what is the value of x?

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.

Answer

Charlie paid $5.94

Step-by-step explanation:

0.76x2 3/4=2.09

1.40x2.75=3.85

3.85+2.09=$5.94

Answer:

ytjyhyjhuyjhytujhyuhjnfh

Step-by-step explanation:

Answer:

Step-by-step explanation:

??? do you need help or is this free points?

Answer: ight bet

i/yes

ii/no

iii/no

iv/no

v/no

vi/no

Step-by-step explanation:

Answer:

parallel

Step-by-step explanation:

The answer is parallel because Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines

Answer:

x : 5

Step-by-step explanation:

I hope this is right! Good luck!

Answer:

I believe that the answer is the 5th one (Adjacent angles).

Step-by-step explanation:

Adjacent angles are two angles that share a common side and vertex.

Complementary angles are mostly the same but their degrees add up to 90.

Supplementary angles are similar to complementary angles but add up to 180 degrees.

Vertical angles intersect though each other and are not perpendicular (which perpendicular angles also intersect, but all angles are 90 degrees and they all add up to 360 degrees).

Linear angles are like their name, they are linear. And, they usually intersect like vertical angles. Have a linear relationship between the angles.

The angles shown on the pictures are not any of the answers, except adjacent. They don't add up to 90 degrees, so they are not complementary. They share the same common side and vertex. These facts lead up to one answer which is adjacent. These angles are adjacent.

Hope this explanation helps! :)

Answer:

H + 20.9

Step-by-step explanation:

add 7.9 and 13 = 20.9

Answer:

5.1

Step-by-step explanation:

You subtract 7.9 from both sides of the equation in order to find the answer. 13 minus 7.9 is 5.1, so h is equal to 5.1

Answer:

A rational expression that has the nonpermissible values [tex]x = 0[/tex] and [tex]x = 17[/tex] is [tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex].

Step-by-step explanation:

A rational expression has a nonpermissible value when for a given value of [tex]x[/tex], the denominator is equal to zero. In addition, we assume that both numerator and denominator are represented by polynomials, such that:

[tex]f(x) = \frac{p(x)}{q(x)}[/tex] (1)

Then, the factorized form of [tex]q(x)[/tex] must be:

[tex]q(x) = x\cdot (x-17)[/tex] (2)

If we know that [tex]p(x) = 4[/tex], then the rational expression is:

[tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex] (3)

A rational expression that has the nonpermissible values [tex]x = 0[/tex] and [tex]x = 17[/tex] is [tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex].

Answer: n+(n+6)=24,where n is the number of blue marbles. 3. n+6n=24,where n is the number of blue marbles.

Step-by-step explanation:

Hello! Lets take a look.

To do this problem you would have to divide.

"75/9"

So what is the answer to that?

8!

Answer:

X= -4

Step-by-step explanation:

Hello. For to solve that, you need to use the sustitution method:

1. You need clear X in the first equation and put in the second

X+Y = -10

X = -10-Y

2.  Y = X-2, then you replaced the X in this equation:

Y = (-10-Y) - 2

Y+2=-10-Y

2Y=-10-2

2Y= -12

Y= -12/2

Y=-6

3. Now you use the Y value for to solve X:

X=-10-Y, then

X =- 10-(-6)

X = -4

Answer

If u fail the 3 main courses math, ela, and social studies you would fail, but two F's I dont think ur going to fail good luck though

Step-by-step explanation:

Answer:

p = −7

Step-by-step explanation:

96=−8(p−5)

96=(−8)(p)+(−8)(−5)(Distribute)

96=−8p+40

Step 2: Flip the equation.

−8p+40=96

Step 3: Subtract 40 from both sides.

−8p+40−40=96−40

−8p=56

Step 4: Divide both sides by -8.

−8p /−8 = 56 /−8

Answer:

I believe the answer is 34 cm (I may be wrong but I'm 98% that my answer is correct)

Step-by-step explanation:

(excuse my handwriting on the ss its hard to write on a computer lol)

hope this helps :)

Answer:

5 feet away

Step-by-step explanation:

i am not sure but did mental math

Answer:

35

Step-by-step explanation:

if GFL = 34 and GEL = 36 FLG would be 35

Answer:

[tex]2\sqrt[3]{2}[/tex]

Step-by-step explanation:

This is equal to [tex]\sqrt[3]{8} * \sqrt[3]{2} = 2\sqrt[3]{2}[/tex]

Answer:

-7.333

Step-by-step explanation:

Answer:

-7 1/3

Step-by-step explanation:

Answer:

A is a function

Step-by-step explanation:

Hope the image helps.

Answer:

-4 is a real number, but not a whole number.

All non zero numbers are real.

All numbers without a decimal, fraction, or negative are whole numbers.

Step-by-step explanation:

Answer:

Yes -4 is a real number. No, -4 is not a whole number.

Step-by-step explanation:

Real numbers include all positive and negative numbers. A whole number is any number that does not contain a fraction, decimal, or negative value.

Answer:  [tex](-\infty, -4][/tex]

Curved parenthesis at negative infinity

Square bracket at -4

====================================================

Work Shown:

[tex]5(x+4) \le 0 \\\\x+4 \le \frac{0}{5} \\\\x+4 \le 0 \\\\x \le 0-4 \\\\x \le -4 \\\\[/tex]

The last inequality shown above is the same as saying [tex]-\infty < x \le -4[/tex]

Converting this to interval notation leads to the final answer of [tex](-\infty , -4][/tex]

Note the use of a square bracket at -4 to include this endpoint. We can never include either infinity, so we always use a parenthesis for either infinity.

Answer:

0.7

Step-by-step explanation:

To get 7/10 as a decimal you simply divide 7 by 10 which gets you 0.7.

Answer:

What is your question?

Step-by-step explanation:

Answer:

x=81.2

Step-by-step explanation:

Answer:

As time increases, the height of the person riding the Ferris wheel goes up and down. The Ferris wheel makes 4 rotations. The highest points on the graph are when the Ferris wheel is at its highest height. The lowest points on the graph are when the Ferris wheel is at the starting position.

Step-by-step explanation:

Answer:

The Ferris wheel makes 4 rotations. The maximum points on the graph represent when the Ferris wheel is at the top, and the minimum points on the graph represent when the Ferris wheel is at the bottom. This is what it said                      

step-by-step explanation:

Sample question endogeneity 2021

44%

I hope this helped!!!

Answer:

ummmmmmmmm 44?

Step-by-step explanation: