All categories

3 years ago

PLEASE HELP! 8 POINTS!! Find the value

Mathematics

1 answer:

Pepsi [2]3 years ago

5 0

Answer:

-sqrt(3)/2

Step-by-step explanation:

Use double angle identity for sin(2x)

sin(2x)=2sin(x)cos(x)

We are given sin(x)=-1/2 so we already have so far that:

sin(2x)=2(-1/2)cos(x)

sin(2x)=-1*cos(x)

We just need to find cos(x).

x is in the fourth quadrant so cosine will be positive there

knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.

So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2

You might be interested in

Solve each quadratic equation by completing the square. 6. x2 + 2x = 8 7. x2 - 6x = 16 8. x2 - 18x = 19 9. x2 + 3x = 3 10. x2 +

Andrei [34K]

Lets get started :)

These questions have asked us to solve by completing the square.
How do we? I have attached a picture, which will explain

6. x² + 2x = 8
→ b is the coefficient of x, which is 2
→ We take half of 2 and square it. Then, we add it to either side

x² + 2x $+ (\frac{2}{2} )^2 = 8 + ( \frac{2}{2})^2$
x² + 2x + 1 = 8 + 1
( x + 1 )( x + 1 ) = 9
( x + 1 )² = 9
$\sqrt{( x + 1 )^2} = \sqrt{9}$
x + 1 = + 3 or x + 1 = - 3
x = 2 or x = - 4

7. x² - 6x = 16

→ We do the same thing we did in the previous question

x² - 6x + $(\frac{6}{2})^2 = 16 + (\frac{6}{2})^2$
x² - 6x + 9 = 16 + 9
(x - 3)² = 25
$\sqrt{(x-3)^2} = \sqrt{25}$
x - 3 = + 5 or x - 3 = - 5
x = 8 or x = - 2

8. x² - 18x = 19

x² - 18x + $( \frac{18}{2} )^2 = 19 + ( \frac{18}{2})^2$
x² - 18x + 81 = 19 + 81
( x - 9 )( x - 9 ) = 100
( x - 9 )² = 100
$\sqrt{(x-9)^2} = \sqrt{100}$
x - 9 = + 10 or x - 9 = -10
x = 19 or x = - 1

9. x² + 3x = 3

x² + 3x + $( \frac{3}{2} )^2 = 3 + (\frac{3}{2} )$
$x^2 + 3x + \frac{9}{4} = 3 + \frac{9}{4}$
$x^{2} + 3x + \frac{9}{4} = \frac{21}{4}$
$(x^2 + \frac{3}{2} ) ( x^2 + \frac{3}{2} ) = \frac{21}{4}$
$( x^2 + \frac{3}{2} )^2 = \frac{21}{4}$
$\sqrt{ x^2 + \frac{3}{2} } = \sqrt{ \frac{21}{4} }$
x + $\frac{3}{2}$ = + $\frac{ \sqrt{21} }{2}$ or x + $\frac{3}{2} = - \frac{ \sqrt{21} }{2}$
x = $\frac{-3+ \sqrt{21} }{2}$ or x = $\frac{-3 - \sqrt{21}}{2}$

7 0

3 years ago

David's phone bill each month is $30. He is also charged $0.10 per GB of data he uses. If his phone bill in July was $42, how ma

Aleonysh [2.5K]

Answer:

120

Step-by-step explanation:

Okay so the equation would be like this
30 + 0.10g = P

g = GB of data used

P = Total Price

Let's work this out now!

So. If his total bill was $42 lets subtract the 30 that comes out every month automatically, now we are just left with 12, if each GB costs 0.10 then all you would do to find out how many GB he used is do 12/0.10 (which is really just 12*10) which will get you 120

Meaning that he used 120 GB

(That's a lot!)

7 0

2 years ago

Read 2 more answers

A line through the origin has a slope of 1 / 3. Carlos thinks the slope of a perpendicular line at the origin will be 3.

OLEGan [10]

Answer:

Carlos is incorrect.

Step-by-step explanation:

We have been given that a line through the origin has a slope of $\frac{1}{3}$ . Carlos thinks the slope of a perpendicular line at the origin will be 3.

We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.

The slope of the perpendicular line at the origin will be negative reciprocal of $\frac{1}{3}$ .

Let us find negative reciprocal of $\frac{1}{3}$ as:

$-\frac{1}{\frac{1}{3}}=-\frac{1\cdot 3}{1}=-3$

Since the slope of a perpendicular line at the origin is $-3$ , therefore, Carlos is incorrect.

4 0

3 years ago

The first term of an arithmetic sequence is 7 and the sixth term is 22. Find(a)the common difference;(2)(b)the twelfth term;(2)(

SVEN [57.7K]

d = 3 , a₁₂ = 40 and S $x_{100}$ = 7775

In an arithmetic sequence the nth term and sum to n terms are

<h3>• a $n$ = a₁ + (n-1)d</h3><h3>• S $_n$ = $\frac{n}{2}$ [2a + (n-1)d]</h3><h3>where d is the common difference</h3><h3>a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3</h3><h3>a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40</h3><h3>S₁₀₀ = $\frac{50}{2}$ [(2×7) +(99×3)</h3><h3> = 25(14 + 297) = 25(311)= 7775</h3>

7 0

2 years ago

A store has apples on sale for 28.00 for 8 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $112.0

mrs_skeptik [129]

Answer:

112 divided by 4 is 28. So 16 times 4 = 64. 64 divided by 5 is 12. 12 apples per 8 pounds. so 12 times 4 is 48 so your answer is 48

Step-by-step explanation:

7 0

3 years ago