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goblinko [34]
3 years ago
9

4sin^2 + 13cos^2 = 7. Find cos Please read the picture question carefully and help !!

Mathematics
1 answer:
Vanyuwa [196]3 years ago
5 0
4 sin^2 θ + 13cos^2 θ = 7
sin^2 θ = 1 - cos^ θ
4 - 4cos^2 θ + 13cos^2 θ = 7
9cos^2 θ = 3
cos^2 θ = 1/3
cos θ = # (1/3) # - square root
Square root of (1/3) has +1/3 and -1/3 as values of cos
Find the key angle by doing the cos inverse of #1/3
K.A = cos^-1 #(1/3) = 0.955
θ lies in all 4 quadrants
The values of θ are:
θ = 0.955, 2.186, 4.096, 7.23
Ignore 0.955, 2.186, 4.096, 7.23 as they are out of range pi/2 = 1.571
The the value of θ = 0.955 = 0.96 (to 2 d.p) radian

Hope it helped!
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3 years ago
Will a 11.5-inch x 18-inch rectangular tray fit in<br> the box shown? Explain.
pychu [463]

Answer:

Option D

Step-by-step explanation:

From the picture attached,

In the parallelogram ABCD,

Length of diagonals AC and BD are equal.

By the property,

"If the lengths of the diagonals of a parallelogram are equal, parallelogram will be a rectangle".

Therefore ABCD is a rectangle.

That means all interior angles of the given rectangle will be 90°.

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AC² = AB² + BC²

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484 - 144 = (BC)²

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BC = 18.44 inches

Dimensions of the given box are 12 inches by 18.44 inches.

Dimensions of the rectangular tray is 11.5 inches by 18 inches.

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Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements a
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Answer:

The answer is given below

Step-by-step explanation:

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u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.

There exist two real numbers such that their sum is less than the difference between them

This is true when atleast one of the numbers is negative, for example u = 2 and v = -2

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x² < x means that the square of a real number is less than the real number

We can rewrite the statement as: There exist a real number such that its square is smaller than itself.

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We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.

This statement is true for all real numbers.

4 0
2 years ago
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