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Topic: **How to write a word problem into an equation****Question:**
Brian is creating a collage on a piece of cardboard that has an area of 110r3 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of √r^5 square centimeters. Use the given information to determine an expression for the total number of pieces of paper used.
Can someone please tel me how I would solve this. Or could you just write this in equation form, I have trouble doing so. Word problems just aren't my best. Please and thank you to whoever is able to help me! :)
The cardboard that has an area of 110r3 square centimeters
Each piece has an area of √r^5 square centimeters
I hope that helps!

July 17, 2019 / By Filbert

Since each piece of paper has the same area ( √r^5 cm^2 ) You need to put √r^5 into exponential notation --> √r^5 = r^5/2 This can be thought of in two ways a) the square root of r taken to the fifth power or b) finding the square root of the fifth power or r. they are equivalent Multiply it by a variable and set it equal to 110r^3 cm^2. N(r^(5/2) ) =110 r^3 N = 110 r^3 / (r^(5/2)) = 110 r^(3 - (5/2)) = 110r^(1/2) N = 110 r^(1/2) = 110√r

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Note: I'm not sure if this is the 5-step method or not, it has been a long time since I took math. You need to set up 2 equations because you have 2 unknowns, so: Let X = Marco's age, Let Y = Eddie's age: They said right now, Eddie's age is 4 x as old as Marco's so: Right now Y = 4X They said, in 10 years, Eddie will be twice as old as Marco, so: Y + 10 = 2(X + 10) Y + 10 = 2X + 20 Y = 2X + 10 Now, we know that Y also = 4x so we substitute the term 4X for Y: 4X = 2X + 10 2X = 10 X = 5 Y = 4X = 20 So, right now, Marco is 20 & Eddie is 5 In 10 years, Marco will be 30 and Eddie will be 15 (so, the numbers seem to be OK).

I don't know what the 5-step method is but what you have to do is just interpret the problem and be careful while manipulating the constants and unknowns. Take the first sentence. Eddie's age is 4 times Marco's I'll use E for Eddie's age and M for Marco's. The first sentence gives you this equation M=4E. Now you need another equation to solve this since we have two unknowns. Use the next sentence, In 10 years Eddie will be twice as old as Marco will be, which implies (M+10)=2(E+10) You add 10 years to ages that were given before. Now, you have two equations and two unknowns, solve for one of the variables and plug that into the other equation. M=4E this equation is already solved for M so plug that into the other equation, (M+10)=2(E+10) the M in this equation is going to become 4E (4E+10)=2(E+10) Now, distribute the 2 on the right hand side. 4E+10=2E+20 Subtract 10 and 2E to both sides. 2E=10 Divide by 2 E=5 Now just use any of the two equations to find M. M=4E So M=4(5) Thus M=20

Well your equation of motion is clearly a quadratic equation. One condition in this case however is that t >= 0. Meaning that time must be bigger than 0; obviously. The answers you came up with are almost correct I'm afraid to say. The two answers should have been t = -1/8 and t = 3. Which then makes sense, as t cannot be smaller than 0, t = 3 is the correct answer.

it actually factorises to give t = - 1/8 and t = 3, so since you cant have a negative time in this scenario it will be t = 3. the reason that you will get two points is because solving this equation gives you where the parabola/graph that is modelling the position of the egg meets the x-axis (or h in this case i guess) because it is simply model it doesn't account for the egg obviously stopping when it hits the ground or starting when it is thrown and would continue in both directions. so the time - 0.125 secs is when it "would" have taken off had it started at ground level rather than 6 feet up.

You are almost correct. Your answers should be t= -1/8 and t=3. Since you are solving a quadratic you should get two answers for x. Now all you have to do is decide which one is appropriate. Since time cannot be negative in this case, you know your answer must be t=3seconds.

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