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2 years ago

The data in the table illustrate a linear function -3

Mathematics

1 answer:

FrozenT [24]2 years ago

6 0

Do you mean x= -3 or y= -3

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Hello , how to do 6(iii)?

Doss [256]

Answer:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}$

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

$\displaystyle V=\frac{4}{3}\pi r^3$

Therefore:

$\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Next, the surface area of a sphere S is given by:

$\displaystyle S=4\pi r^2$

Therefore:

$\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}$

We can divide both sides by 2:

$\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}$

We can substitute this into dV/dt. Rewriting:

$\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)$

So:

$\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}$

Since dV/dt = 0.03 or 3/100:

$\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}$

Therefore:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)$

Where k = 3/50.

And we have shown that dS/dt is directly proportional to 1/r.

4 0

3 years ago

What is the value of x?

tekilochka [14]

Answer:

Step-by-step explanation:

since we can see that the lines are parallel

and we can see that the both are interior angles and when we sum up both angles we get 180

2x - 5 + 45 = 180

2x + 40 =180

2x = 180 - 40

2x =140

x = 140/2

x = 70

4 0

3 years ago

Ms. Knight's two cooking classes are

Radda [10]

Answer:

Step-by-step explanation:

In class 1, they used 10 sweet potatoes.

If they need 30, in class 2, they used 20.

5 0

2 years ago

Be sure to use a comma after three please value of one need it 945×1000

JulijaS [17]

Answer:

94,5000

Step-by-step explanation:

7 0

2 years ago

An HMO charges $35 per doctor visit (d) and $15 per prescription (p). Which expression shows the total cost for prescriptions an

Alecsey [184]

Answer:

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Step-by-step explanation:

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2 years ago