express as a simple logarithm and simplify. PLEASE HELP!!!! asap!!! will give brainliest!!! thank you!!!

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:

Yes this statement is correct.

Step-by-step explanation:

just mental math

The statement given that ∠OLF = ∠OMG is found to be; Correct from theorem of corresponding angles.

We are told that;

BC is parallel to CF

Now, we are told that;

∠OLF = ∠OMG

We can see that line DH is a transverse line that crosses the two parallel lines given as BG and CF

Now, according to theorem of corresponding angles, the angle's that are formed when two parallel lines are crossed by a transverse line are said to be equal because they correspond to one another.

In conclusion, it is true from corresponding angles that ∠OLF and ∠OMG are equal.

Read more about corresponding angles at; https://brainly.com/question/12054594

Answer:

The center circle of this question is (2,3)

Answer:

The price of the stock is now $5.60

Step-by-step explanation:

$5.25 - $3.75 = $1.50

$1.50 + $1.85 + $2.25 = $5.60

Answer:

They have $4.10

Step-by-step explanation:

Take out all the other stuff my 1.85 and 2.25 because all that other stuff doesn't matter now just add $1.85 + $2.25

   1   1

+ 1.85

  2.25

-------------

    $4.10

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

Explanation:

The point (0,0) means x = 0 and y = 0 pair up together.

Recall that any point is always of the form (x,y).

If we plug x = 0 and y = 0 into the equation, we end up with,

y = 3x

0 = 3*0

0 = 0

We get the same thing on both sides, so we have a true equation.

Since we have a true equation, we've shown that  (0,0) is a solution.

Visually this indicates (0,0) is on the line y = 3x. Put another way, the line y = 3x goes through the origin.

Answer:

5

Step-by-step explanation:

When dividing numbers by fractions, we can simply multiply the  umber by the reciprocal of the decimal. So,

4 ÷ 1/5 = 4 × (reciprocal of 1/5)

A reciprocal of a number is the same number written under 1. aka, 1 divided by that number, which simply is flipping the numerator and denominator of a number.

So the reciprocal of 1/5 is 5/1 = 5.

So 4 ÷ 1/5 = 4 × 5.

So your answer is 5.

hope it was useful!

Answer:

80 ft/s

Step-by-step explanation:

Given that,

A ball is thrown vertically upward from the top of a 96-ft tower, with an initial velocity of 16 ft/sec. Its position function is given by :

[tex]s(t)=-16t^2 + 16t + 96[/tex] ...(1)

When it hits the ground, s(t) = 0

[tex]-16t^2 + 16t + 96=0\\\\t=3\ s[/tex]

At t = 3 s it will hit the fround.

We need to find its velocity when it hits the ground.

Differentiate equation (1) to find its velocity.

[tex]v=\dfrac{ds(t)}{dt}\\\\v=\dfrac{d(-16t^2 + 16t + 96)}{dt}\\\\v=-32t+16[/tex]...(2)

Put t = 3 in equation (2)

[tex]v=-32(3)+16\\\\v=-80\ ft/s[/tex]

Hence, when it will ground its velocity is 80 ft/s.

Answer:

45° and 12

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

(8)

The polygon has n = 8, that is 8 exterior angles, thus

exterior angle = 360° ÷ 8 = 45°

(9)

The number of sides n is

n = 360 ÷ 30 = 12

Answer:

45° 12 sides

Step-by-step explanation:

1) Every polygons interior angles is equal to 180 times two less than the amount of sides it has (i.e 180•(4-2)=360:quadrilateral) So applying that here we have eight sides so 180(8-2)=1080. Now divide that by 8 to get the measure of one angle and subtract it from 180 to get the exterior angle 45°

2) if the exterior angle is 30° then the interior angle is 150°. For this part i guess and checked but you can refer to the equation above. (180(x-2)=y/150)

Thislink has the answer: https://brainly.com/question/19701013?answering=true&answeringSource=greatJob%2FquestionPage%2F3

Answer:

Step-by-step explanation:

Answer:

A. 63/100

Step-by-step explanation:

100-37= 63.

Answer:

Step-by-step explanation:

true false true false

Step-by-step explanation:

Simplifying

5x = 3x + 8

Reorder the terms:

5x = 8 + 3x

Solving

5x = 8 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

5x + -3x = 8 + 3x + -3x

Combine like terms: 5x + -3x = 2x

2x = 8 + 3x + -3x

Combine like terms: 3x + -3x = 0

2x = 8 + 0

2x = 8

Divide each side by '2'.

x = 4

Simplifying

x = 4

Answer:

x = -y + 4

Step-by-step explanation:

2y + 5x = 3x + 8

2x + 2y = 8

2x = −2y + 8

x= −y + 4

Answer:

Step-by-step explanation: They measured the length to be 5.08 cm, the width to be 5.09 cm, and the ... The actual volume of the block is 15.3 cm3. What is the percent error? thanks for your help in advanced. ... were measuring the volume of a cube shaped wooden block. ... Should I convert units before or after solving the problem?

Answer:$240.00

Step-by-step explanation:

$240.00

Answer:

It depends on how much the computer costs originally and the model of computer.

Step-by-step explanation:

Say the computer costs 151.98 USD with the tax added, then the computer would cost 148.00 USD without tax.  Or if the computer costs 162.79 USD with the tx added, then the computer would cost 160.00 USD without tax. It's the same for the rest but it also depends on the model of computer. (My calculations of adding 3 or 2 USD as the tax is just for example, i don't know how they calculate tax for computers)

151.98-148.00= 3.98$

162.79-160.00=2.79$

Answer:

oh you do 3 - 8 witch equals -3=x minus 6 = -9

Step-by-step explanation:

hope this helps

Answer:

126

Step-by-step explanation:

72/4=18 hot dogs sold per day

18*7=126 hot dogs in a week.

Answer:

Look for the incenter and place it there.

Step-by-step explanation:

Since there are three angles of 50°, 70° and 60°. If the designer is to place a sculpture on a round central position equidistant from all three walls, then he is looking for the incenter.

The incenter is simply the point where the bisectors of all the three angles intersect. This point is also the center of the largest circle that can be drawn inside the triangle where it touches all three sides of the triangle. Definitely, if the incenter is the middle of the circle that touches all the three sides, then the incenter will be equidistant from the three walls due to the fact that radius will always be the same in a circle.

This is why, he is to look for the incenter.

Answer:

84 degrees i think

Step-by-step explanation:

polygons have their interior angles add up to 540, so you just add up all the angles given and subtract them from 540, then you get your answer.

Answer: C. (2, -4)

Step-by-step explanation:

Take into consideration that y is less than or equal to -2. The only option in which the y value is less than or equal to -2 is option C., thus C would correctly solve the system of inequalities.

Answer:

The percent error of the cyclist's estimate is 5.63%

Step-by-step explanation:

Percentages

The cyclist estimates he will bike 80 miles this week, but he really bikes 75.5 miles.

The error of his estimate in miles can be calculated as the difference between his estimate and the real outcome:

Error = 80 miles - 75.5 miles = 4.5 miles

To calculate the error as a percent, we divide that quantity by the original estimate and multiply by 100%:

Error% = 4.5 / 80 * 100 = 5.625%

Rounding to the nearest hundredth:

The percent error of the cyclist's estimate is 5.63%

Answer:

1.a

2.b

3.e

4.f

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

Answer:

3143

Step-by-step explanation:

Answer:

p > d

c < p

Step-by-step explanation:

Answer:

It depends on the person mental state or past. But red often gives the person a sense of danger or fear

Step-by-step explanation:

Answer:

not true

Step-by-step explanation:

The actual answer is 8/9.

Answer:

B because 3*3=9 And 3*1=3 so it would be 3(3y-1) foil the answer

Step-by-step explanation:

The answer is B, I took the test.