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# 24 Problems : Word Problems, Simplify, Area, LCM, Solve for X and Hypotenuse

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Divide
(12a squared - 25a -7 divided by (3a-7)
(x cubed - 6x squared + 7x -2 divided by (x-1)

A circle has a radius of 10 inches. Find the increase in area that occurs when the radius is increased by 2 in. Round to the nearest hundredth.

An object is released from the top of an building 320 ft high. The initial velocity is 16ft/s. How many seconds later will the object hit the ground?

How many consecutive natural numbers beginning with 1 will give the sum of 120?

Write each fraction in terms of the LCM of the denominators

x-3 divided by 3x squared + 4x-4 ; 2 divided by x + 2
2x divided by 10 + 3x-x squared; x + 2 divided by x squared -8x + 15

Simplify
3 over 2x + 1 minus 3 divided by 2 minus 4 x over 2x + 1

2 plus 5 over x minus 12 over x squared divided by 4 minus 4 over x minus 3 over x squared

1+ 4 over x + 4 over x squared divided by 1- 2 over x - 8 over x squared

1 minus 2x -2 over 3x -1 divided by x minus 4 over 3x -1

x+3 minus 18 over 2x +1 divided by x minus 6 over 2x +1

Solve the formula for the variable given

C= 5 over 9 (F-32);F (temperature conversion)
T=fm-gm;m (engineering)
a=S-Sr; S 9mathematics)

Solve. round to the nearest hundredth

The two legs of aright triangle measures 8in and 4 in. Find the length of the hypotenuse.

Marta leaves a dock in her sailboat and sails 2.5 mi due east. She then tacks and sails 4 mi due north. The walkie talkie Marta has on board has a range of 5 mi. Will she be able to call a friend on the dock from her location using the walkie talkie?

How far would a submarine periscope have to be above the water for the lookout to locate a ship 7 mi away? The equation for the distance in miles that the lookout can see is d+ square root 1.5 h, where h is the height in feet above the surface of the water.

The speed of a child riding a merry go round is given by the equation v= square root 12r, where v is the speed in feet per second and r is the distance in feet from the center of the merry go round to the rider. If a child is moving 15 ft/s, how far is the child from the center of the merry go round?

Find the length of a pendulum that makes one swing in 2s. The equation for the time of one swing is T=2 pi square root L over 32, where T is the time in seconds and L is the length in feet.

A commuter plane leaves an airport traveling due south at 400mph. Another plane leaving at the same time travels due east at 300mph. Find the distance between the two planes after 2 h.

A stone is dropped into a mine shaft and hits the bottom 3.5 s later. How deep is the mine shaft? The equation for the distance an object falls in T seconds is T=square root d over 16, where d is the distance in feet.

A model rocket is launched with an initial velocity of 200 ft/s. The height, h, of the rocket t seconds after launch is given by h= -16t squared plus 200t. How many seconds after the launch will the rocket be 300 ft above the ground. Round to the nearest hundredth.

In a slow pitch softball game, the height of the ball thrown can be modeled by the equation h= -16t squared plus 24t plus 4, where h is the height of the ball in feet, and t is the time, in seconds, since it was released by the pitcher. If the batter hits the ball when it is 2 ft off the ground, how many seconds has the ball been in the air? Round to the nearest hundredth.

The hang time of a football that is kicked is given by s= -16t squared plus 88t plu 1, where s is the height. in feet, of the football t seconds after leaving the kicker's foot. What is the hang time of a kickoff that hits the ground without being caught? Round to the nearest tenth.

https://brainmass.com/math/basic-algebra/word-problems-simplify-area-lcm-solve-hypotenuse-43098

#### Solution Preview

Please see the attached file for the complete solution.

Divide
(12a squared - 25a -7 divided by (3a-7)
Solution. Since , we have

(x cubed - 6x sqyared + 7x -2 divided by (x-1)
Solution. Since , we have

A circle has a radius of 10 inches. Find the increase in area that occurs when the radius is increased by 2 in. Round to the nearest hundredth.

Solution. We know that r=10inches, . So, the increase in area is

An object is released from the top of an building 320 ft high. The initial velocity is 16ft/s. How many seconds later will the object hit the ground?
Solution. Assume that the acceleration of gravity is . Now we need to convert feet to meters, we know that 1m=3.28(feet). So, the initial velocity is v0=16ft/s is
4.878m/s. h=320ft=97.56(m). Use a formula

We have

So,

So,

So, 194.62 seconds later the object will hit the ground

How many consecutive natural numbers beginning with 1 will give the sum of 120?

Solution. We know that . So, if , then

So,
(n+16)(n-15)=0
So, n=15 (since n>0).

So, 15 consecutive natural numbers beginning with 1 will give the sum of 120

Write each fraction in terms of the LCM of the denominators

x-3 divided by 3x squared + 4x-4 ; 2 divided by x + 2

Solution.
and
Since , the LCM of the denominators is .
So,
=
and

2x ...

#### Solution Summary

24 problems regarding Word problems, simplify, area, LCM, solve for X and hypotenuse are solved and discussed in the solution. The solution is detailed and well presented.

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