Answers
Answer:
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Step-by-step explanation:
∫ 15 sin(√(at)) dt
Use substitution:
If x = √(at), then:
dx = ½ (at)^-½ (a dt)
dx = a / (2√(at)) dt
dx = a/(2x) dt
dt = (2/a) x dx
Plugging in:
∫ 15 sin x (2/a) x dx
30/a ∫ x sin x dx
Integrate by parts:
If u = x, then du = dx.
If dv = sin x dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 30/a (-x cos x − ∫ -cos x dx)
= 30/a (-x cos x + ∫ cos x dx)
= 30/a (-x cos x + sin x + C)
Substitute back:
30/a (-√(at) cos(√(at)) + sin(√(at)) + C)
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Related Questions
A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.
Student Math Writing
1 540 474
2 432 380
3 528 463
4 574 612
5 448 414
6 502 526
7 480 430
8 499 453
9 610 615
10 572 541
11 390 335
12 593 613
(a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)
(b) Calculate the test statistic.
Answers
Answer:
Calculated t= 0.011659
t ≥ t ( 0.025,11) = 2.201
So the null hypothesis is accepted.
Step-by-step explanation:
Student Math Writing Difference d²
math score − writing score
1 540 474 66 4356
2 432 380 52 2704
3 528 463 65 4225
4 574 612 -38 1444
5 448 414 34 1156
6 502 526 -24 576
7 480 430 50 2500
8 499 453 46 2116
9 610 615 -5 25
10 572 541 31 961
11 390 335 55 3025
12 593 613 -20 400
∑ 6168 5856 312 23488
1) We state our null and alternative hypothesis as
H0: ud= 0 Ha: ud≠0
2) The significance level alpha is set at α= 0.05
3) The test statistic under H0 is
t= d`/ sd/√n
which has t distribution with n-1 degrees of freedom.
4) The critical region is t ≥ t ( 0.025,11) = 2.201
5) Computations
d`= ∑di/n= 312/12= 31.2
Variance = ∑(di- d`)²/n-1= 1/n-1 [ ∑di²-( ∑di)²/n]
= 1/11[ 23488- (312)²/12]
= 1/11[ 23488- 8112] = 1/11[15376]= 5976.7272
Standard Deviation= √ 5976.7272= 77.2510= 77.25
Now t= 3.12/77.25/√12= 0.011659
The calculated t value= 0.011659 falls in the acceptance region . So we accept our null hypothesis and reject the alternative hypothesis.
Give the most appropriate reason for using three significant figures in reporting results of typical engineering calculations.a. Three significant figures gives better than one-percent accuracy. b. Most of the original data used in engineering calculations do not have accuracy better than one percent. c. Historically slide rules could not handle more than three significant figures. d. Telephone systems designed by engineers have area codes consisting of three figures
Answers
Answer:
The answer is "Option b".
Step-by-step explanation:
In the calculation of engineering or modeling, it is used to assess its necessary system, that performance, and also used to evaluate the distribution network adjustments, which is used to accommodate the slew of other distribution network adjustments, that's why except "choice b" all were incorrect.
6. aA box in a certain supply room contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected. a. What is the probability that exactly one of the selected bulbs are rated 75-watt? b. What is the probability that all three of the elected bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. What is the probability that at least two of the selected bulbs are rated 75-watt?
Answers
Answer:
A) 0.2967
B) 0.0747
C) 0.2637
D)0.6933
Step-by-step explanation:
We are told the box contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs.
Thus, total number of bulbs = 4 + 5 + 6 = 15 bulbs
This is a combination problem.
Thus;
A) probability that exactly one of the selected bulbs are rated 75-watt will be = ((6C2) × (9C1))/(15C3)
= (15 × 9)/455
= 0.2967
B) probability that all three of the elected bulbs have the same rating;
Number of ways to select three 40 watt bulbs out of the 4 in the box = 4C1 = 4!/(3! × 1!) = 4
Number of ways to select three 60 watt bulbs out of the 5 in the box = 5C1 =
5!/(3! × 2!) = 10
Number of ways to select 75 watt bulbs out of the 6 in the box = 6C1 = 6!/(3! × 3!) = 20
Total number of ways = 4 + 10 + 20 = 34.
Thus, probability that all three of the elected bulbs have the same rating = 34/15C3 = 34/455
= 0.0747
C) probability that one bulb of each type is selected =
[(4C1) × (5C1) × (6C1)]/(15C3)
= (4 × 5 × 6)/455
= 0.2637
D) probability that at least two of the selected bulbs are rated 75-watt =
[(4C1 × 5C1 × 6C2)/15C3] + 6C3/15C3
= (4 × 5 × 15/455) + 20/455
= 0.6493 + 0.044
= 0.6933
h(x)=x^2+1 k(x)=x-2
(h+k)(2)=
(h-k)(3)=
Evaluate 3h(2)+2k(3)=
Answers
(h + k)(2) = 5
(h - k)(3) = 9
evaluate 3h(2) + 2k(3) = 17
The composition of functions is solved
a) ( h + k ) ( 2 ) = 5
b) ( h - k ) ( 3 ) = 9
c) 3h ( 2 ) + 2k ( 3 ) = 17
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
h ( x ) = x² + 1
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
k ( x ) = x - 2
Now , the composition of function is
To calculate (h+k)(2), we substitute x = 2 in both h(x) and k(x), add them together and simplify:
h(2) = 2² + 1 = 5
k(2) = 2 - 2 = 0
(h+k)(2) = h(2) + k(2) = 5 + 0 = 5
To calculate (h-k)(3), we substitute x = 3 in both h(x) and k(x), subtract k(x) from h(x), and simplify:
h(3) = 3² + 1 = 10
k(3) = 3 - 2 = 1
(h-k)(3) = h(3) - k(3) = 10 - 1 = 9
To evaluate 3h(2)+2k(3), we substitute x = 2 and x = 3 in h(x) and k(x), respectively, and simplify:
3h(2) + 2k(3) = 3(5) + 2(3-2) = 15 + 2 = 17
Therefore , ( h + k ) ( 2 ) = 5 , ( h - k ) ( 3 ) = 9, and 3h( 2 ) + 2k( 3 ) = 17
Hence , the composition of functions is solved
To learn more about composition of functions click :
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Which angles are congruent to each other?
Answers
Answer:
<8 and <6 are congruent to each other.
Step-by-step explanation:
A protractor was used to determine the answer. They both measured to 140 degrees.
Peter bought 45 greeting cards at 3 for $2.00. he sold them for 5 for $4.00. how much money did he make
Answers
Step 1) Set up a proportion to find how much Peter spent
45 cards / x dollars = 3 cards / 2 dollars
Step 2) Cross-multiply to solve the proportion
3x = 90
x = $30
Step 3) Set up a proportion to find how much Peter made
45 cards / x dollars = 5 cards / 4 dollars
5x = 180
x = $36
Step 4) Subtract the amount Peter made by the amount he spent
36 - 30 = $6
Answer: Peter made $6
($2/3) * 45 = $30
($4/5) * 45 = $36
$36 - $30 = $6
Please Please help! I am so beyond stuck. I have figured out what is wrong with the first step but I cant figure out what is going on with the second one!
Answers
Answer:
[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]
Step-by-step explanation:
So we have the equation:
[tex]|-4x+1|>3[/tex]
First, note that since the sign is greater than, this is an or inequality (not an "and" inequality). This is the student's first mistake.
So, let's solve this inequality.
Case 1:
[tex]-4x+1>3[/tex]
Subtract 1 from both sides:
[tex]-4x>2[/tex]
Divide both sides by -4:
[tex]x<-\frac{1}{2}[/tex]
The student did not flip the sign when doing this step, hence the incorrect answer.
You correctly spotted the student's mistake. Nicely done!
Case 2:
[tex]-4x+1<-3[/tex]
This is what you're missing: for this second instance, we must flip the sign to less than right away. This is because we are essentially multiplying the 3 by a negative. So, we must flip the sign in order to be correct.
Now solve. Subtract 1 from both sides:
[tex]-4x<-4[/tex]
Divide both sides by -4. Since we're dividing by a negative, flip the sign:
[tex]x>1[/tex]
So, our solutions are:
[tex]x<-\frac{1}{2}, x>1[/tex]
As mentioned previously, this is an or inequality. Therefore, our final answer is:
[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]
Edit: Improved Answer
Jaquarius has a pair of limited edition Jordan tennis shoes that are 12 inches long each. What is the total length of both of his shoes in feet?
Answers
Answer:
Total length of shoes in feet = 2 feet
Length of each shoe = 1 feet
Step-by-step explanation:
Given:
Length of each shoe = 12 inches
Find:
Total length of shoes in feet
Computation:
Total length of shoes = [12 + 12] inches
Total length of shoes = 24 inches
12 inches = 1 feet
Total length of shoes in feet = 24 / 12
Total length of shoes in feet = 2 feet
Length of each shoe = 1 feet
Name the rays on line c.
Answers
Answer:
BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD
Step-by-step explanation:
"BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD" Are all the possible rays on line c.
the difference of a number k and 8.1 is greater than 24
Answers
Difference means subtract.
Set up the equation:
K - 8.1 > 24
Solve for k by adding 8.1 to both sides:
K > 32.1
which number represents a whole number
Answers
Answer: The answer is D
Step-by-step explanation:
I divided 24 by 3 and it gave me 8 which is a whole number.
6. Joe runs 3/4 mile in 1/2 hour. Find his average speed in miles per hour.
Answers
Answer:
1.5 MPH
Step-by-step explanation:
3/4 = 0.75
3/4 x 2 = 0.75 x 2 = 1.5
what does this sideways E stands for in alg 2 ?
Answers
Answer:
The sideways E is used for indcating that a point, object, or number belongs to a certian set.
Step-by-step explanation:
what value does the 2 represent in the number 168,526
Answers
Answer:it is the tens place
Step-by-step explanation:
Answer:
2 represents the the tenths place
Step-by-step explanation:
You have 168,526 remember your tenth hundred and thousands 2 is in the tenth place that is what represents
Hope that answers ur question
The expression (q16)(q−5)2 is equivalent to qn. What is the value of n? 42 22 -160 13
Answers
Answer:
22
Step-by-step explanation:
In order to get one of the answer choices, it appears we need to interpret your input as ...
[tex](q^{16}q^{-5})^2 = (q^{16-5})^2=q^{11\cdot 2}=q^{22}[/tex]
The value of n is 22.
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
Answer:
6
Step-by-step explanation:
What is your average speed in miles per hour and in feet per second if you travel a mile in 16 minutes?
Answers
Step-by-step explanation:
Mile Per Hour to Foot Per Second Conversion Table
Miles Per Hour Feet Per Second
16 mph 23.47 ft/s
17 mph 24.93 ft/s
18 mph 26.4 ft/s
19 mph 27.87 ft/s
A particular computer takes 14 minutes to download a 42-minute TV show. How long will it take the computer to download a 2.5-hour movie?
Answers
Answer
about 15 min to 1 hour
How do you evaluate 6-2
Answers
Answer:
4
Step-by-step explanation:
6 - 2 = 4
Write 2^-3 in word form
Answers
Answer:
two raised to the power of -3
Two to the power of negative 3
Step-by-step explanation:
[tex]2^-^3 = \frac{1}{2^3}[/tex]
1 divided by 2 to the power of 3
what is the solution of the equation? 3(y-5)+2=5
Answers
Answer:
Y=- 6
3(y-5)+2=5
multiply
3y-15+2=5
add
3y-13=5
add pos 13 to the neg 13 to
cancel it out and add +13 to 5
3y=18
divide -3 to pos 3 and 18 to cancel it out
y= -6
What is 8.6 increased by 75%
Answers
Answer:
15.05
Step-by-step explanation:
8.6 is 100% of 8.6.
To increase it by 75%, you'll end up with 175% of 8.6
175% of 8.6 =
= 1.75 * 8.6
= 15.05
Determine the number of degrees for the angle in section B of the pie chart . Round to the nearest whole degree Please assist me
Answers
Answer:
115°
Step-by-step explanation:
Measure of the degree of the angle represented by section B on the chart = percentage in the pie chart ÷ 100 × 360. A full circle makes 360°.
Section B represents 32% of the pie chart, therefore, number of degrees for section B = [tex] \frac{32}{100}*360 = \frac{32*360}{100} [/tex]
[tex] = 115.2 [/tex]
Section B = 115° (to the nearest whole number)
[tex] \frac{3}{4} x + \frac{5}{6} = 5x - \frac{125}{3} [/tex]
Answers
Answer:
nos agoi o se
Step-by-step explanation:
Answer:
[tex]\boxed{\bold{\huge{\boxed{x = 10}}}}[/tex]
Step-by-step explanation:
=> [tex]\sf \frac{3}{4} x + \frac{5}{6} = 5x - \frac{125}{3}[/tex]
Combining like terms
=> [tex]\sf \frac{3x}{4} - 5x = -\frac{125}{3} - \frac{5}{6}[/tex]
Taking LCM to make the denominator same
=> [tex]\sf \large{\frac{3x-20x}{4} = \frac{-250-5}{6} }[/tex]
=> [tex]\sf \frac{-17x }{4} = \frac{-255}{6}[/tex]
=> [tex]\sf \frac{17x }{4} = \frac{255}{6}[/tex]
Cross Multiplying
=> [tex]\sf 17x * 6 = 4 * 255[/tex]
=> [tex]\sf 102x = 1020[/tex]
Dividing both sides by 102
=> x = 10
What does point A represent on the graph? Jordan needs 3 cups of diced chicken for 2 salads. Jordan needs 2 cups of diced chicken for 3 salads. Jordan needs 3 cups of diced chicken for 1 and one-half salads. Jordan needs 1 and one-half cups of diced chicken for 3 salads.
Answers
Answer:
The answer is 3
Step-by-step explanation:
At the beginning of a snowstorm, Sydney had 11 inches of snow on her lawn. The
snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow
was melting, how much snow would Sydney have on her lawn 3 hours after the snow
began to fall? How much snow would Sydney have on her lawn after t hours of snow
Answers
Answer:
12.5in.
x=.5t+11
Step-by-step explanation:
First of all, create the equation so you can solve both questions at once. We know that Sydney had eleven inches of snow on her lawn, and it doesn't dissapear, so it starts with x=11. Then every hour she gets .5 inches per hour, and the amount of hours is t, so that will translate to .5t. that makes the equation x=.5t+11. To find out how much she would have in three hours, substitute 3 for t, which which goes like this: x=.5(3)+11
x=1.5+11
x=12.5
Answer:
Snow after 3 hours: 12.5
Snow after t hours: 11+0.5t
What is the equation of the line that passes through the point (-2,-2) and
has a slope of 42
Answers
Answer:
The answer is
[tex]y = 42x + 82[/tex]Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
m is the slope
( x1 , y1) is the point
From the question the point is (-2,-2) and slope 42
The equation of the line is
[tex]y + 2 = 42(x + 2) \\ y + 2 = 42x + 84 \\ y = 42x + 84 - 2[/tex]
We have the final answer as
[tex]y = 42x + 82[/tex]
Hope this helps you
(-5) (-10) what does this equal
Answers
Answer:
50
Step-by-step explanation:
When parethesis are next to each other than you need to multiply them.
- times - is positive so -5*--10 would be 50.
If M2BAC = (3x – 1)º, m_chD = (6x + 10)°, m2DAE (2x + 6)°, and m_BAE = 103°, then find the mZCAD
Answers
Answer:
mZCAD=310°
Step-by-step explanation:
M2BAC=1,m2DAE=3 and m-BAE=0 therefore solution will be 310°
Setup an equation then find x
Answers
Answer: 2
Step-by-step explanation:
Solve for x. 95=35 Express the answer to the hundredths place (i.e., two digits after the decimal point).
Answers
Answer:
[tex]x = 1.28[/tex]
Step-by-step explanation:
Given
[tex]95 = 35^x[/tex]
Required
Solve for x
[tex]95 = 35^x[/tex]
Take Log of both sides
[tex]Log95 = Log35^x[/tex]
Apply law of logarithm
[tex]Log95 = xLog35[/tex]
Divide both sides by Log35
[tex]x = \frac{Log95}{Log35}[/tex]
[tex]x = \frac{1.97772360529}{1.54406804435}[/tex]
[tex]x = 1.28085262338[/tex]
Approximate
[tex]x = 1.28[/tex]