The radius of a circle is 1 foot. What is the length of a 45 degree arc
1 answer:
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This question is incomplete, the complete question is;
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis
Answer:
V = π (512/15)
Step-by-step explanation:
Given that;
region of rotation
y² = 2x, x = 2y
Region is rotated about y-axis as shown in the image
for the point of intersection,
y²/2 = 2y
y² - 4y = 0
y(y-4) = 0
∴ y = 0, y = 4
so the region lies in 0 ≤ y ≤ 4
Now cross section area of washer is
A(y) = π(outer radius)² = π(inner radius)²
A(y) = π(2y)² - π(y²/2)²
A(y) = π(4y²) - π(y⁴/4)
A(y) = π(4y² - (y⁴/4))
now volume of the solid of revolution is
V = ⁴∫₀ A(y) dy
V = ⁴∫₀ π(4y² - (y⁴/4))dy
V = π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }
V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }
V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }
V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }
V = π { 256/3 - 1024/20 }
V = π { (5120 - 3072) / 60 }
V = π (512/15)
Answer:
The equation of line is given as
Step-by-step explanation:
Point on the line given :
We can find the slope of the line first from the given points.
Slope= Undefined.
The slope of the line is undefined which means that the line is parallel to y-axis.
From the points known to us we can tell that the line passes through
∴ The equation of line is given as
Answer:
<h3>33.3%</h3>Step-by-step explanation:
Using the formula for calculating simple interest as shown;
Simple Interest = Principal * Rate *Time/100
Principal = Cost of tablet = $1500
Interest after one year = $1500-$1000 = $500
Time = 1year
Substituting this values into the formula;
The interest rate that her parents assumed is 33.3%