Math Answers

The movement of the crest of a wave is modelled with the equation h(t)=0.3cos3t+0.4sin3t. Find the maximum height of the wave and the time at which it occurs.

I found the max which is 0.5 but I do not know how to find the time?

 Determine the direction of the hypothesis test (one-sided left, one-sided right, bidirectional)
 Determine the test statistic (z* or t*) and the p-value for each of the following situations and
 Determine if they would cause the rejection of the null hypothesis if the confidence level was set
at 95% in each case. (Hint: be wary of the sample size)

Ho: μ = 380 s, Ha: μ ≠ 380 s, sample mean = 357, s = 75, n = 40

Please help solve explaining step by step

44. Capital value: find the capital value of an asset that generates $7200 yearly income if the interest rate is as follows.

a.) 5% compounded continuously
b.) 10% compounded continuously

Solve explaining step by step:

Find the cost function for each marginal cost function.

46. c'(x)=0.2x^2+5x; Fixed cost is $10

Right now dealing with transformations of sine and cosine functions. Here's the equation I'm stumped on:
F (x)=3 cos (4 pi x - (pi/2)) - 2

I'm trying to put this into the form:
A cos [B (x - C)] + D
But I can't figure out how to factor the
(4 pi x - (pi/2)) into the form [B(x - C)].
I'm confused because if B is 4pi, and the period is (2pi/B), wouldn't I end up with a pi-less period? I haven't encountered that yet.
Also, if the phase shift is C/B, wouldn't I also end up with a pi-less phase shift?

A manufacturer has 600 litres of 12% acid solution. How many litres of 30% acid solution must be added
to it so that acid content in the resulting mixture will be more than 15% but less than 18%?

solve dy/dx=y3+3x2y/x3+3xy2

A manufacturer of coffee vending machines has designed a new, less expensive machine. The current machine is known to dispense an average of 6 fl. oz., with a standard deviation of .2 fl. oz., into cups. When the new machine is tested using 15 cups, the mean and the standard deviation of the fills are found to be 6 fl. oz. and .214 fl. oz. Test H0: σ = 0.2 versus Ha: σ ≠ 0.2 at levels of significance .05 and .01. Assume normality. (Round your answer to 4 decimal places.)

chi-square

1.
Write the quadratic expression x^2 − 24x − 12 in completed square form.

2.
Use the completed square form from above to solve the equation x^2 − 24x − 12 = 0, leaving your answer in exact (surd) form.

3.
Use the completed square form from part 1 to write down the vertex of the parabola
y = x^2 − 24x − 12.

What does this equation tell you about a graph?

y = 5x^2 − 11x + 8