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Slav-nsk [51]
3 years ago
9

A boy walks 6 km from a point P to a point Q on a bearing of 065. He then walks to a point R at a distance of 13 km on a bearing

of 146.
(1) sketch the diagram of his movements (2) calculate correct to the nearest kilometre, the distance PR​
Mathematics
1 answer:
Usimov [2.4K]3 years ago
6 0

9514 1404 393

Answer:

  1. see below for a sketch
  2. 12 km

Step-by-step explanation:

The distance can be calculated using the Law of Cosines. The angle internal to the triangle at Q is (180°-(146° -65°)) = 99°. Then the distance PR can be found from ...

  PR² = PQ² +QR² -2·PQ·QR·cos(∠PQR)

  PR² = 6² +10² -2·6·10·cos(99°) ≈ 154.77

  PR ≈ √154.77 ≈ 12.44 . . . . km

The distance PR is about 12 km.

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Plz help, I'm taking an Advanced class (Algebra) Will give brainliest ✔✔✔✔✔✔✔✔✔
bija089 [108]

Part A:

The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:

m = \dfrac{y_2 - y_1}{x_2 - x_1}

  • (x_1, y_1) and (x_2, y_2) are points on the function

You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:

h(0) = 3(5)^0 = 3 \cdot 1 = 3

h(1) = 3(5)^1 = 3 \cdot 5 = 15

h(2) = 3(5)^2 = 3 \cdot 25 = 75

h(3) = 3(5)^3 = 3 \cdot 125 = 375


Now, let's find the slopes for each of the sections of the function:

<u>Section A</u>

m = \dfrac{15 - 3}{1 - 0} = \boxed{12}

<u>Section B</u>

m = \dfrac{375 - 75}{3 - 2} = \boxed{300}


Part B:

In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.

\dfrac{m_B}{m_A} = \dfrac{300}{12} = 25


It is 25 times greater. This is because 3(5)^x is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.

7 0
3 years ago
Helppppppp mathhhhhhhh
aivan3 [116]
Again using the Pythagorean Theorem:

h^2=x^2+y^2, where h is the hypotenuse of a right triangle and x and y are the side lengths.  You are given that the hypotenuse is 34 ft and the base side is 16ft. Let h=34, x=16, and y=height, then you have:

34^2=16^2+y^2

y^2=34^2-16^2

y^2=1156-256

y^2=900

y=√900

y=30 ft

So the ladder will reach a spot 30 feet high on the building. 
8 0
3 years ago
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g100num [7]

Answer:

-17

Step-by-step explanation:

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Write a linear function f with the values f(5) = -1 and f(0) = -1.
vichka [17]

Answer:

Step-by-step explanation:

F(x)=-1

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Find the equation of the line through (10, 4) that is parallel to the line with the equation
lyudmila [28]

Answer:

x + y = 14

Step-by-step explanation:

Parallel lines have the same slope, so the line's slope will be -1.

Plug this slope and the given point into y = mx + b to find b:

y = mx + b

4 = -1(10) + b

4 = -10 + b

14 = b

Then, plug this and the slope into y = mx + b

y = -x + 14

Then, put this into standard form by moving the x to the other side:

x + y = 14 is the equation in standard form

6 0
3 years ago
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