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Radda [10]
3 years ago
14

A spherical block of ice melts so that its surface area decreases at a constant rate: ds/dt = - 8 pi cm^2/s. calculate how fast

the radius is decreasing when the radius is 3cm. (recall that s = 4 pi r^2.)
Mathematics
1 answer:
sveticcg [70]3 years ago
5 0
The rate a which the surface area, S, decreases is
\frac{dS}{dt} =-8 \pi \, cm^{2}/s

The surface area is
S = 4πr²
where r =  the radius at time t.

Therefore
\frac{dS}{dt} = \frac{dS}{dr}  \frac{dr}{dt} =8 \pi r  \frac{dr}{dt} \\\\ -8 \pi  = 8 \pi r  \frac{dr}{dt} \\\\  \frac{dr}{dt} =- \frac{1}{r}

When r = 3 cm, obtain
\frac{dr}{dt}]_{r=3} = - \frac{1}{3} \, cm/s

Answer:  -1/3  cm/s  (or -0.333 cm/s)
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Evaluate 5k + 1 when: *
wlad13 [49]

1

k^2 = 4k

k = 0, k = 4

#2

k^2 - 5k = k + 7

k^2 - 6k = 7

k^2 - 6k + 9 = 16

k - 3 = 4 ⇒ k = 7

k - 3 = -4 ⇒ k = -1

#3

k^3 - 5k^2 + 3k = -k

k^3 - 5k^2 + 4k = 0

k(k^2 - 5k + 4) = 0

k = 0, k = 1, k = 4

#4

|k + 1| + 2 = 8

|k + 1| = 6

k = 5, k = -7

5 0
2 years ago
What is the value of x?<br><br><br><br> Enter your answer in the box.
Andrews [41]

Answer:

\displaystyle 7 = x

Step-by-step explanation:

Five is <em>one-eighth</em> of forty, so relatively proportional to that, <em>one-eighth</em> of twenty-four is three, so you do this:

24 = 2x + 10

- 10 - 10

__________

\displaystyle \frac{14}{2} = \frac{2x}{2} \\ \\ 7 = x

I am joyous to assist you anytime.

5 0
3 years ago
Write the number that is poitioned at point b
defon

Answer:

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Step-by-step explanation:

7 0
2 years ago
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Which of the following is a point-slope equation of a line that passes through the points (-1,4) and (8,-2)
dexar [7]

Answer:

y = (2/3)x + 4 2/3

Step-by-step explanation:

For reference, a linear function has an equation of y = mx + b

The first thing we're going to do is use the slope formula, \frac{y2-y1}{x2-x1} or rise over run. In this case that looks like:

(-2-4) - (8 - -1)

-2 -4 comes out to - 6, and the denominator comes out to 9.

6/9 is equal to 2/3, which is our m or slope value.

Next we want to find the b value, or our y-intercept. To do that we'll plug one of the points into the equation with our new-found slope:

4 = (2/3)-1 +b

4 = -2/3 + b

4 2/3 = b

That means our complete equation is:

y = (2/3)x + 4 2/3

OR

y = (2/3)x + 14/3 (equivalent but an improper fraction rather than a mixed fraction).

4 0
3 years ago
Elimination_4x_2y=14<br> _10x+7y=_24
Gnesinka [82]

Answer:

The answer is x=-\frac{50}{8}  and y=\frac{11}{2}.

Step-by-step explanation:

Given:

-4x-2y=14

-10x+7y=-24

Now, to solve it by elimination:

-4x-2y=14   ......(1)

-10x+7y=-24 ......(2)

So, we multiply the equation (1) by 7 we get:

-28x-14y=98

And, we multiply the equation (2) by 2 we get:

-20x+14y=-48

Now, adding both the new equations:

-28x-14y+(-20x+14y)=98+(-48)

-28x-14y-20x+14y=98-48

-28x-20x-14y+14y=50

-8x=50

<em>Dividing both the sides by -8 we get:</em>

x=-\frac{50}{8}

Now, putting the value of x in equation (1):

-4x-2y=14

-4(-\frac{50}{8})-2y=14

\frac{200}{8} -2y=14

25-2y=14

<em>Subtracting both sides by 25 we get:</em>

-2y=-11

<em>Dividing both sides by -2 we get:</em>

y=\frac{11}{2}

Therefore, the answer is x=-\frac{50}{8}  and y=\frac{11}{2}.

5 0
3 years ago
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