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serious [3.7K]
1 year ago
8

Use the drop-down menus to complete the solution to the equation cosine (startfraction pi over 2 endfraction minus x) = startfra

ction startroot 3 endroot over 2 endfraction for all possible values of x on the interval [0, 2pi].
Mathematics
1 answer:
Lilit [14]1 year ago
6 0

Use the drop-down menus to complete the solution to the equation cosine (start fraction pi over 2 end fraction minus x) = start fraction start root 3 end root over 2 end fraction for all possible values of x on the interval [0, 2pi].

Using trigonometric identities, the solution to the equation cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2} for all possible values of x on the interval [0, 2π].

What are trigonometric identities?

Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2}  \\\\cos(x)cos\frac{\pi }{2}+sin(x)sin \frac{\pi }{2} = \frac{\sqrt{3} }{2}\\\\cos(x)(0)+sin(x)(1) = \frac{\sqrt{3} }{2}\\\\sin(x) = \frac{\sqrt{3} }{2}\\\\x = \frac{\pi }{3}, \frac{2\pi }{3}

To learn more about trigonometric identities click here brainly.com/question/7331447

#SPJ4

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A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the bod
adell [148]

Answer: a - 4.512 hours

b - 1.94 hours

Step-by-step explanation:

Given,

a) A(t) = 10 (0.7)^t

To determine when 2mg is left in the body

We would have,

A(t) = 2, therefore

2 = 10(0.7)^t

0.7^t =2÷10

0.7^t = 0.2

Take the log of both sides,

Log (0.7)^t = log 0.2

t log 0.7 = log 0.2

t = log 0.2/ 0.7

t = 4.512 hours

Thus it will take 4.512 hours for 2mg to be left in the body.

b) Half life

Let A(t) = 1/2 A(0)

Thus,

1/2 A(0) = A(0)0.7^t

Divide both sides by A(0)

1/2 = 0.7^t

0.7^t = 0.5

Take log of both sides

Log 0.7^t = log 0.5

t log 0.7 = log 0.5

t = log 0.5/log 0.7

t = 1.94 hours

Therefore, the half life of the drug is 1.94 hours

6 0
3 years ago
Which is NOT true regarding the hypotenuse? *
Usimov [2.4K]

Answer:

It helps form the right angle = FALSE

Step-by-step explanation:

The legs form the angle

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3 years ago
What equals c? <br><br> c- 7.6= -4
lord [1]
The answer is...
C = 7.6 
5 0
3 years ago
Read 2 more answers
A blue print for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the bluep
solniwko [45]
3 inches long and 5.5 inches wide.....1 inch = 10 ft

3 inches = (3 * 10) = 30 ft long <==
5.5 inches = (5.5 * 10) = 55 ft wide <==
8 0
3 years ago
Read 2 more answers
Answer with explanation please!
VLD [36.1K]

Answer:

E

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

8x + 15 is an external angle of the triangle, thus

8x + 15 = 3x + 20 + 4x + 5, that is

8x + 15 = 7x + 25 ( subtract 7x from both sides )

x + 15 = 25 ( subtract 15 from both sides )

x = 10

Thus none of them on the list → E

3 0
3 years ago
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