Answer:
Option B. Cosec θ = –5/3
Option C. Cot θ = 4/3
Option D. Cos θ = –4/5
Step-by-step explanation:
From the question given above, the following data were obtained:
Tan θ = 3/4
θ is in 3rd quadrant
Recall
Tan θ = Opposite / Adjacent
Tan θ = 3/4 = Opposite / Adjacent
Thus,
Opposite = 3
Adjacent = 4
Next, we shall determine the Hypothenus. This can be obtained as follow:
Opposite = 3
Adjacent = 4
Hypothenus =?
Hypo² = Opp² + Adj²
Hypo² = 3² + 4²
Hypo² = 9 + 16
Hypo² = 25
Take the square root of both side
Hypo = √25
Hypothenus = 5
Recall:
In the 3rd quadant, only Tan is positive.
Therefore,
Hypothenus = –5
Finally, we shall determine Sine θ, Cos θ, Cot θ and Cosec θ to determine which option is correct. This can be obtained as follow:
Opposite = 3
Adjacent = 4
Hypothenus = –5
Sine θ = Opposite / Hypothenus
Sine θ = 3/–5
Sine θ = –3/5
Cos θ = Adjacent / Hypothenus
Cos θ = 4/–5
Cos θ = –4/5
Cot θ = 1/ Tan θ
Tan θ = 3/4
Cot θ = 1 ÷ 3/4
Invert
Cot θ = 1 × 4/3
Cot θ = 4/3
Cosec θ = 1/ Sine θ
Sine θ = –3/5
Cosec θ = 1 ÷ –3/5
Invert
Cosec θ = 1 × –5/3
Cosec θ = –5/3
SUMMARY
Sine θ = –3/5
Cos θ = –4/5
Tan θ = 3/4
Cot θ = 4/3
Cosec θ = –5/3
Therefore, option B, C and D gives the correct answer to the question.
Answer:
x = 3.4
Step-by-step explanation:
Step 1: Isolate <em>x</em>
0.5x = 1.7
Step 2: Divide both sides by 0.5
x = 3.4
And we have our final answer!
9514 1404 393
Answer:
- 326.6 square inches
- 3402 square feet
Step-by-step explanation:
The net will be a rectangle representing the lateral area. Its length will be 2π(4 in), the circumference of the box, and its height will be 9 in, the height of the box. On either side of that rectangle will be an 8-in diameter circle representing the ends of the box.
The total surface area is given by the formula ...
SA = 2πr(r +h)
For one box, the area is ...
SA = 2(3.14)(4 in)(4 in +9 in) ≈ 326.6 in² . . . . area of one box
__
There are 144 square inches in a square foot, so the area required for 1500 boxes is ...
(1500)(326.56 in²)/(144 in²/ft²) ≈ 3402 ft² . . . area of 1500 boxes
Answer:
A. 5
Step-by-step explanation:
It says that the sample is normally distributed, which means it follows the bell curve in terms of spreading. That means that 68% of the numbers are within two standard deviations, centered on the mean, one standard deviation below, one up.
That's confirmed by the fact that 1,360 numbers (exactly 68% of 2,000) are between 40 and 50. Since the mean is 45, that gives a spread of ± 1 standard deviation for 68% of the numbers.
One standard deviation goes from 40 to 45, another from 45 to 50.
So, the standard deviation of this sample is 5.
