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Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

[tex]V = \frac{1}{3}\pi r^{2}h[/tex]

Differentiate the equation with respect to time t, such that

[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]

[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]

To differentiate the product,

Let r² = u, so that

[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]

Then, using product rule

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]

Since [tex]u = r^{2}[/tex]

Then, [tex]\frac{du}{dr} = 2r[/tex]

Using the Chain's rule

[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]

∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]

Then,

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]

Now,

From the question

[tex]\frac{dr}{dt} = 7 m/min[/tex]

[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]

At the instant when [tex]r = 99 m[/tex]

and [tex]V = 180 m^{3}[/tex]

We will determine the value of h, using

[tex]V = \frac{1}{3}\pi r^{2}h[/tex]

[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]

[tex]180 \times 3 = 9801\pi h[/tex]

[tex]h =\frac{540}{9801\pi }[/tex]

[tex]h =\frac{20}{363\pi }[/tex]

Now, Putting the parameters into the equation

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]

[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]

[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]

[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]

[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]

[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]

[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]

[tex]\frac{dh}{dt} = 0.021 m/min[/tex]

Hence, the rate of change of the height is 0.021 meters per minute.

7/36

[tex]\frac{1}{6} /\frac{6}{7}=\frac{1}{6}*\frac{7}{6}=\frac{7}{36}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

wait, what is the question?

Answer: B

Step-by-step explanation:

Each month, the person seems to grow taller. So, there IS a positive association between height and age.

Answer:

(0, 5)

Step-by-step explanation:

Answer:

-5/10 or -1/2

Step-by-step explanation:

Answer:

Approximately 11 feet.

Step-by-step explanation:

Let the length of the third side of the triangle be represented by x. Applying Cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

⇒ [tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]12^{2}[/tex] - 2(8 x 12) Cos[tex]65^{o}[/tex]

       = 64 + 144 - 192 x 0.42262

       = 208 - 81.143

       = 126.857

x = [tex]\sqrt{126.857}[/tex]

  = 11.2631

x ≅ 11

The length of the third side of the triangle is approximately 11 feet.

Answer: The shirt's price after reduction = $ 84.15

Step-by-step explanation:

Given: Price of shirt= $ 85

Marked up percent = 10%

Reduced percent = 10%

Price after mark up = (Price of shirt) + 10% of (Price of shirt)

= $ (85+10% x 85)

= $ (85+(0.1) x (85))

= $ (85+8.5)

= $ 93.5

Price after 10% reduction = (Price after mark up)- 10% of (Price after mark up)

= $ (93.5-0.1 x 93.5)

= $ (93.5-9.35)

= $ 84.15

Hence, the shirt's price after reduction = $ 84.15

Answer:

The total cost of an item can be calculated by adding the sales tax to the retail cost:

Step-by-step explanation:

Sales tax = 7%

                = 7/100

                 = 0.07

Total cost of an iten can be calculated by adding the sales tax to the retail cost.

i.e. c + .07c

Therefore, the total cost of an item can be calculated by adding the sales tax to the retail cost:

Answer:

She saved 90 dollars and she owes her brother 40 still.

Step-by-step explanation:

Answer:

5,000

Step-by-step explanation:

no interest‍♀️

Answer:

8 liters

Step-by-step explanation:

because after pouring 2 liters bucket was full so we wiil minus 2 from 10

Answer:

8 + x = 10

x. = 10 - 8

x. = 2 liters

Answer:

$1.23

Step-by-step explanation:

divide 8.61 by 7 binders to get the final answer of $1.23

Answer: y+3= -1/4(x-8)

Step-by-step explanation: so if y-y1=m(x-x1) and y1= -3 and x1=8 and m=(-1/4) u just plug in those number to the equation

Answer:The slope represents ur mom

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

1.08

Step-by-step explanation:

Answer:

-5/36

Step-by-step explanation:

-1*5 = -5

6*6 = 36

-5/36

9514 1404 393

Answer:

  3, 0, 2, -2

Step-by-step explanation:

Put x=2 into each equation and solve for y.

2 + y = 5

  y = 5 -2

  y = 3

3x +2y = 6

  3·2 +2y = 6

  2y = 6 -6 = 0

  y = 0

2x +y = 6

  2·2 +y = 6

  y = 6 -4

  y = 2

5x +3y = 4

  5·2 +3y = 4

  3y = 4 -10 = -6

  y = -2

Answer: 132 hamburgers and 30 sodas

Step-by-step explanation:

x= Number of hamburgers

y= Number of sodas

1 x + 1 y = 102

1 x -1 y = 30

Eliminate y

Add the two equations

2 x = 132

/ 2

x = 66

plug value of x in (1)

1 x + 1 y = 102

132 + y = 102

y = 102 -132

y = 30

y = 30

x= 132 Number of hamburgers

y= 30 Number of sodas

Answer:

Hotdogs=36

Sodas=66

Step-by-step explanation:

X-Hotdogs

Y-Sodas

Y-30=X

Y+X=102

New equation: 102-X-30=X

Add X to both sides

102-30=2x

x=36

y=66

Answer:

Step-by-step explanation:

Given the expression, 32/52

Juan need to divide the numerator and the denominator by the greatest common factor

For 32;

32 = 8 * 4

For 53

52 = 13 * 4

Find the ratio

32/52 = (8*4)/(13*4)

32/52 = 8/13

Since 4 is common to both factors, Hence the greatest common factor is 4

Answer:

its 160 miles

Answer:

If they work together, they will take 6.16 days.

Step-by-step explanation:

Elsa takes 14 days to complete the work.

So, 1 day work by Elsa is [tex]\frac{1}{14}[/tex]

Anna takes 11 days to complete the work.

So, 1 day work by Anna is [tex]\frac{1}{11}[/tex].

So, Let if they work together, it would take x number of days.

So, we can set up equation as

[tex]\frac{1}{14} +\frac{1}{11}=\frac{1}{x}[/tex]

Find LCD, which is 154.

[tex]\frac{11}{154} +\frac{14}{154} =\frac{1}{x}[/tex]

Simplify

[tex]\frac{25}{154} =\frac{1}{x}[/tex]

Cross multiply,

25x=154

Divide both sides by 25

x=6.16 days

If they work together, they will take 6.16 days.

Answer:

6

Step-by-step explanation:

There is 1 cup of cream for every 2 cups of chocolate. That means there are 3 cups of cream and 6 cups of chocolate. Each cup of cream = 2 cups of chocolate, so you would do 3*2 which equals 6

6 + 3 = 9

Answer:

Step-by-step explanation:

4 z ^3 √ y / x ^2 y

Answer:

plot a point at (0,-8) and another one at (5,-7)

Step-by-step explanation:

connecting the dots would create the slope