In order to calculate rate or average speed you divide miles by time
I got 153.8 by dividing 500 by 3.25 (the .25 is because 15 minutes is 1/4 of 60) hope this helped!!
15+22(4+11)=x
4+11=15
22*15=330
15+330=345
x=345
Answer:
a) 52.5 ft. b)40.1ft c)12.5ft d) 72.6
Step-by-step explanation:
a) The height of the lighthouse is 84ft, and the angle of elevation is 58 degrees.
tan58=84/x
find x by dividing 84 by tan58, and you get 52.5ft.
b) do the same thing, except 131 is in the base of the right triangle shape. That being said, do tan17=x/131.
multiply 131 by tan17, and you get x=40.1 feet.
c) This question wants you to find the length of the slide, (basically the hypotenuse).
given the angle to be 46, do sin46=9/x
since sin is opp/hyp
9/sin46= 12.5ft
d) Find the angle of elevation by using inverse tan given the base to be 5, and the height to be 16ft.
tan^-1=(16/5)=theta
x=72.6 hope this helps!
The area bounded by the 2 parabolas is A(θ) = 1/2∫(r₂²- r₁²).dθ between limits θ = a,b...
<span>the limits are solution to 3cosθ = 1+cosθ the points of intersection of curves. </span>
<span>2cosθ = 1 => θ = ±π/3 </span>
<span>A(θ) = 1/2∫(r₂²- r₁²).dθ = 1/2∫(3cosθ)² - (1+cosθ)².dθ </span>
<span>= 1/2∫(3cosθ)².dθ - 1/2∫(1+cosθ)².dθ </span>
<span>= 9/8[2θ + sin(2θ)] - 1/8[6θ + 8sinθ +sin(2θ)] .. </span>
<span>.............where I have used ∫(cosθ)².dθ=1/4[2θ + sin(2θ)] </span>
<span>= 3θ/2 +sin(2θ) - sin(θ) </span>
<span>Area = A(π/3) - A(-π/3) </span>
<span>= 3π/6 + sin(2π/3) -sin(π/3) - (-3π/6) - sin(-2π/3) + sin(-π/3) </span>
<span>= π.</span>
Answer:
The dimension of the rug would be 17 ft × 9 ft.
Step-by-step explanation:
Given
length of the room = 27 ft.
width of the room = 19 ft.
suppose, she leaves a uniform strip of x ft. around the rug.
So,
The length of rug = (27-2x)ft.
Width of rug= (19-2x)ft.
∴ Area of the rug= length×width
According to the question,
( subtract 153 both sides)
( Middle term splitting)
or 
( zero product property)
or 
if x=18, dimension would be negative ( Not possible)
Thus, x= 5
Hence,
length of rug= 27-10=17 ft.
width of rug= 19-10=9 ft.
