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3 years ago

)) In a right triangle, a and b are the lengths of the legs and c is the length of the

Mathematics

1 answer:

gtnhenbr [62]3 years ago

7 0

Answer:

3.008 km or 3.0 km

Step-by-step explanation:

According to the Pythagoras theorem:

${c}^{2} = {a}^{2} + {b}^{2} \\ \therefore \: {a}^{2} = {c}^{2} - {b}^{2} \\ \therefore \: {a}^{2} = {(9.3)}^{2} - {(8.8)}^{2} \\ \therefore \: {a}^{2} = {(9.3 + 8.8)}{(9.3 - 8.8)} \\ \therefore \: {a}^{2} = 18.1 \times 0.5 \\ \therefore \: {a}^{2} = 9.05 \\ \therefore \: {a} = \sqrt{9.05} \\ \therefore \: {a} = 3.00832179 \\ \therefore \: {a} = 3.0 \: km$

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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

Que es una Progresión Aritméticas

wolverine [178]

Una progresión aritmética o secuencia aritmética es una secuencia de números tal que la diferencia entre los términos consecutivos es constante. Por ejemplo, la secuencia 5, 7, 9, 11, 13, 15 ... es una progresión aritmética con una diferencia común de 2

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2 years ago

What is the result of subtracting a number greater than -3 but less than -2 from a number greater than 1 and less than 6

leva [86]

Answer:

2/2 - 4 = -3

Step-by-step explanation:

I don't know really but, hopefully this helps. Are there any answer choices?

5 0

2 years ago

Can you please check if this is correct?

Reika [66]

Answer: not sure how helpful this is, but the second one is correct (if it's the one that's corresponding to the blue line). The pink line, however, is incorrect if it is corresponding to the first equation. The first equation must have a y-intercept of 1.

Step-by-step explanation:

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2 years ago

Plz explain.

slega [8]

Idk, why does the world need problems like this, not like everyone is going to grow up to be a math teacher.

8 0

3 years ago