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dalvyx [7]
3 years ago
10

A problem states that Ursula earns $9 per hour. To write an expression that tells how much money Ursula earns for h hours, Joshu

a wrote 9 divided by h. Sarah wrote 9h. Whose expression is correct and why?
Mathematics
1 answer:
LekaFEV [45]3 years ago
8 0
The correct one would by 9h because you are asking how much will Ursula make per hour. So let's say that h is 10, then in order to know how much Ursula makes per hour, you have to add 9 ten times. A short way to do that would be to simply multiply 9 with 10 so that you can get the answer of 90. It cannot be 9/h because then answer will be much lower than it is supposed to be. So the answer to the question is really 9h. 
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What is the solution to the trigonometric inequality 2sin(x)+3>sin ^2(x) over the interval
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The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π

<h3>How to solve trigonometric inequality?</h3>

We are given the trigonometric Inequality;

2 sin(x) + 3 > sin²(x)

Rearranging gives us;

sin²(x) - 2 sin(x) - 3 < 0

Factorizing this gives us;

(sin(x) - 3)(sin(x) + 1) < 0

Thus;

sin(x) - 3 = 0 or sin(x) + 1 = 0

sin(x) = 3 or sin(x) = -1

sin(x) = 3 is not possible because sin(x) ≤ 1.

Thus, we will work with;

sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.

Then, x = sin⁻¹(-1)

x = 3π/2.

Now, if we split up the solution domain into two intervals, we have;

from 0 ≤ x < 3π/2, at x = 0. Then;

sin²(0) - 2 sin(0) - 3

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= -3 < 0

Thus, the interval 0 ≤ x < 3π/2 is true.

From 3π/2 < x ≤ 2π, take x = 2π. Then;

sin²(2π) - 2 sin(2π) - 3

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= -3 < 0

Thus, the interval 3π/2 < x ≤ 2π is also true.

Read more about trigonometric inequality at; brainly.com/question/27862380

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