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2 years ago

Find all solutions of the equation in the interval [0, 2).

Mathematics

1 answer:

Margaret [11]2 years ago

6 0

Answer:

x = 3π/2

Step-by-step explanation:

The given equation can be rewritten as a quadratic in sin(x), then solved by factoring.

<h3>Rewrite</h3>

Using the identity ...

cos²x = 1 -sin²x

the equation can be rewritten as ...

sin(x) = -(1 -sin²(x)) -1 . . . . . .substitute for cos²x

<h3>Solution</h3>

The new equation can be solved by considering it a quadratic in sin(x).

0 = sin²(x) -sin(x) -2 . . . . . . subtract sin(x)

(sin(x) -2)(sin(x) +1) = 0 . . . . factor quadratic

The solutions to this are ...

sin(x) -2 = 0 ⇒ sin(x) = 2 . . . . no solutions

sin(x) +1 = 0 ⇒ sin(x) = -1 ⇒ x = 3π/2 (one solution)

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2) Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95. How m

d1i1m1o1n [39]

Answer:

13 pencils.

Step-by-step explanation:

Let x be the pens and y be the pencils

Given:

Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.

Total pens and pencils is 22

So, $x+y=22$ ----------------(1)

And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.

$0.75x+0.40y=11.95$ ------------(2)

solve equation 1 and equation 2 for x and y.

From equation 1.

$x+y=22$

$y=22-x$ ----------------(3)

put y value in equation 2.

$0.75x+0.4(22-x)=11.95$

$0.75x+0.4\times 22-0.4x=11.95$

$0.75x+8.8-0.4x=11.95$

$0.75x-0.4x=11.95-8.8$

$0.35x=3.15$

$x=\frac{3.15}{0.35}$

$x=9$

Now substitute x value in equation 3.

$y=22-9$

$y=13$

So, he buy 13 pencils.

5 0

3 years ago

How are positive numbers written in Roman

rosijanka [135]

The system of Roman numerals is based on using special symbols to denote decimal digits I=1, X=10, C=100, M=1000, and their halves V=5, L=50, D=500. Positive integers are written by repeating these numerals.

Brainliest?

5 0

3 years ago

The given equation has been solved in the table.

Alina [70]

From the steps shown in the table given, we can conclude that: D. in solving the equation, the subtraction property of equality was not applied.

<h3>What is the Subtraction Property of Equality?</h3>

If a + b = c, to apply the subtraction property of equality so that b is moved to the other side of the equation, we would have:

a + b - b = c - b

a = c - b

Thus, from the table given, the none of the steps showed that the subtraction property of equality was applied in solving the equation, so, the answer is: D.

Learn more about the subtraction property of equality on:

brainly.com/question/1601404

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