Answer:
Step-by-step explanation:
To convert the statement to decimals, we need to use the following conversion rate.
Since $1 = 100cents
Writing $6.00 to 95 cents as a decimal, we need to writw both units in the same units.
$6.00 to 95 cents = 600cents to 95 cents
= 600cents:95cents
= 600cents/95cents
= 6.32 (to 2dp)
For 3 hours to 35 minutes
SI=ince 1 hour = 60minutes
3 hours to 35 minutes = (3*60)minutes to 35 minutes
= 180minutes : 35 minutes
= 180minutes/35 minutes
= 5.14 (to 2dp)
For 42 inches to 2 feet
Given 12inches = 1 foot
42 inches to 2 feet = 42inches to (2*12)inches
= 42inches to (24)inches
= 42inches : 24 inches
= 42inches/24 inches
= 1.75 (to 2dp)
Cosθ = -12/13.
For π <θ<3π /2 means 180° <θ< 270°. That is the third quadrant.
Let us just have the positive value of Cosθ = 12/13
Cosθ = Adjacent / Hypotenuse = 12 / 13
So we imagine a right angled triangle with adjacent side = 12, and Hypotenuse = 13.
To get the opposite side we apply Pythagoras' Theorem. Let the opposite side be x.
x² + 12² = 13²
x² + 144 = 169
x² = 169 - 144
x² = 25
x = √25
x = 5.
Sinθ = Opposite / Hypotenuse = 5 / 13
Tanθ = Opposite / Adjacent = 5 / 12
Recall the angle is in the third quadrant, and in the third quadrant, only Tangent is positive, Cosine and Sine are both negative.
Therefore
Cosθ = -12/13 Sinθ = -5/13 Tanθ = 5/12
Solving:
i) Sin2θ = 2SinθCosθ. By Trigonometric Identity.
= 2*(-5/13)*(-12/13)
= 120/169
ii) Cos2θ = 2Cos²θ - 1
= 2*(-12/13)(-12/13) - 1
= 288/169 - 1
= (288 - 169) / 288
= 119/288
Tan2θ = 2Tanθ /(1 - Tan²θ)
= 2*(5/12) / ( 1- (5/12)²)
= (5/6) / ( 1 - 25/144)
= (5/6) / ( (144 -25)/144)
= (5/6) / (169/25)
= (5/6) * (25/169)
= 125/1014
I hope this helps.
The questions seems to be lacking some information. By rate I'm going to assume position and in that scenario the answer would be B because the position function is modeled by a linear function.
6 in is (1/2)ft so it grows (1/2) ft each year. Since it starts at 7 ft, the height, in feet, after x years is given by
h = 7 + x/2