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3 years ago

15

Can anyone help me with this ?????

2 answers:

Sophie [7]3 years ago

4 0

Answer:

66.423 degrees

Step-by-step explanation:

The diagram is a right-angled triangle. It has two known sides and one known interior angle which is 90 degrees. The side opposite to the 90 degrees is called the Hypotenuse. it is also the longest side.

To find an angle, you need to know two sides. Per the angle at Y or angle XYZ, XY is adjacent. Using the adjacent XY and Hypotenuse YZ, we can write an expression using the trigonometric ratio called Cosine.

That's, Cos XYZ= 6/15

Angle XYZ=Cosine Inverse of 6/15

Angle XYZ=66.42. (2 dp)

ICE Princess25 [194]3 years ago

3 0

Answer:

66.4°

Step-by-step explanation:

cos XYZ = XY/ZY = 6/15 = 2/5 = 0.4

Using a calculator for cos^(-1) of 0.4 you get 66.42182152°

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3 years ago

The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =

vesna_86 [32]

Answer:

$p(x) = (3x^{2} - 8x + 5)(x - 4)$

Step-by-step explanation:

p(x) has degree 3

(x - 4) has degree 1

So p(x) can be rewritten as a polynomial of degree 2 multiplying (x-4)

So

$p(x) = (ax^{2} + bx + c)(x - 4)$

To find a, b and c, we have to divide p(x) by x - 4.

So

Finding a:

Dividing the first term of p(x) by x - 4.

$\frac{3x^{3}}{x - 4} = 3x^{2}$

So a = 3.

Now multiplying 3x² by, x - 4, we have:

$3x^{2}(x - 4) = 3x^{3} - 12x^{2}$

Subtracting p(x) from this:

$3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20$

Finding b:

Dividing the first term, after the subtraction, by x - 4.

$\frac{-8x^{2}}{x - 4} = -8x$

So b = -8.

Multiplying -8x by x - 4, we have:

$-8x(x-4) = -8x^{2} + 32x$

Then

$-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20$

Finding c:

$\frac{5x}{x - 4} = 5$

So c = 5.

Just to verify if the remainder is 0.

$5(x - 4) = 5x - 20$

$5x - 20 - (5x - 20) = 0$

Ok

Then:

$p(x) = (ax^{2} + bx + c)(x - 4)$

$p(x) = (3x^{2} - 8x + 5)(x - 4)$

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