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anzhelika [568]
3 years ago
11

Aarón made a picture frame with the dimensions show in the figure what is the area of the picture

Mathematics
1 answer:
tatuchka [14]3 years ago
4 0

Answer:

Area of the picture is 72\textrm{ }cm^{2}

Step-by-step explanation:

Given:

Outer rectangle dimensions are 10 cm by 12 cm.

Inner rectangle dimensions are 6 cm by 8 cm.

Area of the picture given as:

Area=\textrm{Outer rectangle area}-\textrm{Inner rectangle area}

Outer rectangle area = 10\times 12=120\textrm{ }cm^{2}

Inner rectangle area = 6\times 8=48\textrm{ }cm^{2}

Therefore, the area of the picture is given:

Area=120-48=72\textrm{ }cm^{2}

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a chord of 12cm long of 8cm is away from the of the circle what is the lenght of the chord which is 6cm away from the centre
lana66690 [7]

Answer:

The length of the chord is 16 cm

Step-by-step explanation:

Mathematically, a line from the center of the circle to a chord divides the chord into 2 equal portions

From the first part of the question, we can get the radius of the circle

The radius form the hypotenuse, the two-portions of the chord (12/2 = 6 cm) and the distance from the center to the chord forms the other side of the triangle

Thus, by Pythagoras’ theorem; the square of the hypotenuse equals the sum of the squares of the two other sides

Thus,

r^2 = 8^2 + 6^2

r^2= 64 + 36

r^2 = 100

r = 10 cm

Now, we want to get a chord length which is 6 cm away from the circle center

let the half-portion that forms the right triangle be c

Using Pythagoras’ theorem;

10^2 = 6^2 + c^2

c^2 = 100-36

c^2 = 64

c = 8

The full

length of the chord is 2 * 8 = 16 cm

5 0
3 years ago
Michela’s skateboard ramp is at an incline of 40°. When she attempts a trick on the ramp, she finds that it is too steep. She ad
marissa [1.9K]

Answer:

22.7604763 degrees

Step-by-step explanation:

Note that the answer is NOT 20 degrees.

She adjusted the ramp to half the original <em>incline</em>

Therefore we have tan 40 = x = 0.839099631.

We want an incline of y degrees where tan y = x/2 = 0.839099631/2 = 0.419549815

Taking the arctan of both sides, we get

y = arctan(0.419549815) = 22.7604763 degrees

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