# 9.6 Solve equations with square roots  (Page 4/6)

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A helicopter dropped a rescue package from a height of 1,296 feet. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground.

$9\phantom{\rule{0.2em}{0ex}}\text{seconds}$

A window washer dropped a squeegee from a platform 196 feet above the sidewalk Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the squeegee to reach the sidewalk.

$3.5\phantom{\rule{0.2em}{0ex}}\text{seconds}$

Police officers investigating car accidents measure the length of the skid marks on the pavement. Then they use square roots to determine the speed, in miles per hour, a car was going before applying the brakes.

## Skid marks and speed of a car

If the length of the skid marks is d feet, then the speed, s , of the car before the brakes were applied can be found by using the formula,

$s=\sqrt{24d}$

After a car accident, the skid marks for one car measured 190 feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

## Solution

 Step 1. Read the problem. Step 2. Identify what we are looking for. The speed of a car. Step 3. Name what we are looking for. Let s = the speed. Step 4. Translate into an equation by writing the appropriate formula. Substitute the given information. Step 5. Solve the equation . Round to 1 decimal place. Step 6. Check the answer in the problem. $\phantom{\rule{1em}{0ex}}67.5\stackrel{?}{\approx }\sqrt{24\left(190\right)}$ $\phantom{\rule{1em}{0ex}}67.5\stackrel{?}{\approx }\phantom{\rule{0.2em}{0ex}}\sqrt{4560}$ $\phantom{\rule{1em}{0ex}}67.5\stackrel{?}{\approx }\phantom{\rule{0.2em}{0ex}}67.5277...$ Is 67.5 mph a reasonable speed? Yes. Step 7. Answer the question with a complete sentence. The speed of the car was approximately 67.5 miles per hour.

An accident investigator measured the skid marks of the car. The length of the skid marks was 76 feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

$42.7\phantom{\rule{0.2em}{0ex}}\text{feet}$

The skid marks of a vehicle involved in an accident were 122 feet long. Use the formula $s=\sqrt{24d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

$54.1\phantom{\rule{0.2em}{0ex}}\text{feet}$

## Key concepts

• To Solve a Radical Equation:
1. Isolate the radical on one side of the equation.
2. Square both sides of the equation.
3. Solve the new equation.
4. Check the answer. Some solutions obtained may not work in the original equation.
• Solving Applications with Formulas
1. Read the problem and make sure all the words and ideas are understood. When appropriate, draw a figure and label it with the given information.
2. Identify what we are looking for.
3. Name what we are looking for by choosing a variable to represent it.
4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
5. Solve the equation using good algebra techniques.
6. Check the answer in the problem and make sure it makes sense.
7. Answer the question with a complete sentence.
• Area of a Square
• Falling Objects
• On Earth, if an object is dropped from a height of $h$ feet, the time in seconds it will take to reach the ground is found by using the formula $t=\frac{\sqrt{h}}{4}$ .
• Skid Marks and Speed of a Car
• If the length of the skid marks is d feet, then the speed, s , of the car before the brakes were applied can be found by using the formula $s=\sqrt{24d}$ .

## Practice makes perfect

When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was$1,585. What is the amount of each loan?
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found$7(+7). Totally you lost just $12 (-12) Annushka I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-$10 ... I also for a long time would draw it out on a number line to visualize it Meg practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact Meg Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles John Reply 168.50=R Heather john is 5years older than wanjiru.the sum of their years is27years.what is the age of each achol Reply 46 mustee j 17 w 11 Joseph john is 16. wanjiru is 11. Felix 27-5=22 22÷2=11 11+5=16 Joyce where's the answers? Ed Reply I don't see where the answers are. Ed Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart? Maddy Reply 3 Christopher 18t+14t=96 32t=96 32/96 3 Christopher show that a^n-b^2n is divisible by a-b Florence Reply What does 3 times your weight right now Cherokee Reply Use algebra to combine 39×5 and the half sum of travel of 59+30 Cherokee What is the segment of 13? Explain Cherokee my weight is 49. So 3 times is 147 Cherokee kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps tyler How to convert grams to pounds? paul What is the lcm of 340 Kendra Reply Yes Cherokee How many numbers each equal to y must be taken to make 15xy Malik Reply 15x Martin 15x Asamoah 15x Hugo 1y Tom 1y x 15y Tom find the equation whose roots are 1 and 2 Adda Reply (x - 2)(x -1)=0 so equation is x^2-x+2=0 Ranu I believe it's x^2-3x+2 NerdNamedGerg because the X's multiply by the -2 and the -1 and than combine like terms NerdNamedGerg find the equation whose roots are -1 and 4 Adda Ans = ×^2-3×+2 Gee find the equation whose roots are -2 and -1 Adda (×+1)(×-4) = x^2-3×-4 Gee yeah Asamoah Quadratic equations involving factorization Winner Reply there's a chatting option in the app wow Nana That's cool cool Nana Nice to meet you all Nana you too. Joan 😃 Nana Hey you all there are several Free Apps that can really help you to better solve type Equations. Debra Debra, which apps specifically. ..? Nana am having a course in elementary algebra ,any recommendations ? samuel Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science Nana me too as part of my core subjects in R M E Ken at ABETIFI COLLEGE OF EDUCATION Ken ok great. Good to know. Joan 5x + 1/3= 2x + 1/2 sanam Plz solve this sanam 5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12 Ranu Thks ranu sanam Please help me solve this 10x+14=-2x+38 Erica the previous equation should be 3x = 1/6 x=1/18 Sriram for the new one 10x + 2x = 38 - 14 Sriram 12x = 24 x=2 Sriram 10x + 14 = -2x +38 10x + 2x = 38 - 14 12x = 24 divide both sides by the coefficient of x, which is 12 therefore × = 2 vida a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions vinaya Reply a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?