One car travels 45 mph and the other one travels 52 mph if they start from the same place at the same time traveling in the same
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Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
. That is, 
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
and replace 
and 
using expressions that contain an expression in terms of x from the first two equations we came up with.
That gives us:
which we solve for x as follows:
Now that we know x we can substitute 36 for x into the equation
and solve for z as follows:
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
That gives us:
Now that we know x we can substitute 36 for x into the equation
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
I might be wrong in this one but I am certain to the right Is definitely -3. If I get it wrong can you tell me what I got wrong to improve from my mistakes.
Answer:
0.20 and 0.36
Step-by-step explanation:
y(t) = 2 sin (4π t) + 5 cos (4π t)
We wish to convert this to:
y = A sin(ωt + φ)
We know that ω = 4π. We also know the following:
5 = A sin φ
2 = A cos φ
Divide the first equation by the second equation:
5/2 = tan φ
φ = tan⁻¹(5/2)
Now, square the two equations and add them together.
5² + 2² = (A sin φ)² + (A cos φ)²
29 = A²
A = √29
The equation of the wave is therefore:
y = √29 sin(4π t + tan⁻¹(5/2))
The maximum negative position is -√29. And half of that is -½√29.
-½√29 = √29 sin(4π t + tan⁻¹(5/2))
-½ = sin(4π t + tan⁻¹(5/2))
7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)
7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π
t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24
Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.
t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24
t ≈ 0.20 or 0.36
