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3 years ago

What is the following product in simplified form?

Mathematics

1 answer:

erastova [34]3 years ago

6 0

Answer:

Step-by-step explanation:

because I just think its a

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Solve 2sin2(x) – 5sin(x) – 3 = 0. Let u = sin(x). Which of the following is equivalent to the given equation?

Orlov [11]

Answer:

$x=(-1)^{k+1}\cdot \dfrac{\pi}{6}+\pi k,\ k\in Z$

Step-by-step explanation:

Consider the equation

$2\sin^2x-5\sin x-3=0$

Substitute

$u=\sin x$

into the equation:

$2u^2-5u-3=0$

This is quadratic equation, where

$D=(-5)^2-4\cdot 2\cdot (-3)=25+24=49\\ \\\sqrt{D}=7$

Hence,

$u_1=\dfrac{-(-5)-\sqrt{D}}{2\cdot 2}=\dfrac{5-7}{4}=-\dfrac{1}{2}\\ \\u_2=\dfrac{-(-5)+\sqrt{D}}{2\cdot 2}=\dfrac{5+7}{4}=3$

Now, use the substitution again:

1. When $u_1=-\dfrac{1}{2},$ then

$\sin x=-\dfrac{1}{2}\\ \\x=(-1)^k\sin^{-1}\left(-\dfrac{1}{2}\right)+\pi k,\ k\in Z\\ \\x=(-1)^k\cdot \left(-\dfrac{\pi}{6}\right)+\pi k,\ k\in Z\\ \\x=(-1)^{k+1}\cdot \dfrac{\pi}{6}+\pi k,\ k\in Z$

2. When $u_2=3,$ then

$\sin x=3$

This equation has no solutions, because the range of $\sin x$ is $[-1,1]$ and 3>1.

4 0

4 years ago

Read 2 more answers

If a standard basketball court is 50 feet by 94 feet. what is the total surface area in square feet

user100 [1]

It's a rectangle so the area is length times width.

A = 50 × 94 = 4700 square feet

Answer: 4700

6 0

3 years ago

Evaluate the following expression. You should do this problem without a calculator. ln e^e

Pie

Lna^b = blna

let y = lne^e

so y = lne^e = e lne

lne = 1

y = e which is a constant (Euler's number) ~= 2.718

For Euler's number estimating methods request in a comment.

8 0

3 years ago

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What kind of transformation converts the graph of f(x)=4x–10 into the graph of g(x)=4x+10?

Viktor [21]

Take the first graph and translate it UP 20 units.

3 0

4 years ago

Lisa knit 3/12 foot of a scarf on Saturday. She knit 8/12 foot of a scarf on Sunday.

Vesna [10]

Answer:

C - 5/12 of a foot

Step-by-step explanation:

Subtract the numerators from 8/12 - 3/12 - keeping the denominator

8 - 3 = 5

5/12

7 0

3 years ago