Answer:
Radius = 11.85yd
Step-by-step explanation:
Volume of a Cone formula: V = πr²(h/3)
We know that;
V = Volume
r = radius
π = pi (this is a sign located on your calculator)
h = height
We are given that;
V = 4,410
r = unknown
h = 30
Let's substitute the values in:
=> V = πr²(h/3)
=> 4,410 = πr²(30/3)
=> 4,410 = πr²(10)
=> 4,410 / 10 = πr²
=> 441 = πr²
=> 441 / π = r²
=> 140.37 = r²
=> = r
=> 11.85 = r
Therefore, <u>the radius of the cone = 11.85yd</u>
Hope this helps!
<em>*To solve for a specified variable, you need to isolate that variable onto one side.</em>
<h3>11.</h3>Firstly, subtract 5r on both sides:
Lastly, divide both sides by 2 and <u>your answer will be </u>
First, subtract z on both sides of the equation:
Next, divide both sides by y and <u>your answer will be </u>
Firstly, multiply both sides by b:
Next, divide both sides by c and <u>your answer will be </u>
Answer:
18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144
b. The maximum height = 400 feet
c. Attached graph
19) The rocket will reach the maximum height after 4 seconds
20) The rocket hits the ground after 9 seconds
Step-by-step explanation:
* Lets study the rule of motion for an object with constant acceleration
# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time
and a is the acceleration of gravity
# The vertical distances h in x second is h(x) - h(0), where h(0)
is the initial height of the object above the ground
∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial
velocity, a is the acceleration of gravity (32 feet/second²) and x
is the time
18)a.
∵ The value of a = -32 ft/sec² ⇒ negative because the direction
of the motion
is upward
∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16
∴ h(x) = vx - 16x² + h(0)
∴ h(x) = -16x² + vx + h(0) ⇒ proved
* Find the height of the object after x seconds from the ground
∵ h(0) = 144 and v = 128 ft/sec
∴ h(x) = -16x² + 128x + 144
b.
* At the maximum height h'(x) = 0
∵ h'(x) = -32x + 128
∴ -32x + 128 = 0 ⇒ subtract 128 from both sides
∴ -32x = -128 ⇒ ÷ -32
∴ x = 4 seconds
- The time for the maximum height = 4 seconds
- Substitute this value of x in the equation of h(x)
∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet
c. Attached graph
19)
- The object will reach the maximum height after 4 seconds
20)
- When the rocket hits the ground h(x) = 0
∵ h(x) = -16x² + 128x + 144
∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16
∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x
∵ x² - 8x - 9 = 0
∴ (x - 9)( x + 1) = 0
∴ x - 9 = 0 OR x + 1 = 0
∴ x = 9 OR x = -1
- We will rejected -1 because there is no -ve value for the time
* The time for the object to hit the ground is 9 seconds
