/dt = 20/380.133
dh/dt = 0.0526ft/min
This means that the height of the pile is increasing at 0.0526ft/min