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3 years ago

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A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and

an airplane is flying east above the second road. At a particular time the car is 15 kilometers to the north of P and traveling at 60 km/hr, while the airplane is flying at speed 185 km/hr 10 kilometers east of P at an altitude of 2 km. How fast is the distance between the car and the airplane changing?

1 answer:

Anettt [7]3 years ago

3 0

Answer:

D^2 = (x^2 + y^2) + z^2

and taking derivative of each term with respect to t or time, therefore:

2*D*dD/dt = 2*x*dx/dt + 2*y*dy/dt + 0 (since z is constant)

divide by 2 on both sides,

D*dD/dt = x*dx/dt + y*dy/dt

Need to solve for D at t =0, x (at t = 0) = 10 km, y (at t = 0) = 15 km

at t =0,

D^2 = c^2 + z^2 = (x^2 + y^2) + z^2 = 10^2 + 15^2 + 2^2 = 100 + 225 + 4 = 329

D = sqrt(329)

Therefore solving for dD/dt, which is the distance rate between the car and plane at t = 0

dD/dt = (x*dx/dt + y*dy/dt)/D = (10*190 + 15*60)/sqrt(329) = (1900 + 900)/sqrt(329)

= 2800/sqrt(329) = 154.4 km/hr

154.4 km/hr

Step-by-step explanation:

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3 years ago

Find the area of the square rug if it is side is (7X +4) feet.

likoan [24]

Answer:

49 $x^{2}$ +56x+16 ft squared.

Step-by-step explanation:

Alright, so we are given that we have a rug that has a side of 7x+4 feet. With this information, we are able to determine the area of the square rug. Considering that it is a square rug, all the sides are equal to each other because a square has four equal sides and angles.

To solve this, you can do it in two ways.

One, write it as (7x+4)2. That 2 is supposed to represent squared.

If you know the rule, this is a perfect square trinomial.

The formula is a squared plus 2ab plus b squared. 7 and 4 are your a and b values. 7x squared is 49x squared and 4 squared is 16.

2ab, multiply 2 times 7x times 4. That is 56x.

Therefore, the area is 49xsquared plus 56x+16.

Another way is to write it like this (7x+4) (7x+4).

Since it is an exponent, we are multiplying the same thing two times. Apply the Distributive Property.

E.G. 2(x+5)= 2x+10.

With this, you are distributing two numbers into another two numbers. 7x times 7x is 49x squared and 7x times 4 is 28x. Then, go to 4. 4 times 7x is also 28 x and 4 times 4 is 16. Now, combine the like terms. 49x squared plus 28x plus 28x or 56x plus 16.

This represents your area.

I hope this helps, and I hope you have a good day!

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3 years ago

If f(x) = x+2, what is the inverse of f(x)?

VMariaS [17]

Answer:

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Step-by-step explanation:

8 0

2 years ago

Answers plz i cant do math

Licemer1 [7]

The slope of all parallel lines are equal.

The slope of a line in the form $y=mx+c$ is m.

1. The given equation is: $y=4x+2$ . The slope of this line is $m=4$ . The slope of the line parallel to this line is also 4.

2. The given equation is $y=\frac{2}{7}x+1$ . The slope of this line is $m=\frac{2}{7}$ .

The slope of the line parallel to it is also $\frac{2}{7}$ .

3. The next equation is $y+9x=13$ . The slope intercept form is $y=-9x+13$ .

The slope of this is $m=-13$ . The line parallel to it also has slope which is -13.

4. The given equation is $y=-\frac{1}{2}x+4$ . The slope of this line and the line parallel to it is $m=-\frac{1}{2}$

5. The equation is 6x+2y=4. We simplify to get: 3x+y=2.

The slope-intercept form is $y=-3x+2$ . The line parallel to this line has slope $m=-3$

6. Assuming the line is $y=-3x+9$ , then the slope is $m=-3$

7. Assuming the line is $-5x+5y=4$ , then the slope-intercept form is $y=x+\frac{4}{5}$ and the slope of the line parallel to this line is m=1

8. The equation is 9x-5y=4. The slope intercept form is $y=\frac{5}{9}x-\frac{4}{9}$ . The slope of the line parallel to this line is $m=\frac{5}{9}$

9. The given equation is $-x+3y=6$ . The slope intercept form is $y=\frac{1}{3}x+2$ . The line parallel to this line also has slope $m=\frac{1}{3}$ .

10. Assuming the given line is 6x-7y=10, then $y=\frac{6}{7}x-\frac{10}{7}$ and the line parallel to it has slope $m=\frac{6}{7}$

11. Assuming the line is $y-x=-3$ , then $y=x-3$ and the slope of the line parallel to it is $m=1$

12. The given line is 3x-5y=6. This implies that $y=\frac{3}{5}x-\frac{6}{5}$

7 0

3 years ago

What is the area of this triangle?<br><br> A=bh2<br><br> 17 m²<br> 30 m²<br> 60 m²<br> 120 m²

e-lub [12.9K]

A = 1/2 x bh
A = 1/2 x 5 x 12
A = 6 x 5
A = 30m

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3 years ago

Read 2 more answers