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vfiekz [6]
2 years ago
10

1. What is the volume for the following rectangular prism?

Mathematics
1 answer:
____ [38]2 years ago
8 0

Answer:

2. c) 1050 mm³

3. c) 8 yards.

Step-by-step explanation:

Given the following data;

Length = 25mm

Width = 7 mm

Height = 6 mm

To find the volume of the rectangular prism;

Volume of rectangular prism = base area * height

First of all, we would determine the base area;

Base area = length * width

Base area = 25 * 7

Base area = 175 mm²

Next, we find the volume;

Volume of rectangular prism = 175 * 6

Volume of rectangular prism = 1050 mm³

Question 2.

Given the following data;

Length = 9 yards

Width = 7.5 yards

Volume = 540 cubic yards

To find the height of the rectangular prism, x;

Volume of rectangular prism = length * width * height

540 = 9 * 7.5 * x

540 = 67.5x

x = 540/67.5

Height, x = 8 yards

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Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
nikitadnepr [17]

Answer:

* sin Ф = -15/17     * cos Ф = 8/17      * tan Ф = -15/8

* csc Ф = -17/15    * sec Ф = 17/8      * cot Ф = -8/15

Step-by-step explanation:

Lets revise the trigonometric function of angle Ф

- Angle θ is in standard position

- Point  (8, -15) is on the terminal ray of angle θ

- That means the terminal is the hypotenuse of a right triangle x and y

  are its legs

∵ x-coordinate is positive and y-coordinate is negative

∴ angle Ф lies in the 4th quadrant

- The opposite side of angle Ф is the y-coordinate of the point on the

  terminal ray of angle Ф and the adjacent side to angle Ф is the

  x-coordinate of that point

∵ The length of the hypotenuse (h) = √(x² + y²)

∴ h = √[(8)² + (-15)²] = √[64 + 225] = √[289] = 17

∴ The length of the hypotenuse is 17

- Lets find sin Ф

∵ sin Ф = opposite/hypotenuse

∵ The opposite is y = -15

∵ The hypotenuse = 17

∴ sin Ф = -15/17

- Lets find cos Ф

∵ cos Ф = adjacent/hypotenuse

∵ The adjacent is x = 8

∵ The hypotenuse = 17

∴ cos Ф = 8/17

- Lets find tan Ф

∵ tan Ф = opposite/adjacent

∵ The opposite is y = -15

∵ The adjacent = 8

∴ tan Ф = -15/8

- Remember csc Ф is the reciprocal of sin Ф

∵ csc Ф = 1/sin Ф

∵ sin Ф = -15/17

∴ csc Ф = -17/15

- Remember sec Ф is the reciprocal of cos Ф

∵ sec Ф = 1/ cos Ф

∵ cos Ф = 8/17

∴ sec Ф = 17/8

- Remember cot Ф is the reciprocal of tan Ф

∵ cot Ф = 1/tan Ф

∵ tan Ф = -15/8

∴ cot Ф = -8/15

5 0
3 years ago
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