Answer:
The answer is
<h2>
</h2>
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The original line is 3x + 5y = 11
We must first write the equation in the general equation above
So we have
5y = - 3x + 11
Divide both sides by 5
<h3>
</h3>
Comparing with the general equation above
Slope = - 3/5
Since the lines are parallel their slope are also the same
Slope of parallel line = - 3/5
So the equation of the line using point
(15, 4) and slope - 3/5 is
<h3>
</h3>
We have the final answer as
<h3>
</h3>
Hope this helps you
Answer:
π/10
Step-by-step explanation:
When we rotate the region about the y-axis, we get something that looks like a volcano, or a bundt cake. Instead of slicing this into flat washers, we'll slice it in concentric rings, or "shells".
Each shell has a radius x, a thickness dx, and a height y. The volume of an individual shell is:
dV = 2π r h t
dV = 2π x y dx
Since y = x² − x³:
dV = 2π x (x² − x³) dx
dV = 2π (x³ − x⁴) dx
The total volume is the sum of all the shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π (x³ − x⁴) dx
V = 2π (¼ x⁴ − ⅕ x⁵) |₀¹
V = 2π (¼ − ⅕)
V = π/10
Answer:
if it took her 14 hours to make a 30-inch scarf, we can assume it will take her to double that time to make a 60-inch scarf. 28 hours is double of 14, if she only knits one hour every day it will take her 4 weeks, 28 days is equal to exactly 4 weeks 28/7=4 weeks
the surface area of the sphere is π/4 cm^3
<h3>How to determine the surface area</h3>
It is important to know the formula for surface area and volume of a sphere
Surface area = 
Volume = 
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
Pi cancels out and we have cross multiply to get the radius
Make r the subject of the formula
![r = \sqrt[3]{\frac{768}{12} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B768%7D%7B12%7D%20%7D)
![r = \sqrt[3]{64}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B64%7D)
r = 4
Let's substitute to find the surface area
Surface area = 
Surface area = π/4
Surface area = π/4 cm^3
Thus, the surface area of the sphere is π/4 cm^3
Learn more about a sphere here:
brainly.com/question/10171109
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