Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be?

Answer:

At t = 3, pilot can hit the target located at the origin.

Step-by-step explanation:

We have been given displacement vector:

r(t) = 5 - t, 21 - t², 3-t³/27

so, in this case r(t) and r'(t) should be in the parallel but opposite direction.

In order to get r'(t) we need to differentiate r(t).

r(t) = 5 - t, 21 - t², 3-t³/27

r'(t) = -1, -2t, -t²/9

Now perform the cross product among these two r(t) and r'(t).

r'(t) x r(t) =

            = i ((-6t + )+ ( - )) -j ((-3 + + - )) + k ((-21 +  + 10t -2))

           = ( + - 6t )i + ( - +3) j + (-t² + 10t -21)k

In order to find the value of t, we need to put

+ - 6t = 0

-t² + 10t -21 = 0

So, after solving for t, we will get

- ( t-3) (t-7) = 0

t = 3 or t = 7

In this case, only t = 3 satisfies the other two equations as well. t=7 is not satisfying. So take t =3 as the time. and for further assurance, we need to check are our vectors r(t) and r'(t) opposite at t = 3 or not. Let's check it out.

r(3) = 5-3, 21 - 3²,  3 - 3³/27

r (3) = 2, 12, 2

r'(3) = -1, -2(3) , -3²/9

r'(3) = -1, -6 -1

Here, we can easily see that, r(3) = -2 r'(3) which is opposite and hence it is proved that, at exactly t = 3, pilot can hit a target located at the origin.

Answer:

The measure of arc ABC is 283°.

Step-by-step explanation:

We know that the whole arc is equal to 360°, that means

Where , and . Replacing these expressiones, we have

But, arc ABC is defined by the sum of arcs AB and BC:

Therefore, the measure of arc ABC is 283°.

Answer:

Arc measure of ABC is 283°

Step-by-step explanation:

We know the total angle of the circle is 360°.

Therefore,

(20y - 11) + (4y +6) + (7y - 7) = 360°

Collecting like terms, we have:

20y + 4y + 7y = 360 + 7 - 6 + 11

31y = 372

Let's divide both sides by 31.

y = 12

The arc measure of ABC is the sum of AB and BC. To find the arc measure of ABC, we have:

(4y +6) + (20y - 11)

Collecting like terms, we have:

4y + 20y + 6 - 11

24y - 5

Let's substitute 12 for y

24(12) - 5

288 - 5 = 283°

Arc measure of ABC is 283°

Answer:

Step-by-step explanation:

The midpoint of AB is (-5,1), if A(-3,8) and B(-7,-6). How to find out the midpoint of coordinates?The midpoint of coordinates is found by measuring the distance between two endpoints and dividing the obtained result by 2. Apart from this, one more method is there which is to add the two X-coordinates of the endpoints and divide them by 2. The same concept is applied to the Y-coordinates as well. According to the question, A = (-3,8) and B = (-7,-6). The formula is as follows:M(x,y) = ((x₁+x₂)/2 , (y₁+y₂)/2). Putting the above values in the mentioned formula, we get:M(x,y) = ((-3-7)/2 , (8-6)/2).

M(x,y) = (-5 , 1). Therefore, the midpoint of AB is (-5,1), if A(-3,8) and B(-7,-6).To learn more about the Midpoint of coordinates, refer to the link: brainly.com/question/28308761