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MatroZZZ [7]
2 years ago
9

Find the differential of

Mathematics
1 answer:
anyanavicka [17]2 years ago
8 0

f(x,y)=x^2+y^3\implies \left.\cfrac{}{} 2x+3y^2 \right]_{\stackrel{\textit{\small x=2}}{\textit{\small y=1}}}\implies 2(2)+3(1)^2\implies 7

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Please explain this problem!!!​
9966 [12]

tis a little of plain differentiation.

we know the radius of the cone is decreasing at 10 mtr/mins, or namely dr/dt = -10, decreasing, meaning is negative.

we know the volume is decreasing at a rate of 1346 mtr/mins or namely dV/dt = -1346, also negative.

so, when h = 9 and V = 307, what is dh/dt in essence.

we'll be needing the "r" value at that instant, so let's get it

V=\cfrac{1}{3}\pi r^2 h\implies 307=\cfrac{\pi }{3}r^2(9)\implies \sqrt{\cfrac{307}{3\pi }}=r

now let's get the derivative of the volume of the cone

V=\cfrac{1}{3}\pi r^2 h\implies \cfrac{dV}{dt}=\cfrac{\pi }{3}\stackrel{product~rule}{ \left[ \underset{chain~rule}{2r\cdot \cfrac{dr}{dt}}\cdot h+r^2\cdot \cfrac{dh}{dt} \right]} \\\\\\ -1346=\cfrac{\pi }{3}\left[2\sqrt{\cfrac{307}{3\pi }}(-10)(9)~~+ ~~ \cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\right]

-\cfrac{4038}{\pi }=-\cfrac{180\sqrt{307}}{\sqrt{3\pi }}+\cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\implies \left[ -\cfrac{4038}{\pi }+\cfrac{180\sqrt{307}}{\sqrt{3\pi }} \right]\cfrac{3\pi }{307}=\cfrac{dh}{dt} \\\\\\ -\cfrac{12114}{307}+\cfrac{180\sqrt{3\pi }}{\sqrt{307}}=\cfrac{dh}{dt}\implies -7.920939735970634 \approx \cfrac{dh}{dt}

5 0
2 years ago
Estimate the line of best fit using two points on the line.(2,64),(6,32)
dem82 [27]

Answer:

estimate the line of best fit using two points on the line.(2,64),(6,32)

Step-by-step explanation:


7 0
3 years ago
Read 2 more answers
Here is a central angle that measures 1.5 radians. Select all true statements. Question 1 options: A) The area of the whole circ
KATRIN_1 [288]

Answer:

  D, E

Step-by-step explanation:

The applicable formula is ...

  s = rθ

so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...

  D) The length of the arc defined by the angle is 1.5 times longer than the radius.

  E) The ratio of arc length to radius is 1.5.

8 0
2 years ago
in a small machine shop, eight 5-gallon drums of oil are on hand. if 2 gallons are used each day and the owner wants a 30-day su
zavuch27 [327]
If 2 gallons of oil are used a day, than he will need 60 gallons of oil, because 30x2=60. For 60 gallons of oil, you would have to have 12 drums because 60÷5=12. Because there is already 8 drums of oil, there would already be 40 gallons because 8x5=40. If the owner already had 40 gallons of oil, they would only have to get 20 more gallons because 60-40=20. That would be 4 drums because 20÷5=4. The owner would have to order 4 more drums of oil.
4 0
3 years ago
suppose the growth of Bermuda grass from germination to lawn-care length is normally distributed with a mean of 20 days with a s
Law Incorporation [45]

I chose D bcuz it the right answer to pick

6 0
2 years ago
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