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neonofarm [45]
3 years ago
8

If the length of AB=12, what is the length of AP?

Mathematics
1 answer:
lara31 [8.8K]3 years ago
7 0

Answer:

AP= 12

Step-by-step explanation:

Here is the complete question: If the length of AB=12, what is the length of AP? picture attached.

Given: AB= 12

          ∠APB= 60°

Remember; sum of all angle of triangle is equal to 180°.

We can look at picture, where two side of triangle is radius of circle.

∴ Angle of two side will also be same for the isosceles triangle.

Lets assume the unknow angle of the triangle be "x".

Now, x+x+60= 180

⇒ 2x+60= 180

subtracting both side by 60

⇒ 2x= 120

∴ x= 60

As now we have all the angle of triangle is 60° (equilateral triangle)

∴ All the side will be same, which is 12

Hence, AP= 12.

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irakobra [83]

Answer:

a) P(0, <u>2</u>), Q(<u>4</u>, 0)

b) Please find attached the plot of the points P and Q on a chart made with MS Excel

c) Please find the graph of the line that represent the function 4·x + 2·y = 8 for values of x from -2 to 3 made with the Insert Chart feature on MS Excel

Step-by-step explanation:

The given equation for the line is 4·x + 2·y = 8

a) The coordinates of P = P(0, _)

Therefore, the point 'P', which is the point where the variable y = 0, is the point the (straight line) graph intercepts the x-axis (the x-intercept)

When y = 0 from the given equation, we get;

4·x + 2·y = 8

At the point y = 0;

4·x + 2 × 0 = 8

x = 8/4 = 2

x = 2

∴ The coordinates of P = P(0, _) = P(0, <u>2</u>)

Similarly, when x = 0, we get;

4·x + 2·y = 8

At the point x = 0;

4 × 0 + 2·y = 8

y = 8/2 = 4

y = 4

∴ The coordinates of Q = Q(_, 0) = Q(<u>4</u>, 0)

b) Rewriting the given equation in terms of 'y' gives;

y = (8 - 4·x)/2 = 4 - 2·x

y = 4 - 2·x

With the help of MS Excel, the points P and Q are plotted in the attached graph

c) The line of the graph of the function 4·x + 2·y = 8 for values of x from -2 to 3 can be added by Changing the Chart Type to 'Scatter with Smooth Lines and Markers' within MS Excel as presented in the included graph of the line.

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