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3 years ago

8

Use the graph to calculate the following

1 answer:

sweet-ann [11.9K]3 years ago

4 0

Answer:

f(x)= { 1 if x≤-2

x2 if -2<x≤0

ln(x) if x>0

Step-by-step explanation:

The first part of the graph (from left to right) is a constant funcion. Since there isn't any pendant, the y value is constant at y=1. This remains this way until x≤-2 (because the value at x=-2 is filled in on the line and blanked out on the curve above)

The second part of the graph, between x>-2 & x=0, is a cuadratic formula.

Finally, the last part of the graph corresponds to the formula ln(x), which is only valid for x>0.

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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

2 years ago

The square of 15 is 225. The square of what other number is 225?

Firlakuza [10]

Answer:

-15

Step-by-step explanation:

-15²

= -15×-15

= 225

hope it helps!!

7 0

2 years ago

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Elis [28]

Answer:

Step-by-step explanation:

2 or 3

6 0

2 years ago

Pls answer I give brainliest thank you! Number 4

soldi70 [24.7K]

Answer:

6

Step-by-step explanation:

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Need to know now!!! giving 10 points what -6+8

Simora [160]

Answer:

the answer is 2...................

Step-by-step explanation:

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2 years ago

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