The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm
Answer:
x = 14/9
Step-by-step explanation:
70 - 8x = 56 + x
- 8x - x = 56 - 70
- 9x = - 14
- x = - 14/9
x = 14/9
Answer:
The rate of decrease is: 
Step-by-step explanation:
Given
---- We used minus because the rate is decreasing
Required
Rate of decrease when:
The volume of the cube is:
Differentiate
Make dV the subject
Divide both sides by dt
Given that: and
<em>Hence, the rate of decrease is: 43.2mm^3/min</em>
Answer:
x = 1
Step-by-step explanation:
Given in the question the equation
y = -x² + 2x - 1
To find the x-intercept, substitute in 0 for y
0 = -x² + 2x - 1
To find value of x use quadratic equation
x = -b ± √b²-4ac / 2a
here a = -1
b = 2
c = -1
x1 = -2 + √2²-4(-1)(-1) / 2(-1)
= -2 + 0 / -2
= -2 / -2
= 1
x2 = -2 - √2²-4(-1)(-1) / 2(-1)
= -2 - 0 / -2
= -2 / -2
= 1
Answer:
Step-by-step explanation:
This is a question that uses the Pythagorean Theorem.
a = 35 feet
b = x which is the height of the tree.
c = 3*x + 1 so we are trying to find x. Substitute into a b and c
a^2 + b^2 = c^2
35^2 + x^2 = (3x + 1)^2
35^2 + x^2 = 9x^2 + 6x + 1 Subtract x^2 from both sides.
35^2 = 8x^2 + 6x + 1 Subtract 35^2 from both sides.
0 = 8x^2 + 6x + 1 - 35^2
0 = 8x^2 + 6x - 1224
Does this factor?
(x + 12.75)(x - 12)
x - 12 = 0 is the only value that works.
x = 12
The tree is 12 feet high.
Note: I used the quadratic formula to solve this.
