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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.

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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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please solve these problems/show work

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 ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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