Answer:
cos 2Ф = - 161/289 , tan 2Ф = - 240/161
Step-by-step explanation:
* Lets explain how to solve the problem
∵ cos Ф = - 8/17
∵ Ф lies in the 3rd quadrant
- In the 3rd quadrant sin and cos are negative values, but tan is
a positive value
∵ sin²Ф + cos²Ф = 1
∴ sin²Ф + (-8/17)² = 1
∴ sin²Ф + 64/289 = 1
- Subtract 64/289 from both sides
∴ sin²Ф = 225/289 ⇒ take √ for both sides
∴ sin Ф = ± 15/17
∵ Ф lies in the 3rd quadrant
∴ sin Ф = -15/17
∵ cos 2Ф = 2cos²Ф - 1 ⇒ the rule of the double angle
∵ cos Ф = - 8/17
∴ cos 2Ф = 2(-8/17)² - 1 = (128/289) - 1 = - 161/289
* cos 2Ф = - 161/289
∵ tan 2Ф = sin 2Ф/cos 2Ф
∵ sin 2Ф = 2 sin Ф × cos Ф
∵ sin Ф = - 15/17 and cos Ф = - 8/17
∴ sin 2Ф = 2 × (-15/17) × (-8/17) = 240/289
∵ cos 2Ф = - 161/289
∴ tan 2Ф = (240/289)/(-161/289) = - 240/161
* tan 2Ф = - 240/161
Total surface area of the triangular prism is 81.6 square m.
Step-by-step explanation:
= 3 × 2.6 + 8.2 ×9
= 7.8 + 73.8
= 81.6
- Total surface area of the triangular prism is 81.6 square m.
Answer:
1.5
Step-by-step explanation:
Let the number be denoted as "a"
-1 (2a + 3) = 2 (-4a + 3)
-2a - 3 = -8a + 6
-2a + 8a = 6 + 3
6a = 9
a = 9/6
a = 3/2 = 1.5
Step-by-step explanation:
1 pound is 16 ounces
2 pounds are 16 x2 which is 32 ounces
she needs 20 ounces
32 -20 is 12
she will have 12 ounces left
