Answer:
Hello,
Step-by-step explanation:
![I=\dfrac{Area}{4} =\int\limits^4_0 {\sqrt{16-x^2} } \, dx \\\\Let\ say\ x=4*sin(t),\ dx=4*cos(t) dt\\\\\displaystyle I=\int\limits^\frac{\pi }{2} _0 {4*\sqrt{1-sin^2(t)} }*4*cos(t) \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {cos^2(t)} \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {\frac{1-cos(2t)}{2}} \, dt \\\\=8*[t]^\frac{\pi }{2} _0-[\frac{sin(2t)}{2} ]^\frac{\pi }{2} _0\\\\=4\pi -0\\\\=4\pi\\\\\boxed{Area=4*I=16\pi}\\](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7BArea%7D%7B4%7D%20%3D%5Cint%5Climits%5E4_0%20%7B%5Csqrt%7B16-x%5E2%7D%20%7D%20%5C%2C%20dx%20%5C%5C%5C%5CLet%5C%20say%5C%20x%3D4%2Asin%28t%29%2C%5C%20dx%3D4%2Acos%28t%29%20dt%5C%5C%5C%5C%5Cdisplaystyle%20I%3D%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20_0%20%7B4%2A%5Csqrt%7B1-sin%5E2%28t%29%7D%20%7D%2A4%2Acos%28t%29%20%5C%2C%20dt%20%5C%5C%5C%5C%3D16%2A%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20_0%20%7Bcos%5E2%28t%29%7D%20%5C%2C%20dt%20%5C%5C%5C%5C%3D16%2A%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20_0%20%7B%5Cfrac%7B1-cos%282t%29%7D%7B2%7D%7D%20%5C%2C%20dt%20%5C%5C%5C%5C%3D8%2A%5Bt%5D%5E%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20_0-%5B%5Cfrac%7Bsin%282t%29%7D%7B2%7D%20%5D%5E%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20_0%5C%5C%5C%5C%3D4%5Cpi%20-0%5C%5C%5C%5C%3D4%5Cpi%5C%5C%5C%5C%5Cboxed%7BArea%3D4%2AI%3D16%5Cpi%7D%5C%5C)
Answer:
70 pounds
Step-by-step explanation:
3 boxes= 105 pounds
2boxes= x pounds
Cross Multiply
3*x=105 *2
3x=210
3x/3=210/3
x=70 pounds
Answer:
The fabric needs 196.4 ft²
Step-by-step explanation:
∵ The tent formed formed from 4 faces
two equilateral triangles with side length 7 ft
two rectangles with dimensions 11 ft and 7 ft
∵ Area equilateral Δ = 1/4 S²√3
∵ Area rectangle = L × W
∴ The area of the prism = 2 × 1/4 × (7)²√3 + 2 × 7 × 11
= 196.4 ft²
Note:
If you find the area of the triangle by the rule 1/2 × base × height
∴ Area Δ = 1/2 × (7) × 6 = 21 ft²
∴ Area tent = 2 × 21 + 2 × 77 = 196 ft²
Two answer very closed
Answer:
The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 9 years is $232.56.
Step-by-step explanation:
Given
- Total accrued Amount A = 400.00 (Let say $)
- Interest rate r = 8% = 0.08
To determine
Principle P = ?
Using the formula
P = A / (1 + rt)
substituting A = 400.00, t = 9 and r = 0.08 in the formula
P = 400 / ( 1 + (0.08 × 9))
P = $232.56
Therefore, the principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 9 years is $232.56.
The answer is "while".
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