Answer:
T(x, y) = (x - 5, y - 6)
Step-by-step explanation:
The transformation T is a translation that creates an image P' of original point P by adding 5 to the x-coordinate and 6 to the y-coordinate of the original point P.
Now you want to transform point P' into point P, so you are undoing the first transformation. You need to do the opposite of what the transformation above does. You need to subtract 5 from the x-coordinate and subtract 6 from the y-coordinate.
Answer: T(x, y) = (x - 5, y - 6)
We'll use the Pythagorean Theorem (otherwise known as the Distance Formula):
Going from Q to P, x increases by 1 and y increases by 7. Thus, the component form of QP is <1,7>, and the magnitude of this vector is √(1^2+7^2) = 5√2.
Note: this is equivalent to <1, 7>, square root of 50.
Answer:
b 4
Step-by-step explanation:
Answer: The volume of the cylinder is 640π cm³
Step-by-step explanation:
The formula of the surface area of a cylinder is SA = 2πrh + 2πr², where r is the radius of its base and h is its height
The formula of the volume of a cylinder is V = πr²h
Let us use the formula of the surface area to find the height of the cylinder, then use the formula of the volume to find its volume
∵ The surface area of a cylinder is 288π cm²
∵ Its radius is 8 cm
∵ SA = 2πrh + 2πr²
- Substitute the SA by 288π and r by 8 in the formula
∴ 288π = 2π(8)h + 2π(8)²
∴ 288π = 16πh + 128π
- Subtract 128π from both sides
∴ 160π = 16πh
- Divide both sides by 16π
∴ 10 = h
∴ The height of the cylinder is 10 cm
Now let us find the volume of the cylinder
∵ V = πr²h
- Substitute r by 8 and h by 10
∴ V = π(8)²(10)
∴ V = π(64)(10)
∴ V = 640π
The volume of the cylinder is 640π cm³
Answer: 32/9
Step-by-step explanation:
-7/9 + 16/9=1
16*2=32
32/9
