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sergey [27]
3 years ago
10

Please answer, Thank you so much in advance ​

Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0
D 8x-3 because must add them all together
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The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu
rjkz [21]

The balloon has a volume V dependent on its radius r:

V(r)=\dfrac43\pi r^3

Differentiating with respect to time t gives

\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}

The surface area of the balloon is

S(r)=4\pi r^2

and differentiating gives

\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}

so that at the moment the radius is 3 m, its area is increasing at a rate of

\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}

4 0
2 years ago
How many feet? Thank you for your time.
kramer

Answer:

1 3/8 Feet

Step-by-step explanation:

Take 2 1/2 and subtract 1 1/8 which gives u 1 3/8

if u don't understand fractions u can always turn ur fractions into decimals that's what I did :)

6 0
2 years ago
Write an equation in point-slope form of a line that has a slope of 2/3 and
Serggg [28]

Answer:

y= 2/3x -1

Step-by-step explanation:

Ok so basically we want to put it in the form y=mx+b where m is 2/3 and passes through the point (9,5). So sub in the x and y of the point in brackets into the equation. 5= 2/3(9) + b and solve for b so b = -1. Therefore the equation is y=2/3x -1

5 0
2 years ago
Javier writes an integer on a piece of paper. The absolute value of his number is less than 4. Which is true of the possible val
alex41 [277]

Answer:

The possible values are less than 4 but greater than –4

Step-by-step explanation:

If the absolute value of integer number is less than 4 then it is 0, 1, 2 or 3.

so the possible integer numbers are: -3, -2, -1, 0, 1, 2 or 3.

All of them are greater than -4 and less than 4

7 0
3 years ago
Read 2 more answers
A can of tomato soup contains 8 ounces of soup. one ounce is equal to 29.35 grams. how many grams of soup are in the can
bulgar [2K]
There will be 234.8 grams of soup in the can. Hope it help!
5 0
2 years ago
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