So,
These are actually special cases.
x = -6
No matter what value we substitute for y, x will always be -6.
These are some solutions to it:
(-6, 0)
(-6, -2)
(-6, 50)
Now, we know that:

But the run is zero, because the line is vertical. And dividing by zero is not allowed. Therefore, the slope of the line x = -6 is undefined.
y = 6
This is basically the same type as the previous one, with one exception.
Some solutions:
(0, 6)
(-47, 6)
(59, 6)
No matter what value we substitute for x, y will always be 6.
Remembering what the slope is equal to, we quickly see that since the rise is zero, and the denominator is infinite, we can conclude that the slope is zero.
Step-by-step explanation:
Area of first triangle = 1/2bh
the base of the triangle = the radius of the semi-circle = 2yd
height = 5yd
Area = 1/2(5yd)(2yd)
A = 5yd(yd)
A = 5y^2d^2 squared units.
since the second triangle also has the same dimensions as the first triangle
hence:
Area of the second triangle = 5y^2d^2 squared units.
Area of semi-circle = πr^2
Area = π(2yd)^2
A = 4πy^2d^2 squared units
<h3>
Answer: Choice A) 252 in^2</h3>
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Explanation:
Refer to the diagram below.
The red rectangle is 6 inches by 12 inches, so its area is 6*12 = 72 square inches. There are two of these rectangles (one on top, one on the bottom). That accounts for 2*72 = 144 square inches so far.
The purple rectangles are 3 inches by 12 inches, yielding an area of 3*12 = 36 square inches each. That's another 2*36 = 72 square inches when we account for the front and back purple rectangles.
The green rectangles are 6 inches by 3 inches. Each green rectangle is 6*3 = 18 square inches. Having two of them means we'll add on 2*18 = 36 square inches.
Overall, the entire surface area is the sum of all the areas we calculated: 144+72+36 = 252 square inches, which is choice A
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Alternative Method:
- L = 12 = length
- W = 6 = width
- H = 3 = height
SA = surface area of the rectangular prism
SA = 2*(L*W + L*H + W*H)
SA = 2*(12*6 + 12*3 + 6*3)
SA = 2*(72 + 36 + 18)
SA = 2*(126)
SA = 252 in^2
So we get the same answer either way
The volume is V=LxWxH. The length x Width is just the area, A, of the bottom (also of the top) So you could also write V=AxH, that is volume is
area x height. Since we know V equals 972 and A equals 81 we can solve for H:
V=AxH
972=81H
972/81=H
H=12cm
Let’s take Sanku as x.
if Madhu is 3 times his age, then he is 3x.
the difference in their age is 14, so
3x - x = 14
2x = 14
x=7
Sanku is 7
Madhu is 21