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3 years ago

What is the value of y in the product of powers below?

Mathematics

1 answer:

lilavasa [31]3 years ago

4 0

Answer:

y = 0

Step-by-step explanation:

8^(3-5) = 8^-2

in this operation we have already the result, so y = 0.

In fact 8^0 = 1 and a number multiplied by i1 give the number itself

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Given that sec (x) = 2 and cosec (x) is negative,

weeeeeb [17]

Answer:

i) sin(2x) = $-\frac{\sqrt{3}}{2}$

ii) cot(x+360) = $-\frac{\sqrt{3}}{3}$

iii) sin(x-180) = $\frac{\sqrt{3}}{2}$

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = $\frac{1}{2}$

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

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

First we need to find the value of sin(x). According to Pythagorean identity:

$sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}$

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

$sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}$

So,

$sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}$

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

$cot(x) = \frac{cos(x)}{sin(x)}\\$

Using the values, we get:

$cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}$

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = $-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}$

6 0

3 years ago

Answer and please show work!

snow_lady [41]

Answer:

Step-by-step explanation:

If we consider half the first purchase, it is

2 used + 1 new = $42

And the second purchase is

6 used + 1 new = $78

Subtracting the first of these equations from the second, we get ...

4 used = $(78 -42) = $36

used = $9 . . . . . . . . . . . . . . divide by 4

Then we can find the price of a new game from ...

new = $42 - 2 used = $42 -2·9 = $24

___

The number of used games Janet can purchase on her budget is ...

($120 -3·$24)/$9 = $48/$9 = 5 1/3 ≈ 5

Janet can purchase 5 used and 3 new video games for $120. (and have $3 left)

6 0

3 years ago

A tabletop in the shape of a trapazoid have an area of 6550 square centimeters. its longer base measures 115 centimeters, and th

Arturiano [62]

A= 1/2 h ( sum of bases) SUBSTITUTE 6550= 1/2h (115+85) 6550=1/2h (200) 6550= 100h 65.5= h height is 65.5 cm Hope this helps

3 0

3 years ago

|x −4| if x >4<br> Please answer quick will award brainliest!

IRINA_888 [86]

Answer:

x = −4

Step-by-step explanation:

Add x to both sides of the equation. x + 4 + x = − 4 Add x and x . 2 x + 4 = −4

Subtract 4 from both sides of the equation. 2 x = −4 − 4 Subtract 4 from - 4. 2x = −8

Divide each term in 2x = −8 by 2. 2x/2 = −8/2

Cancel the common factor. 2x/ 2 = −8/2 Divide x by 1. x = −8/2

Divide −8 by 2. x = −4

3 0

3 years ago

Write a rule for the linear function.

777dan777 [17]

The equation is...
y=-7/2-1

4 0

3 years ago