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nevsk [136]
3 years ago
6

The sum of two numbers is nineteen. One number is five more than the other. Find the numbers.

Mathematics
1 answer:
mestny [16]3 years ago
3 0

Answer:12, 7

Step-by-step explanation:Using the process of elimination, I went through each number and subtracted five and added it until I got 12 and 7.

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Point L is on line segment KM
Anna11 [10]

Answer:

KL = 15

Step-by-step explanation:

Given that,

Point L is on the line segment KM.

We have, KM=5x+10, LM=4x, and KL=3x

ATQ,

KM = KL + LM

Putting all the values, we get :

5x+10=3x+4x

5x+10 = 7x

Taking like terms together

5x-7x=-10

-2x=-10

x=5

Put x = 5 in KL = 3x

KL = 3(5) = 15

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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.

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