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saul85 [17]
2 years ago
6

Q5.Jumbo is standing on top of a cliff looking at a speed boat out at sea.The vertical of the cliff from the base (sea level) to

jumbo is 80m and the straight distance from jumbo to the speed boat is 170m.
A. Find the horizontal distance from the speed boat to the base of the cliff.

B. If a helicopter is flying 20m directly above jumbo, what is the distance between the helicopter and the speed boat?​
Mathematics
1 answer:
Leni [432]2 years ago
8 0

Answer:

A) 150 m

B) 180.28 m

Step-by-step explanation:

A) In order to find the horizontal distance from the base of the cliff to the speed boat, use the Pythagorean theorem to calculate the length of the missing side.

We are told that one of the sides is 80 m and the hypotenuse is 170 m. Therefore,

  • a² + b² = c²
  • (80)² + b² = (170)²
  • b² = 170² - 80²
  • b² = 22500
  • b = 150

The horizontal distance between the base of the cliff and the boat is 150 m.

B) Now, the side that was 80 m is now 100 m (includes the height that the helicopter is above Jumbo). The horizontal distance remains the same, 150 m, but the hypotenuse is different. Solving for the hypotenuse will give us the distance between the helicopter and the speed boat.

  • (100)² + (150)² = c²
  • 32500 = c²
  • 180.28 = c

The distance between the helicopter and the speed boat is 180.28 m.

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Make use of structure. For rectangle ABCD, two vertices are A(-2, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain you
MrRissso [65]

We are given a rectangle ABCD

A(-2, 3)

B(4, 6)

We are asked to find the slopes of sides BC, CD, and DA.

Let me first draw a rectangle to better understand the problem

Recall that the slope is given by

m=\frac{y_2−y_1}{ x_2−x_1}\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(4,6)

So the slope of side AB is

m_{AB}=\frac{6-3}{4-(-2)}=\frac{3}{4+2}=\frac{3}{6}=\frac{1}{2}=0.5

The sides BC and DA are perpenducluar to the side AB.

So their slopes will be

m_{BC}=m_{DA}=\frac{1}{-m_{AB}}

Substituting the value of slope of AB

m_{BC}=m_{DA}=\frac{1}{-0.5}=-2

The side CD is parallel to the side AB.

Parallel sides have equal slopes so

m_{CD}=m_{AB}=\frac{1}{2}

Therefore, the slopes of the rectangle ABCD are

\begin{gathered} m_{AB}=m_{CD}=\frac{1}{2} \\ m_{BC}=m_{DA}=-2 \end{gathered}

3 0
1 year ago
PLEASE HELP zoom in to remove blur
Masja [62]

Answer:

The answer is the second one :)

Good luck!

Hope I helped :)

Step-by-step explanation:

6 0
3 years ago
Please need help on this
mr_godi [17]
Try the first one hunny
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