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arlik [135]
3 years ago
7

Surface Area Homework (Help)

Mathematics
1 answer:
sammy [17]3 years ago
5 0
38.2

sorry if it’s wrong
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Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side
maria [59]

Answer:

cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = -\frac{1}{3}

cos(b) = -\frac{1}{4}

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = -\sqrt{1-(-\frac{1}{3})^2} [Since, sin(a) = \sqrt{(1-\text{cos}^2a)}]

         = -\sqrt{\frac{8}{9}}

         = -\frac{2\sqrt{2}}{3}

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be  negative.

sin(b) = -\sqrt{1-(-\frac{1}{4})^2}

         = -\sqrt{\frac{15}{16}}

         = -\frac{\sqrt{15}}{4}

By substituting these values in the identity,

cos(a + b) = (-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})

                = \frac{1}{12}-\frac{\sqrt{120}}{12}

                = \frac{1}{12}(1-\sqrt{120})

                = \frac{1}{12}(1-2\sqrt{30})

Therefore, cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

5 0
3 years ago
A sofa regularly sells for 680. The sale price is 639.20. Find the percent decrease of the sale price from the regular price.
elena55 [62]
There is a 6% decrease as 639.20 divided 680 is 0.94. Meaning 6% decrease.
6 0
3 years ago
<img src="https://tex.z-dn.net/?f=6%20%5Cfrac%7B2%7D%7B5%7D%20%20-%201%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5C%5C%205%20%5Cfra
lara31 [8.8K]

if i know the anwser,you must gave mini love

8 0
3 years ago
( 8n - 3n^4 + 10n ^2 ) - ( 3n^2 + 11n ^4 - 7)
DanielleElmas [232]

Answer:

-14n^4 + 7n^2 + 8n + 7

Step-by-step explanation:

( 8n - 3n^4 + 10n^2 ) - ( 3n^2 + 11n^4 - 7)

8n - 3n^4 + 10n^2 - 3n^2 - 11n^4 + 7

- 14n^4 + 7n^2 + 8n + 7

3 0
2 years ago
Read 2 more answers
The sum of the speeds of two trains is 724.8 miles per hour. If the speed of the first train is 9.2 mph faster than that of the
olasank [31]

Answer:

The slower train's speed is 359.8 mph

x+5.2mph=359.8mph+5.2mph=365 mph ANSWER 2: The faster trains speed is 365 mph.

CHECK:

359.8 mph + 365 mph = 724.8 mph

724.8 mph = 724.8 mph

Step-by-step explanation:

8 0
3 years ago
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