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3 years ago

Help please? 10 points. Correctly

Mathematics

1 answer:

Romashka [77]3 years ago

4 0

From the Figure :

Point A is (-3 , -3)

Point B is (6 , 6)

We know that, The Mid Point of Two Points (x₁ , y₁) and (x₂ , y₂) is given by :

$\mathsf{\implies [(\frac{x_1 + x_2}{2})\;,\;(\frac{y_1 + y_2}{2})]}$

$\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;[(\frac{-3 + 6}{2})\;,\;(\frac{-3 + 6}{2})]}$

$\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;[(\frac{3}{2})\;,\;(\frac{3}{2})]}$

$\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;(1.5,1.5)}$

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A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat

konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles

First, we need to find b:

$a^{2} + b^{2} = h^{2}$ (1)

$b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles$

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

$\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})$

$2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:

$0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

$\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h$

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

4 0

2 years ago

(15-3)÷12+1<br>How to divide this without using a remainder?

Julli [10]

Answer:

If you solved this, it wouldn't have a remainder. First you would solve the numbers in the parenthesis, (15 - 3), which is 12. Now it should look like, 12 ÷ 12 + 1. Next you divide 12 by 12 and that equals 1. And all you need to do now is add 1 + 1, which is 2. So your answer will be 2.

8 0

3 years ago

Read 2 more answers

Sam takes out a $167,000 mortgage for 20 years. He makes monthly payments and at the end calculates that he has paid $240,141 to

stiv31 [10]

Answer:

About 3%

Step-by-step explanation:

3% of $167,000 is $5,010

5010 times the 20 years is 100200 add that to the 167000 and you get $267,200

The actual answer is about 2.4% but 3% is the closest.

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