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2 years ago

What must you assume when you use a rate for a prediction? (Please Help!! I'm in 6th grade and this is math.)

Mathematics

1 answer:

murzikaleks [220]2 years ago

3 0

Answer:

For anything to do with force you have to assume an even amount of force is spread out evenly. But for things like growing rate you have all those variables so you can't assume a constant growing rate like acceleration.

Step-by-step explanation:

hope it helps (:

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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

3 years ago

What is translation with 5 units right and 1 up

Leviafan [203]

Since you did not provide the coordinates, I can't provide an exact answer.
However, I can tell you this; from the initial x-coordinate, move right 5 units. from the initial-y coordinate, move up 1 unit and you will have your answer.

4 0

3 years ago

I need help rn PLEASEEE heheheh

snow_lady [41]

Diameter = 51 cm
Radius (r) = 51 cm ÷ 2 = 25.5 cm
π = 3.14
Circumference
= 2πr
= 2 × 3.14 × 25.5 cm
= 160.14 cm
Area of a circle
= πr^2
= 3.14 × (25.5)^2 cm^2
= 3.14 × 25.5 × 25.5 cm^2
= 2041.785 cm^2

Hope you could understand.

If you have any query, feel free to ask.

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2 years ago

6.1 m A 85.4 sq m ⓅⓁⓈ ⒽⒺⓁⓅ

Mrac [35]

The teacher probably wants you to multiply cause area refers to that

8 0

3 years ago

Is this correct? pls be sure of yourself. if you arent, pls check

Elza [17]

Answer:

Yes It Is.

Step-by-step explanation:

8 0

3 years ago