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3 years ago

How do you find the equation of a line if it is like 2x-3y=6? Please show work

Mathematics

1 answer:

tatiyna3 years ago

6 0

Answer:y=2/3x-2

Step-by-step explanation:

you need to get “Y” by itself therefore you subtract 2x on each side you will end up with -3y=-2x+6 then to get “Y” by itself you divide by -3 on both side and since there is a negative 2 on the other side a negative and a negative makes a positive and then you divide the 6 by -3 , that will give you y=2/3x-2

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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

3 0

3 years ago

The ratio of boys to girls in a group is 3:1. If there are 52 more boys than girls, work out how many people there are in total.

UkoKoshka [18]

Answer: 104 (Good chance its wrong)

Step-by-step explanation: if the ratio is 3:1 then there's 3 times as much boys as girls. if there are 52 more boys then that means 52 is twice as much as the number of girls so if we divide is by 2 we get 26. if we add 26 with 52 we get 78 and if we divide 78 by 3 we get 26. so I believe there are 26 girls and 78 boys. 26+78=104

I believe 104 is the answer but there's a good chance i'm wrong.

7 0

3 years ago

The function (f) is given by <img src="https://tex.z-dn.net/?f=f%28x%29%3De%5E%28x-11%29%20-8" id="TexFormula1" title="f(x)=e^(x

Vitek1552 [10]

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7 0

3 years ago

Re-write 15/9 as a mixed number

Y_Kistochka [10]

Answer:

1 6/9

Step-by-step explanation:

3 0

3 years ago

4 less than a number is it the same as a number decreased by 4?

beks73 [17]

Yes it is the same thing ! :)

3 0

4 years ago