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3 years ago

Type the correct answer in the box,

Mathematics

1 answer:

HACTEHA [7]3 years ago

3 0

We'll assume the quadratic equation has real coefficients

Answer:

The other solution is x=1-8i.

Step-by-step explanation:

The Complex Conjugate Root Theorem

if P(x) is a polynomial in x with real coefficients, and a + bi is a root of P(x) with a and b real numbers, then its complex conjugate a − bi is also a root of P(x).

The question does not specify if the quadratic equation has real coefficients, but we will assume that.

Given x=1+8i is one solution of the equation, the complex conjugate root theorem guarantees that the other solution must be x=1-8i.

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Write the expression as the sine, cosine, or tangent of an angle. sin 5x cos x - cos 5x sin x

mrs_skeptik [129]

Answer:

sin 5x cos x - cos 5x sin x = sin(4x)

Step-by-step explanation:

Given that the trigonometric expression,

sin 5x cos x - cos 5x sin x

Here we use the "sum and difference formulas"

Sum and Difference Formulas

sin(A+B)=sin A cos B + cos A sin B

sin(A-B)=sin A cos B - cos A sin B

cos(A+B)=cos A cos B - sin A sin B

cos(A-B)=cos A cos B + sin A sin B

So,

sin 5x cos x - cos 5x sin x = sin (5x - x)

sin 5x cos x - cos 5x sin x = sin(4x)

That's the final answer.

6 0

3 years ago

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Svetach [21]

Answer:

Step-by-step explanation:

⅔ ×3³/5

⅔×18/5

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15 15

=36

5 0

2 years ago

Choose which group of sets the following number belongs to. Be sure to account for ALL sets.

liberstina [14]

Whole numbers, integers, rational numbers, natural numbers, real numbers

All of those are correct

5 0

3 years ago

Two positive integers have a sum of 23 and a product of 126. Find the two numbers.

meriva

Answer:

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Step-by-step explanation:

6 0

3 years ago

1+Sin/Cos + Cos/1+Sin = 2Sec

Bond [772]

Step-by-step explanation:

Consider the left-hand side:

$\dfrac{1+\sin{\theta}}{\cos{\theta}} + \dfrac{\cos{\theta}}{1+\sin{\theta}}$

$\:\:\:\:= \dfrac{(1+\sin{\theta})^2 + \cos^2{\theta}}{\cos{\theta}(1+\sin{\theta})}$

$\:\:\:\:=\dfrac{1+2\sin{\theta}+\sin^2{\theta} + \cos^2{\theta}}{\cos{\theta}(1+\sin{\theta})}$

$\:\:\:\:=\dfrac{2+2\sin{\theta}}{\cos{\theta}(1+\sin{\theta})} =\dfrac{2(1+\sin{\theta})}{\cos{\theta}(1+\sin{\theta})}$

$\:\:\:\:= \dfrac{2}{\cos{\theta}} = 2\sec{\theta}$

7 0

3 years ago