What equation could be used to find the number of minutes, m, in h hours?

The radius of the base of a cylinder is increasing at a rate of 777 millimeters per hour. The height of the cylinder is fixed at

Tatiana [17]

Answer:

252π or 791.7 mm³/h

Step-by-step explanation:

The volume of a cylinder is given by

$V = \pi r^2h$

We desire to find the volume rate, that is, $\dfrac{dV}{dt}$

$\dfrac{dV}{dt} = \dfrac{dV}{dr}\cdot\dfrac{dr}{dt}$

dr/dt is the rate of change of the radius which is 7 mm/h.

dV/dr is derived by differentiating the volume equation, yielding

$\dfrac{dV}{dt} = 2\pi rh$

At r = 12 mm and h = 1.5 mm,

$\dfrac{dV}{dt} = 2\pi\times12\times1.5\times7 = 252\pi = 791.7$

5 0

3 years ago

Subtract. Simplify, if possible. 5/8 - * 2 1 / 2 - 3

Nat2105 [25]

$2\frac{1}{2} - \frac{5}{8}$

Convert the mixed number to an improper fraction:

$\frac{5}{2} - \frac{5}{8}$

Subtract the fractions to get your final answer:

$\frac{15}{8}$

8 0

3 years ago

A Farmer plants the same amount everyday, adding up to 1 3/4 acres at the end of the year. If the year is 1/2 over how many acre

DochEvi [55]

Answer:

1/45 acres the farmer planted

8 0

3 years ago

Which statements are true about the solid, which has a length of 6 inches, a width of 3 inches, and a height of 2 inches?

bonufazy [111]

The volume would be 36 cubic inches.

7 0

3 years ago

Solve the following System of Three Equations: x−3y+z=−15 2x+y−z=−2 x+y+2z=1

SashulF [63]

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = -3 , y = 4 , z = 0

4 0

3 years ago