The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to a pole at a point 20 feet above the ground. The combine length of the two cables
is 70 feet. If cable r is attached to the ground 8 feet from the base of the pole, what is the
measure of the angle, x, to the nearest degree, that cable s makes with the ground?

x =

Step-by-step explanation:

r + s = 70 feet

Applying Pythagoras theorem to the triangle formed by cable r;

= +

= +

= 400 + 64

   = 464

r =

 = 21.541

Length of cable r is 21.54 feet.

So that,

r + s = 70 feet

21.54 feet + s = 70 feet

s = 70 feet - 21.54 feet

  = 48.46 feet

Length of cable s is 48.46 feet.

Applying trigonometric function to the triangle formed by cable s, we have;

Sin θ =

Sin x =

        = 0.4127

x = 0.4127

  = 24.3746

x =

The measure of angle that s makes with the ground is approximately .

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.