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3 years ago

What is the range of function y=√(-2cos^2x+3cosx-1)

1 answer:

8 0

Hello Friend,here is the solution for your question

so the given function is 
y= √(-2cos²x+3cosx-1)
i.e = √[-2(cos²x-3/2+1/2)]
i.e = √[-2(cosx-3/4)²-9/16+1/2]
i.e. = √[-2(cos-3/4)²-1/16]
i.e. = √[1/8-3(cosx=3/4)²]-----------(1)

Now here in this equation is this quantity :-
(cosx=3/4)²----------------(2) is to it's minimum value then the whole equation 
i.e. = √[1/8-3(cosx=3/4)²] will be maximum and vice versa 

And we know that cosx-3/4 will be minimum if cosx=3/4
therefore put this in (1) we get 
(cosx=3/4)²=0 [ cosx=3/4]
hence the minimum value of the quantity (cosx=3/4)² is 0 

put this in equation (1) 
we get ,
i.e. = √[1/8-3(cosx=3/4)²]
 =√[1/8-3(0)] [ because minimum value of of the quantity (cosx=3/4)² is 0 ]
 =√1/8
 =1/(2√2)

this is the maximum value now to find the minimum value 

since this is function of root so the value of y will always be ≥0 

hence the minimum value of the function y is 0 

Therefore, the range of function y is [0,1/(2√2)]

__Well,I have explained explained each and every step,do tell me if you don't understand any step._

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Solve for x. 83 = 35^x Express the answer to the hundredths place (i.e., two digits after the decimal point). x =

devlian [24]

Answer:

x = 1.24

Step-by-step explanation:

In order to get that x down from its current position of exponential, you need to take either the log or the natural log of both sides. The power rule tells us that we can then pull the exponent down in front. So let's take the natural log of both sides:

$ln(83)=ln(35)^x$

We can bring the x down in front to give us:

ln(83) = x ln(35)

The right side of this is "stuck" together by multiplication, so we can undo that multilication by division of the ln(35). That leaves us with just x on the right:

$\frac{ln(83)}{ln(35)}=x$

Do this on your calculator and find that x = 1.24

7 0

3 years ago

7/6 divided by 8 write in simplest form

quester [9]

Answer: the answer is 7/48

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Does anyone know the answer to these two problems?

Nady [450]

Answer:

8) -8, -9

9) 4, $\frac{1}{2}$

Step-by-step explanation:

8) x² + 12x + 27

Solutions of a polynomial means the values of $x$ such that the polynomial becomes zero. $i.e., y = 0$ .

We use the following formula to determine the solutions of a quadratic equation of the form: $ax^2 + bx + c = 0$

$\implies x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this equation, $a = 1; b = 12; c = 27$

Substituting in the formula, we have:

$x = \frac{-12 \pm \sqrt{144 - 108}}{2}$

$\implies x = \frac{-12 \pm 6}{2}$

Taking 2 common outside we get:

$x = - 6 \pm 3$

Therefore, we get two solutions viz, x = -3, -9.

9) 2x² - 9x + 4 = y

X- intercepts of a polynomial means the value of x such that y = 0. It means the roots of the polynomial.

Solving the equation using the formula above, we get:

$x = \frac{-(-9) \pm \sqrt{81 - 32}}{2(2)}$

$\implies x = \frac{9 \pm 7}{4}$

The values of x = 4, $\frac{1}{2}$ .

Hence, the answer.

8 0

3 years ago

Angles ∠ABC= x and ∠CBD=(2y+4) are complementary. ∠CBD and ∠DBE=(3y+x) are supplementary.

Basile [38]

The missing question is find x , y and the measure of each angle

The values of x and y are x = 28 and y = 30

The measures of ∠ABC is 26°, ∠CBD is 64° and ∠DBE is 116°

Step-by-step explanation:

Let us revise the meaning of complementary angles and supplementary angles

Two angles are complementary if their sum is 90°
Two angles are supplementary if their sum is 180°

∵ ∠ABC = x

∵ ∠CBD = 2y + 4

∵ ∠ABC and ∠CBD are complementary

- That means their sum is 90°, add their values and equate

the sum by 90

∴ x + (2y + 4) = 90

∴ x + 2y + 4 = 90

- Subtract 4 from both sides

∴ x + 2y = 86 ⇒ (1)

∵ ∠DBE = (3y + x)

∵ ∠CBD and ∠DBE are supplementary

- That means their sum is 180°, add their values and equate

the sum by 180

∵ ∠CBD = (2y + 4)

∴ (2y + 4) + (3y + x) = 180

- Add like terms

∴ x + 5y + 4 = 180

- Subtract 4 from both sides

∴ x + 5y = 176 ⇒ (2)

Now we have a system of equations to solve them

Subtract equation (1) from equation (2) to eliminate x

∵ 3y = 90

- Divide both sides by 3

∴ y = 30

- Substitute the value of y in equation (1) to find x

∵ x + 2(30) = 86

∴ x + 60 = 86

- Subtract 60 from both sides

∴ x = 26

∵ ∠ABC = x

∴ The measure of angle ABC is 26°

∵ ∠CBD = 2y + 4

∴ ∠CBD = 2(30) + 4 = 60 + 4 = 64°

∴ The measure of angle CBD is 64°

∵ ∠DBE = 3y + x

∴ ∠DBE = 3(30) + 26 = 90 + 26 = 116°

∴ The measure of angle DBE is 116°

The values of x and y are x = 28 and y = 30

The measures of ∠ABC is 26°, ∠CBD is 64° and ∠DBE is 116°

Learn more:

You can learn more about the complementary angles and supplementary angles in brainly.com/question/10483199

#LearnwithBrainly

6 0

3 years ago

1. Find the values of X and Y.

Andrei [34K]

156 and (14y+30) are opposite angles so they are the same. You can use this information to put them into an equation to solve;

14y+30 = 156
You want you the the y's alone, so you subtract 30 from each side.
14y = 126
Then divide each side by 14 to get what just 1 y is.
y = 9

Then to find what the other pair of opposite angle add up to subtract 156x2 from 360
156x2 = 312 360-312 = 48

Halve 48 to get the sum of just one of the opposite angles
48/2 = 24
Now you know that 3x = 24. Solve this equation
x = 8

4 0

3 years ago