A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 18° with the horizontal. The flagpole
casts a 12-meter shadow up the slope when the angle of elevation from the tip of the shadow to the sun is 19°. What is the height of the pole?
1 answer:
Answer:
height = 9.28m
Step-by-step explanation:
Sum of angle in a triangle = 180°
To find the third angle, we have
180° = 71° + 62° + α
180° = 133° + α
α = 180° - 133°
α = 47°
To find the height use sine rule
h/sin47° = 12/sin 71°
h(sin71°) = 12sin47°
h = 12sin47° / sin71°
h = 12(0.7314) / 0.9455
h = 8.7768/0.9455
h = 9.28m
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Answer:
Step-by-step explanation:
f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4
Step 1. Calculate the difference between the functions
(a) Write the two functions, one above the other, in decreasing order of exponents.
ƒ(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
(b) Create a subtraction problem using the two functions
ƒ(x) = 9x³ + 2x² - 5x + 4
-g(x) = <u>-(5x³ - 7x + 4) </u>
ƒ(x) -g(x)=
(c). Subtract terms with the same exponent of x
ƒ(x) = 9x³ + 2x² - 5x + 4
-g(x) = <u>-(5x³ - 7x + 4) </u>
ƒ(x) -g(x) = 4x³ + 2x² + 2x
Step 2. Factor the expression
y = 4x³ + 2x² + 2x
Factor 2x from each term
y = 2x(2x² + x + 1)