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Volgvan
3 years ago
10

Give the domain and range of T.

Mathematics
1 answer:
madreJ [45]3 years ago
8 0
Domain= {-5,-7}
range= {-8,-2,6}
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Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the inter
hoa [83]

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

5 0
2 years ago
What is the radius of 48mm
pantera1 [17]
If you mean that the diameter is 48mm... 24.
6 0
3 years ago
Please help me idk this
Stells [14]
We are given that Donna knit a total of 12 blankets.

She took 4 months in doing it.

To find the number of blankets in 1 month, take ratio of number of blankets to number of months.

\frac{number \: of \: blnkets}{number \: of \: months}  \\  \\  =  \frac{12 \: blankets}{4 \: months}  \\  \\  =  \frac{3 \: blankets}{1 \: months}

Thus, she knit 3 blankets in 1 months
4 0
3 years ago
Read 2 more answers
3. Choose the equation of the line parallel to the line 5 = -10x - 5y that passes through the point (-2,5). A y=-2x + 1 C y=x-5
storchak [24]

Answer:

y = -2x + 1

Step-by-step explanation:

The equation is in standard form, first, we need to convert it to slope-intercept form.

5 = -10x - 5y

5 + 10x = -5y

Divide both sides by -5 to isolate y variable.

y = -2x - 1

If the line is parallel, the slope remains the same.

To find the y-intercept, you need to plug the values of x and y into the equation, which is y = 2x + b

5 = -2(-2) + b

5 = 4 + b

1 = b

The equation is -2x + 1

5 0
2 years ago
Campbell food distribution pays frank bell a $1290 monthly salary plus a 11% commission on merchandise he sells each month. assu
rjkz [21]

Answer:

1. Amount of commission =$3476

2.Gross pay = $4766

Step-by-step explanation:

commission =(11/100)×31,600

=$3476

Gross pay = 3476+1290

=$4766

8 0
2 years ago
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