Question 1137015: Applications of Polynomial Multiplication or Division
The trowel shown is in the shape of an isosceles triangle.Find the polynomial that represents its height if the area of the trowel is represented by the polynomial 6+18t+t^2+3t^3 square inches.
The height is blank but the base is t^2+6 that what the picture shows.
The height is ____ in
2) the moon is about 240,000 miles from earth.
a) write this in scientific notation.
b)if a rocket traveled at 4*10^4 miles per hour, how long would it take for it to reach the moon? Use scientific notation and exponent rules to find the answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The trowel shown is in the shape of an isosceles triangle.Find the polynomial that represents its height if the area of the trowel is represented by the polynomial 6+18t+t^2+3t^3 square inches.
The height is blank but the base is t^2+6 that what the picture shows.
The height is ____ in
the formula for the area of a triangle is A = 1/2 * b * h.
A is the area.
b is the base.
h is the height.
the area is given as 6 + 18t + t^2 + 3t^3 square inches
re-arrange this in descending order of degree and the area if given as 3t^3 + t^2 + 18t + 6.
the base is given as t^2 + 6.
A = 1/2 * b * h becomes 3t^3 + t^2 + 18t + 6 = 1/2 * (t^2 + 6) * h
divide both sides of this equation by t^2 + 6 and you get (3t^3 + t^2 + 18t + 6) / (t^2 + 6) = 1/2 * h.
perform the division on the left side of the equal sign and you get (3t + 1) = 1/2 * h
multiply both sides of this equation by 2 and solve for h to get h = 6t + 2.
the height of the isosceles triangle is 6t + 2.
that's your solution.
A = 1/2 * b * h becomes A = 1/2 * (t^2 + 6) * (6t + 2), where t^2 + 2 is the base and 6t + 2 is the height.
multiply out the right side of the equation and you will find that it is equal to 3t^3 + t^2 + 18t + 6 which is the area of the triangle.
the attached worksheet shows the result of the division of 3t^3 + t^2 + 18t + 6 by t^2 + 6
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2) the moon is about 240,000 miles from earth.
a) write this in scientific notation.
240,000 is equal to 2.4 * 10^5.
your decimal point starts immediately after 240,000 to get 240,000.
you move it to the left 5 places to get it immediately after the 2.
that's the same as dividing 240,000 by 10^5.
so, you get 2.4 = 240,000 / 10^5.
multiply both sides of that equation by 10^5 and you get 2.4 * 10^5 = 240,000.
you can use your calculator to confirm.
you can make the calculator divide (2.4 * 10^5) by 240,000 and the calculator will tell you that the answer is 1.
any time you divide something by itself, the answer will be 1.
b)if a rocket traveled at 4*10^4 miles per hour, how long would it take for it to reach the moon? Use scientific notation and exponent rules to find the answer.
the moon is 2.4 * 10^5 miles away from the earth.
if the rocket travels at 4 * 10^4 miles per hour, then to figure out how long it would take to get to the moon, you need to divide 2.4 * 10^5 by 4 * 10^4.
there are several ways to do this, but let's try this way.
(2.4 * 10^5) / (4 * 10^4) is equal to (2.4 / 4) * (10^5 / 10^4).
10^5 / 10^4 is equal to 10^(5-4) which is equal to 10^1 which is equal to 10.
you get (2.4 / 4) * 10.
this is equal to (2.4 * 10) / 4 which is equal to 24 / 4 which is equal to 6.
the rocket would take 6 hours to get to the moon.
4 * 10^4 miles per hour times 6 = 24 * 10^4 miles.
if you divide 24 by 10, you need to multiply 10^4 by 10 to keep the same value.
therefore 24 * 10^4 is equal to (24 / 10) * (10^4 * 10) which is equal to 2.4 * 10^5.
your solution is that it will take 6 hours for the rocket to get to the moon.
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