Question:
Karina has recently begun kickboxing and purchased training equipment as modeled in the diagram below. The cylindrical base is 15 inches tall with a diameter of 22 inches.
Karina wants to fill the base so that it is 85% full. What is the volume of the base that she is filling? (Find 85% of the volume).
Answer:
Step-by-step explanation:
Given
-- height
-- diameter
Required
85% of the volume
First, calculate the radius
The volume (V) is then calculated using:
85% of the volume is:
-x^2 + 4 = 2x + 1
-x^2 - 2x + 4 - 1 = 0
-x^2 - 2x + 3 = 0
(x + 3)(-x + 1)= 0
x + 3 = 0 -x + 1 = 0
x = -3 -x = -1
x = 1
so x = -3 and x = 1
It is 3 x -5 = -15 (x is times )
Answer: The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
Let x represent the number of 3-point questions.
Let y represent the number of 5-point questions.
The maths test consists of 24 questions. This means that
x + y = 24
Each question is worth either 3 points or 5 and the test is worth 100 points. This means that
3x + 5y = 100 - - - - - - - - - - -1
Substituting x = 24 - y into equation 1, it becomes
3(24 - y) + 5y = 100
72 - 3y + 5y = 100
- 3y + 5y = 100 - 72
2y = 28
y = 28/2 = 14
Substituting y = 14 into x = 24 - y , it becomes
x = 24 - 14 = 10
