Pythagorean theorem
the shadow legnth=bottom leg
legnth from top of tower to end of shadow=hypotounuse
height of tower=vertical leg
a^2+b^2=c^2
a and b are legs
c=hypotonuse
11^2+b^2=61^2
121+b^2=3721
minus 121 both sides
b^2=3600
sqrt both sides
b=60
height of toer is 60 feet
Answer:
62.4 ft²
Step-by-step explanation:
The unmarked horizontal dimension at the bottom of the triangle is ...
(8 ft)sin(30°) = 4 ft
The unmarked vertical dimension of the triangle (the height of the trapezoid) is ...
(8 ft)cos(30°) ≈ 6.93 ft
Then the area of the trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
A = (1/2)((4 ft+7 ft) +(7 ft))(6.93 ft) ≈ 62.4 ft²
_____
The mnemonic SOH CAH TOA can remind you of the relationships between right triangle dimensions and angles.
Sin = Opposite/Hypotenuse ⇒ Hypotenuse×Sin = Opposite
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse×Cos = Adjacent
Your answer would be:
(-x)^2 = 4(-x)+32
or
(-x)^2 = -4x+32
-5y+8=-3y+10
-5y+3y=10-8
-2y=2
-2y/-2=2/-2
y=-1
I grouped the alike variable to one side, and the number to the other side, added and subtracted it, divided both sides by -2, and got -1
The exponential function which has the greatest average rate of change over the interval [0, 2] is option B.
<h3>How to calculate the average rate of change?</h3>
Mathematically, the average rate of change between two (2) points can be calculated by using this expression;
For option A, we have:
when x = 0; when x = 2;
y = 3(1.6)^x y = 3(1.6)^x
y = 3(1.6)^0 y = 3(1.6)^2
y = 3. y = 7.68
ΔA = (7.68 - 3)/(2 -0) = 2.34.
For option B, we have:
ΔA = (9 - 4)/(2 -0) = 2.5.
For option C, the exponential function has a common ratio of 2.
ΔA = 2.
For option D, we have:
ΔA = (10 - 8)/(1 -0) = 2.
In conclusion, we can logically deduce that the exponential function which has the greatest average rate of change over the interval [0, 2] is option B i.e 2.5.
Read more on average rate of change here: brainly.com/question/3493733
#SPJ1
