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velikii [3]
3 years ago
10

The radius, r, of a sphere is increasing at 0.03 meters per second. The rate of increase is constant.

Mathematics
1 answer:
Vladimir79 [104]3 years ago
3 0
A)
Given: dr/dt = .03 m/s and r = 18 m
Volume of a sphere = (4/3)*PI*r^3
Take the derivative of both sides, so
dv/dt = 4*PI*r^2*dr/dt
Plug in the givens and you have the rate of increase of the volume
B)
Given: V = 288 m^3 and I'm going to assume that r and dr/dt are the same as in part A
Surface Area = 4*PI*r^2
Take the derivative on both sides, so
dA/dt = 8*PI*r*dr/dt
Again, plug in the givens and you'll have the rate of increase in the surface area
C)
This part, it's been awhile since I've done related rates, so it may take me awhile, but perhaps the next person can answer it before I finish.

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The rate charged per hour by each mechanic was:  x = 75 $ / hr and y = 115 $ / hr.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours.

Together they charged a total of $3225.

For this case we have the following variables:

x be the amount of $ / hr that the mechanic obtains 1.

y be the amount of $ / hr obtained by mechanic 2.

An equation to express this would be:

x + y = 190

20x + 15y = 3225

Solving the system of equations we have:

20x + 15(190 -x) = 3225

20x + 2850 - 15x = 3225

5x = 375

x = 75

simililary

y = 190 - x

y = 115

Hence, the rate charged per hour by each mechanic was:

x = 75 $ / hr

y = 115 $ / hr

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brainly.com/question/10413253

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Answer:

See below

Step-by-step explanation:

Essentially, we have to replace "quantifier words" like "All", "Every" by the universal quantifier ∀.

a) ∀ dinosaur x, x is extinct.

b) ∀ real number x, x is positive, negative, or zero.

c) ∀ irrational number x, x is not an integer.

d) ∀ logician x, x is not lazy.

e) ∀ integer x, x²≠ 2,147,581,953.

f)  ∀ real number x, x²≠ -1.

In a) and b) we replace the words without major changes. In the other statements, we modify the statement using negation. For example, "No irrational numbers are integers." is equivalent to "Every irrational number is not integer".

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3 years ago
5g−2≤ 3g+8 3g+8<br><br> it says to solve for g.
Bess [88]

Answer:g is greater than or equal to 6g + 18/5, or g >_ 6g + 18/5

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Add 2 to the 16. 5g <_ 6g + 18.

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