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grigory [225]
3 years ago
8

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

Mathematics
2 answers:
Orlov [11]3 years ago
4 0

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.

katovenus [111]3 years ago
3 0

Answer:

(2u + 1)(u – 3) = 0 is equivalent to the given equation

For the second part of the question, the solutions to the equation are C and D, 7π/6 +2kπ and 11π/6 + 2kπ

Step-by-step explanation:

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Diano4ka-milaya [45]

Answer:

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8 0
3 years ago
You roll two dice. What is the probability you get a 2 and a number greater than 2?
abruzzese [7]
Hello!

You have to find the probability of getting a 2

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Then you have to find the chance of getting a number greater than 2

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6 0
4 years ago
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Vaselesa [24]
Well, you can only combine the numbers with the variable (the x) in front of them, since there’s no other number on the left side of the equation to combine that lone number with

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6 0
3 years ago
a clerk is paid $45.25 per hours for 40 hours a week, 1.50 times the regular rate of overtime and double the rate for a holiday.
KonstantinChe [14]

Given :

A clerk is paid $45.25 per hours for 40 hours a week, 1.50 times the regular rate of overtime and double the rate for a holiday.

To Find :

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Solution :

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Amount from overtime = $ (45.25×1.5) × 5 = $339.375 .

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