Answer: 829 3/4 or 829 75/100
Step-by-step explanation:
Answer:
40 ft²
Step-by-step explanation:
Let the length of the original rectangle be L and original Breadth be B
it is given that the original area is 5/8 ft²
i.e.
Original Length x Original Breadth = Original Area, or,
LB = 5/8 ft² ------------------(1)
Given that the dilation factor is 8,
Hence,
New Length = 8L and New Breadth = 8B
THerefore,
New Area = 8L x 8B
= 64 LB (from (1) above , we know that LB = 5/8 ft², substitute into expression)
= 64 (5/8)
= 40 ft²
Answer:
B. 2010.62 ft³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . . where r is the radius and h is the height
Filling in the numbers and doing the arithmetic, we get ...
V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³
The volume of the cylinder is about 2010.62 ft³.
Answer:
x = 10
Step-by-step explanation:
Solve for x:
-8 (8 - x) = (4 (x + 10))/5
Multiply both sides by 5:
-8×5 (8 - x) = (5×4 (x + 10))/5
(5×4 (x + 10))/5 = 5/5×4 (x + 10) = 4 (x + 10):
-8×5 (8 - x) = 4 (x + 10)
5 (-8) = -40:
-40 (8 - x) = 4 (x + 10)
Expand out terms of the left hand side:
40 x - 320 = 4 (x + 10)
Expand out terms of the right hand side:
40 x - 320 = 4 x + 40
Subtract 4 x from both sides:
(40 x - 4 x) - 320 = (4 x - 4 x) + 40
40 x - 4 x = 36 x:
36 x - 320 = (4 x - 4 x) + 40
4 x - 4 x = 0:
36 x - 320 = 40
Add 320 to both sides:
36 x + (320 - 320) = 320 + 40
320 - 320 = 0:
36 x = 40 + 320
40 + 320 = 360:
36 x = 360
Divide both sides of 36 x = 360 by 36:
(36 x)/36 = 360/36
36/36 = 1:
x = 360/36
The gcd of 360 and 36 is 36, so 360/36 = (36×10)/(36×1) = 36/36×10 = 10:
Answer: x = 10
The answer is
round cake - 82.42 in²
rectangular cake - 114 in²
Round cake:
d = 7 in
r = d/2 = 7 in / 2 = 3.5 in
h = 2 in
The surface are of a cylinder is:
A = 2πr² + 2πrh
The surface are of the round cake (which is actually a cylindrical cake) excluding the bottom is:
A = 2πr² + 2πrh - πr²
A = πr² + 2πrh
A = 3.14 * 3.5² + 2 * 3.14 * 3.5 * 2
= 38.46 + 43.96
= 82.42 in²
Rectangular cake:
w = 6 in
l = 9 in
h = 2 in
The surface are of a rectangle is:
A = 2wl + 2wh + 2lh
The surface are of the rectangular cake excluding the bottom is:
A = 2wl + 2wh + 2lh - wl
A = wl + 2wh + 2lh
A = 6 * 9 + 2 * 6 * 2 + 2 * 9 * 2
= 54 + 24 + 36
= 114 in²
Step-by-step explanation: This answer is not mine but JcAlmighty’s so all credits go to them.
