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3 years ago

Please can someone help me with both questions. Thank you. Work is due tomorrow.

Mathematics

1 answer:

Mariulka [41]3 years ago

7 0

So let's begin!
So the length is 25 and the entire perimeter is 106. Lets put these both of these numbers as information we know.

We know the length is 25.
We know the full perimeter is 106.
We also know a rectangle has 2 pairs of congruent sides.

Okay so, the length is 25.
Since there are two sides that are the same we would multiply 25 by 2 to get 50.

Now we know 2 sides out of the four sides on a rectangle.

106 is the final perimeter, if we subtract 50 from 106, we get 56. That is the measurement for both sides we're missing but we need to know the width for just one side.
So we divide 56 by 2 to get 28.
The width is 28.

Heres the show your work part:

25 x 2 = 50
Gets both lengths for rectangle.

106 - 50 = 56
Gets the product for the widths.

56 / 2 = 28
Gets the width of just one side.

Your final answer: 28

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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

Hey I'm Chloe Can you Help Me, I will give Brainlest, Thank you :)

almond37 [142]

Answer:

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Step-by-step explanation:

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Answer:

5(-5x - 2) =

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Answer:

(x, y) = (8, -3)

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You can substitute for x in the first equation:

3(-3y -1) +3y = 15

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The solution to this system of equations is (x, y) = (8, -3).

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Answer:

Step-by-step explanation:

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