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Reil [10]
3 years ago
8

Write each percent increase or decrease as a percentage of the initial amount.

Mathematics
2 answers:
True [87]3 years ago
7 0

Answer:

?

Step-by-step explanation:

olya-2409 [2.1K]3 years ago
5 0

Answer:

18%

Step-by-step explanation:

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An object is launched from a launching pad 144 ft. above the ground at a velocity of 128ft/sec. what is the maximum height reach
ollegr [7]

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

8 0
3 years ago
Solve for x<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B2%7D%20%20%2B%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%2010" id=
Degger [83]

Answer:

x = 18.5

Step-by-step explanation:

Given

\frac{x}{2} + \frac{3}{4} = 10

Multiply through by 4 to clear the fractions

2x + 3 = 40 ( subtract 3 from both sides )

2x = 37 ( divide both sides by 2 )

x = \frac{37}{2} = 18.5

6 0
3 years ago
Read 2 more answers
How many times can 9 go into 82
Assoli18 [71]
The answer is 9.1.
3 0
3 years ago
Two numbers are randomly selected on a number line numbered 1 through 9. The same number can be chosen twice. What is the probab
Effectus [21]
(3)/(8+7+6+5+4+3+2+1)(no repitition)
=3/36
=1/12
4 0
3 years ago
Read 2 more answers
Find NP from the rectangle
serious [3.7K]

The diagonals of a rectangle are equal and bisect each other.

NQ= 2×5 =10

Using Pythagoras theoram,

PQ²+NP²=NQ²

4²+ NP²= 10²

NP²= 100-16

NP²= 84

NP =√84

<h3>NP=2√21 = 9.2</h3>

5 0
2 years ago
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