C
first set up an equation
$52+8n ≥ 144
bacause she can spend 144 or less
solve 144-52=92
92/8=11.5
<span>Position at t=0.35s is 0.2 m
Velocity at t = 0.35s is -0.2 m/s
Since this is college level mathematics, the use of the word "acceleration" should indicate to you that you've been given the 2nd derivative of a function specifying the location of point a. And since you've been asked for the velocity, you know that you want the 1st derivative of the function. And since you've also been asked for the position, you also want the function itself. So let's calculate the desired anti-derivatives.
f''(t) = -1.08 sin(kt) - 1.44 cos(kt)
The integral of f''(t) with respect to t is:
f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k + C
In order to find out what C is, we know that at time t=0, v = 0.36 m/s. So let's plug in the values and see what C is:
f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k + C
0.36 = (1.08 cos(3*0) - 1.44 sin(3*0))/3 + C
0.36 = (1.08 cos(0) - 1.44 sin(0))/3 + C
0.36 = (1.08*1 - 1.44*0)/3 + C
0.36 = 0.36 + C
0 = C
So the first derivative will be f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k
Now to get the actual function by integrating again. Giving:
f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 + C
And let's determine what C is:
f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 + C
0.16 = (1.08 sin(3*0) + 1.44 cos(3*0))/3^2 + C
0.16 = (1.08 sin(0) + 1.44 cos(0))/9 + C
0.16 = (1.08*0 + 1.44*1)/9 + C
0.16 = 1.44/9 + C
0.16 = 0.16 + C
0 = C
So C = 0 and the position function is: f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2
So now, we can use out position and velocity functions to get the desired answer:
Position:
f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2
f(t) = (1.08 sin(3*0.35) + 1.44 cos(3*0.35))/3^2
f(t) = (1.08 sin(1.05) + 1.44 cos(1.05))/9
f(t) = (1.08*0.867423226 + 1.44*0.497571048)/9
f(t) = (0.936817084 + 0.716502309)/9
f(t) = 1.653319393/9
f(t) = 0.183702155
So the position of point a at t=0.35s is 0.2 m
Now for the velocity:
f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k
f'(t) = (1.08 cos(3*0.35) - 1.44 sin(3*0.35))/3
f'(t) = (1.08 cos(1.05) - 1.44 sin(1.05))/3
f'(t) = (1.08*0.497571048 - 1.44*0.867423226)/3
f'(t) = (0.537376732 - 1.249089445)/3
f'(t) = -0.711712713/3
f'(t) = -0.237237571
So the velocity at t = 0.35s is -0.2 m/s</span>
the prime factorization is 99
Answer:
The mean is 15.93 ounces and the standard deviation is 0.29 ounces.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
7% of the bottles containing this soft drink there are less than 15.5 ounces
This means that when X = 15.5, Z has a pvalue of 0.07. So when X = 15.5, Z = -1.475.
10% of them there are more than 16.3 ounces.
This means that when X = 16.3, Z has a pvalue of 1-0.1 = 0.9. So when X = 16.3, Z = 1.28.
From above
So
The mean is
The mean is 15.93 ounces and the standard deviation is 0.29 ounces.
<h3>
Answer: 56/65</h3>
Work Shown:
sin(angle) = opposite/hypotenuse
sin(F) = EG/FE
sin(F) = 56/65
Refer to the diagram below.
