Consider an isosceles triangle with two sides of length x and angle θ included between them. We have already shown that the area of the triangle is given by A = 1 2 x 2 sin θ If an isosceles triangle has two 6-in. sides, what angle is required to make the area 10 in . 2 ? Give the exact value and approximate to the nearest one-hundredth of a degree.
Consider an isosceles triangle with two sides of length x and angle θ included between them. We have already shown that the area of the triangle is given by A = 1 2 x 2 sin θ If an isosceles triangle has two 6-in. sides, what angle is required to make the area 10 in . 2 ? Give the exact value and approximate to the nearest one-hundredth of a degree.
Solution Summary: The author calculates the angle required to make an isosceles triangle with two sides equal in length and angle theta included between them.
Consider an isosceles triangle with two sides of length
x
and angle
θ
included between them. We have already shown that the area of the triangle is given by
A
=
1
2
x
2
sin
θ
If an isosceles triangle has two 6-in. sides, what angle is required to make the area
10 in
.
2
? Give the exact value and approximate to the nearest one-hundredth of a degree.
After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked,
its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released.
s(t)=-16t² + 30t+3
a. How high will it go?
b. How long is it in the air?
+6x²+135x+1) (0≤x≤10). a) Find the number of units
The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+
that should be sold in order to maximize the total profit. b) What is the maximum profit?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
University Calculus: Early Transcendentals (4th Edition)
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