Question 206924: This is a problem solving question. It's the homework of my son and I'm trying to help him solve these problems but I can't seem to solve them either. Please help y
us. Thank you very much!
The problems are:
1. Find three consecutive integers if the product of the second and third integer is 78 more than 9 times the first.
2. The product of two integers is 64 and their difference is 12. Find the two integers.
3. An object is dropped from the top of the Empire State Building in New York, which is approximately 1444 ft tall. The equation that gives the distance of the object has fallen is d=16t(squared), where d is the distance in feet and t is the time in seconds. How long has the object been falling when it has traveled 400 ft? When does the object hit the ground?
4. The length of the base of a triangle is three times the height. The area of the triangle is 24sqcm. Find the base and height of the triangle.
I hope you can help me. Thank you very much.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 1. Find three consecutive integers if the product of the second and third integer is 78 more than 9 times the first.
x-1, x and x+1
x*(x+1) = 9(x-1) + 78
x^2+x = 9x-9 + 78 = 9x+69
x^2 - 8x - 69 = 0
There are no integer solutions. Typo?
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2. The product of two integers is 64 and their difference is 12. Find the two integers.
x*y = 64
x-y = 12 -->x = y+12
Sub into 1st eqn
y*(y+12) = 64
y^2 + 12y - 64 = 0
(y+16)*(y-4 = 0
y = 4, x = 16
y = -16, x = -4
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3. An object is dropped from the top of the Empire State Building in New York, which is approximately 1444 ft tall. The equation that gives the distance of the object has fallen is d=16t(squared), where d is the distance in feet and t is the time in seconds. How long has the object been falling when it has traveled 400 ft? When does the object hit the ground?
d = 16t^2
400 = 16t^2
t^2 = 25
t = 5 seconds
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When does the object hit the ground?
1444 = 16t^2
t^2 = 90.25
t = 9.5 seconds
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4. The length of the base of a triangle is three times the height. The area of the triangle is 24sqcm. Find the base and height of the triangle.
Area = bh/2
24 = 3h*h/2
3h^2 = 48
h^2 = 16
h = 4 cm
b = 12 cm
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