Answer:
A. v(t) = sin (2πft + π/2) = A cos (2πft)
Step-by-step explanation:
According to trigonometry friction, the following relationship are true;
Sin(A+B) = sinAcosB + cosAsinB
We will be using this relationship to check which option is true.
Wave equation is represented as shown;
y(t) = Asin(2πft±theta)
For positive displacement,
y(t) = Asin(2πft+theta)
If theta = π/2
y(t) = Asin(2πft+π/2)
y(t) = A[ sin 2πftcosπ/2 + cos2πft sin π/2]
Since sinπ/2 = 1 and cos (π/2) = 0
y(t) = A[ sin 2πft (0)+ cos2πft (1)]
y(t) = A[0+ cos2πft]
y(t) = Acos2πft
Hence the expression that is true is expressed as;
v(t) = Asin(2πft+π/2) = Acos2πft
The area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.
<h3>What is the area of trapezoid?</h3>
The area of the trapezoid is the space occupied by it on the two dimensional plane. The area of this figure is half of the product of height and sum of sides.

Here, (a and b) are the base sides of the trapezoid and (h) is the height.
A room is shaped like a trapezoid which has the height of 28 feet and the length of sides as 23 ft and 35 ft. Thus, the area of it is,

Carpet costs $8.30 per square foot. Thus, the cost of carpet with area 812 ft² is,
C=812×$8.30
C=$6739.6
Furniture covers 25% of the floor. Thus, the remaining square feet of carpet are covered by furniture is,

Thus, the area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.
Learn more about the area of trapezoid here;
brainly.com/question/1410008
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Answer:
It is the second triangle.
Step-by-step explanation:
This is because the area of the square is given as 25^2 as the perpendicular, 144^2 as the base, and the hypotenuse is 169^2.
Length of the perpendicular = 5^2 (Because 25^2 / 5^2)
Length of the base = 12^2
Length of the hypotenuse = 13^2
So, the Pythagoras theorem is,
=> 
=> 
This is true, because, 13*13 = 12*12 + 5*5
=> 169 = 144 + 25
=> 169 = 169
If my answer helped, kindly mark me as the brainliest!!
Thanks!!
Step-by-step explanation:
3 tan 2x - 4 tan 3x = tan² 3x * tan 2x
3 (tan 2x - tan 3x) = tan 3x + tan² 3x * tan 2x
= tan 3x (1 + tan 3x * tan 2x)
3 (tan 2x - tan 3x)/(1 + tan 3x * tan 2x) = tan 3x
3 * (- tan x) = tan 3x
-3tanx = (3 tan x - tan³ x) / (1 - 3 tan² x)
3 - tan² x = - 3 + 9 tan² x
tan x = + √3 /√5 or - √3/√5
So 2 gallons every 5 minutes
2/5= .4
so .4 a minute
and you already have 5 gallons in so those need to be added
m=minutes
y=0.4m + 5 will be what you want to find out if you are looking to find out how much will be there in a certain time
for 50 minutes you will have
y=0.4(50) +5
20+5
25 gallons
HOWEVER, the equation has to be changed if you want to tell how long you have to wait for it to fill.
m=2.5(g-5)
m=minutes
g= gallons
you subtract 5 because they are already there
you multiply by 2.5 because it fills at a rate of 1 gallon every 2.5 minutes.
m=2.5(1500-5)
for the sake of it being easier i will do the -5 separately
2.5(1500 = 3750
2.5(-5= -12.5
3750-12.5
3737.5 minutes to fill the pool.
3720/60 = 62
17.5/60 = .292
62.292 hours to fill the pool.
p.s. you have a really slow hose.
Its good you didn't wait for it to fill, you would have died from lack of water before then if you just sat and waited.
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