The most reasonable answer would be H.
Answer:
1661.06 cm²
Step-by-step explanation:
From the question given above, the following data were obtained:
Radius (r) = 11.5 cm
Size of synthetic leather needed =?
To know how many square centimetres of synthetic leather needed to cover the ball, we shall determine the area of the ball. This can be obtained as follow:
Radius (r) = 11.5 cm
Pi (π) = 3.14
Area of ball =?
The shape of a ball is spherical in nature. Thus, we shall apply the formula for calculating the area of a sphere. This is illustrated below:
A = 4πr²
A = 4 × 3.14 × 11.5²
A = 4× 3.14 × 132.25
A = 1661.06 cm²
Thus, 1661.06 cm² of synthetic leather needed to cover the ball.
<h3>
Answer: B. (3,-2)</h3>
There are two ways to confirm this is the answer. The first is to note that (3,-2) is on the boundary, so it is part of the solution set. This only works if the boundary line is a solid line (as opposed to a dashed or dotted line).
The second way is to plug (x,y) = (3,-2) into the given inequality to find that
which is a true statement. So this confirms that (3,-2) is in the solution set of the inequality.
Step-by-step explanation:
a. we simply subtract 3. from 2.
x + 2y + z = 15
- -3x + y + z = 2
--------------------------
4x + y 0 = 13
b. we multiply 3. by 3 and then subtract from 1.
2x - 4y + 3z = -7
- -9x + 3y + 3z = 6
-----------------------------
11x - 7y 0 = -13
c. we multiply the result of a. by 7, and then simply add a. and b., because the y terms have different signs already.
28x + 7y = 91
+ 11x - 7y = -13
--------------------------
39x 0 = 78
39x = 78
x = 2
d. we use this x = 2 in the result of a.
4×2 + y = 13
8 + y = 13
y = 5
e. using x = 2 and y = 5 in 2.
2 + 2×5 + z = 15
2 + 10 + z = 15
12 + z = 15
z = 3
the solution is therefore (2, 5, 3).
