Evaluate the indicated integrals if b is a positive real number constant.
∫tan (x/b) dx
Answers
Substituting back x in the final expression we get:∫tan (x/b) dx = -b ln|cos (x/b)| + C The required integral is -b ln|cos (x/b)| + C, where C is the constant of integration.
We are required to find the integral of ∫tan (x/b) dx given that b is a positive real number constant.Step 1: First we need to substitute u
= x/b then we have x
= bu Therefore, dx
= b du.Step 2: Now we replace x and dx in the given integral, we have:∫tan (x/b) dx
= ∫tan u * b du. Using the integration by substitution rule,∫tan u * b du
= -b ln|cos u| + C, where C is the constant of integration.Substituting back x in the final expression we get:∫tan (x/b) dx
= -b ln|cos (x/b)| + C The required integral is -b ln|cos (x/b)| + C, where C is the constant of integration.
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Related Questions
What’s the volume to this shape?
Answers
Answer:
30x^6
Step-by-step explanation:
5×2×3=30
x+x+x+x+x+x=6x
Indices gets added when they are multiplied
Answer:
\(540x^{3}\)
Step-by-step explanation:
First, we need to simplify all over the cubes and squares.
2x^2 = 4x
3x^3 = 27x
5x=5x
Then , we need to multiply them together.
27x*4x= 108x
108x*5x = 540x
Now, we have our answer
mark has 15 coins in dimes and quarters valuing $2.10 how many dimes does he have?
A 4
B 10
C 9
D 11
Answers
Write the slope intercept form of the equation of each line .Plz help
Answers
Answer:D
y = -5/3x +4
Step-by-step explanation:
What is the simplified version of
6(m - 2m) - (4m - 5m) ?
Answers
Answer:
-5m
Step-by-step explanation:
6m-12m-4m+5m
-6m+1m
=-5m
what is the full from of MICR
Answers
The full form of MICR is:-magnetic ink character recognition
U can search the defention in Gogle
Hope it helps
Need help pls pls!!!!
Answers
Find the GCF of 14 and 15. GCF=
Answers
Answer:
1
Step-by-step explanation:
14 - 2 x 7
15 - 3 x 5
GCF of 14 and 15: 1
b^(3) * b^(4) write without exponents
Answers
Answer:
(b×b×b)×(b×b×b×b)
Step-by-step explanation:
Writing the equation out is the only way to remove the exponents.
In order to study the mean video views of people on his website, Richard samples the population by dividing the viewers by age and randomly selecting a proportionate number of viewers from each age group. Which type of sampling is used
Answers
Using sampling concepts, it is found that stratified sampling is used.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, the population is divided into groups according to their ages, then equal proportions of each group are taken, hence stratified sampling is used.
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ax+3=23 if a=0 plz help
Answers
Answer:
x = \(\frac{23}{a}\)
Step-by-step explanation:
Given equation is,
ax + 3 = 23
To solve this equation for the value of x isolate the variable 'x' on the one side of the equation.
Step 1,
Subtract 3 from both the sides of the equation.
ax + 3 - 3 = 23 - 3
ax = 20
Step 2,
Divide the equation by a,
\(\frac{ax}{a}=\frac{23}{a}\)
x = \(\frac{23}{a}\)
Therefore, x = \(\frac{23}{a}\) will be the answer.
The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities.
The Gades Foundation donated
$
250
$250dollar sign, 250 in the first month, and each month afterward their cumulative donation total increases by
$
100
$100dollar sign, 100.
The HBM Corporation donated
$
64
$64dollar sign, 64 in the first month, and each month afterward their cumulative donation total increases by
75
%
75%75, percent.
They started making donations at the same time, and they both make their monthly donations at the beginning of each month.
What is the first month in which HBM Corporation's cumulative donation total exceeds the Gades Foundations' cumulative total?
Answers
The first month in which HBM Corporation's cumulative donation total exceeds the Gades Foundation's cumulative total is the sixth month. This is calculated by finding an equation for each organization's cumulative donation total and solving an inequality.
Let's start by finding an equation for the cumulative donation total for each organization after n months. Let GF(n) and HBM(n) represent the cumulative donation totals for the Gades Foundation and HBM Corporation, respectively.
The Gades Foundation's cumulative donation total can be represented by the arithmetic sequence
GF(n) = 250 + 100(n-1)
The HBM Corporation's cumulative donation total can be represented by the geometric sequence
HBM(n) = 64(1.75)ⁿ⁻¹
To find the month in which HBM Corporation's cumulative donation total exceeds the Gades Foundation's cumulative total, we need to solve the inequality
HBM(n) > GF(n)
Substituting the expressions for GF(n) and HBM(n), we get
64(1.75)ⁿ⁻¹ > 250 + 100(n-1)
Simplifying and solving for n, we get
1.75ⁿ⁻¹ > (250/64) + (100/64)(n-1)
Taking the logarithm of both sides, we get
(n-1)log(1.75) > log(250/64) + log(1+(100/250)(n-1))
Using a calculator to evaluate the logarithms, we can solve for n
n > 5.74
Since n must be an integer, the smallest integer greater than 5.74 is 6. Therefore, the first month in the Gades Foundation's cumulative total is the sixth month.
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In which shapes does the measure of
∠
K
=
40
°
∠
K
=
40
°
?
Select the shapes you want to choose.
Answers
Answer:
Step-by-step explanation:
Help me please
Look at this graph
Answers
Answer:
Slope = Rise/Run
Slope = 1/2
Step-by-step explanation:
Pick two points randomly, it doesn't matter.
Count the rise, then count the run.
Simplify the fraction.
Boom! You got it!
pick a point, for this example i’ll use (20,20)
then calculate how far up and over you need to go to hit another point on the graph:
here we need to go up 1 over 2
so the slope is 1/2
Graph the function f(x)={x+1ifx<0}
Real equation |
v
on the coordinate plane.
Answers
Answer: The graph is shown below
====================================================
Explanation:
This piecewise function
\(f(x) = \begin{cases}x+1 \ \ \text{ if } x < 0\\2 \ \ \ \ \ \ \ \text{ if } 0 \le x \le 1\\x \ \ \ \ \ \ \ \text{ if } x > 1\\\end{cases}\)
is the same as saying...
when x < 0, f(x) = x+1when \(0 \le x \le 1\), f(x) = 2or when x > 1, f(x) = xAll three of those statements combine to form the piecewise function.
In other words, f(x) has a split personality. It depends on what x is that will determine what f(x) is. To graph this, we graph the pieces of y = x+1, y = 2 and y = x based on the restrictions for x above.
The first piece y = x+1 is graphed when x < 0The second piece y = 2 is graphed when \(0 \le x \le 1\)The third piece y = x is graphed when x > 1The graph is shown below. Note the use of open holes vs closed circle endpoints (indicating which points are not part of the graph vs those that are). The closed endpoints happen when the inequality sign has a "or equal to" as part of it; otherwise, we'll have an open endpoint.
BRAINLIEST AWAITS!
Solve this question and you may get 15 points and brainliest!
Answers
Answer:
Step-by-step explanation:
a) Age of Jeff = j
Tina's age = j - 4
b) j = 15 years
Tina's age = 15 - 4 = 11 years
j = 20 years
Tina's age = 20 - 4 = 16 years
j = 58 years
Tina's age = 58 - 4 = 54 years
Proving Vertical Angles Are Congruent
Answers
Answer:
Vertical angles are always congruent
Step-by-step explanation:
Answer:
Statement
Measure of angle 2 and 3 are a linear pair and
Reason
Definition of linear pair
Step-by-step explanation:
Hook me up with a 5 star and a Thanks :)
PLEASEE ANSWERR IT IN MIDDLE OF TEST
Answers
Answer:
i can not see it to much do you know if you can make it bigger for me
Step-by-step explanation:
Divide negative 5 and one eighth ÷ negative 6 and three fourths.
Answers
Answer: 270
-5 divided by 1/8 divided by -6 and 3/4 is 270
4d-(5b+3) for d=-8 and for b=-3
Answers
Answer:
I believe the answer would be 384
Step-by-step explanation:
4×-8 (5× -3+3)
-32 × -12
384
BOOM!!! Your Welcome
reak-Even and Target Proff Analyels LO5-4, LO5-5, LO5-6 Outback Outfitters sells recreational equipment. One of the company's products, a small camp stove, sells for $50 per unit. Variable expenses are $32 per stove, and fixed expenses associated with the stove total $108,000 per month. Requlred: 1. What is the break-even point in unit sales and in dollar sales? 2. If the variable expenses per stove increase as a percentage of the selling price, will it ressit in a higher or a lower break-even point? Why? (Assume that the fixed expenses remain unchanged.) 3. At present, the company is selling 8;000 stoves per month. The sales manager is convinced that a 10% reduction in the selling price would result in a 25% increase in monthly sales of stoves. Prepare two contribution format income statements, one ander present operating conditiors, and one as operations would appear after the proposed changes. Show both total and per unit data on your statements. 4. Refer to the data in (3) above. How many stoves would have to be sold at the new selling price to attain a target profit of $35,000 per month?
Answers
1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.
2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.
3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.
4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.
1. The break-even point in unit sales and dollar sales is computed as follows:
Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units
Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000
2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.
3. Present Income Statement
Sales (8,000*$50) $400,000
Less variable expenses (8,000*$32) (256,000)
Contribution Margin $144,000
Less fixed expenses 108,000
Net Income $36,000
Income Statement if Changes are Implemented
Sales (8,000*$45) $360,000
Less variable expenses (8,000*$35) (280,000)
Contribution Margin $80,000
Less fixed expenses 108,000
Net Loss $(28,000)
4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:
$35,000 / 0.36 = $97,222
The number of units required to be sold is:
$97,222 / $18 = 5,401 units
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What is the slope of the line shown below?
A. - 1/2
B. 1
C. -1
D. 1/2
Answers
Answer:
C. -1
Step-by-step explanation:
Slope is: \(m=\frac{y_2-y_1}{x_2-x_1}\)
We are given the points (1,7) and (3,5).
\(m=\frac{5-7}{3-1} =\frac{-2}{2} =-1\)
The slope is -1, and therefore, Option C should be the correct answer.
A triangle has sides with lengths of 10 yards, 12 yards, and 14 yards. Is it a right triangle?
yes or no?
Answers
Answer:
No
Step-by-step explanation:
The sum of the squares of the lengths of the two shorter sides is \(10^2+12^2=244\).
The square of the length of the largest side is \(14^2=196\).
Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.
Find −523−16. Write your answer as a mixed number in simplest form.
Answers
Answer:
(-523) - 16 is -539
Step-by-step explanation:
mathmathmathmathmsthmatj
PLEASE HELP!! the polynomial expression x(2x^2+15)(4x^2+5x+3 where x is in inches can be used to model the number of cubic inches of cement that will be needed for a new porch. The cement contractor used 2 for the value of x. Determine the dimensions in inches of the cement needed for the porch. Height(shortest length side) width(medium length side) and length(longest length side)
Answers
Answer:
height 2 incheswidth 23 incheslength 29 inchesStep-by-step explanation:
For x=2, the dimensions are ...
height = x = 2 inches
width = 2x² +15 = 2(2²) +15 = 8 +15 = 23 inches
length = 4x² +5x +3 = (4x +5)x +3 = (4·2 +5)2 +3 = 29 inches
Pls help. Write an equation where the solution is 2.
Answers
Answer:
Step-by-step explanation:
x = 2 works lol
but if you want a more complicated one:
4x - 4 = 4
there's infinite equations
Suppose you were sketching the graph of y X + 2, Why does it make sense to begin with the y-intercept instead of the slope?
(help me out please)
Answers
It makes sense to begin with the y-intercept when sketching the graph of y = mx + b because the y-intercept is the point at which the line intersects the y-axis, where x = 0. This point gives us a starting point for the graph and allows us to plot a single point before determining the slope of the line. Once we have the y-intercept, we can use the slope to find additional points on the line, and then connect the points to create the graph of the line.
Answer:
Step-by-step explanation:
When graphing a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept, it makes sense to begin with the y-intercept instead of the slope because the y-intercept gives us a point on the y-axis where the line crosses it.
In the case of the equation y = X + 2, the y-intercept is the point (0,2) on the y-axis, which is a point we can easily plot on the graph. Once we have plotted the y-intercept, we can then use the slope, which is 1 in this case, to find another point on the line by moving one unit to the right along the x-axis and one unit up along the y-axis. We can then draw a straight line through these two points to complete the graph of the line.
Starting with the y-intercept also makes sense because it gives us a sense of the vertical position of the line before we consider its slope. This can be helpful in cases where the y-intercept is a large or small number, as it can affect the scale of the graph and make it easier to read. Additionally, starting with the y-intercept can help us to quickly identify whether the line intersects the y-axis or not, and at what point.
Write the polynomial in standard form. Then classify its degree and by number of terms
7x²+10+4x³
Answers
Step-by-step explanation:
4x^3 + 7x^2 + 10 <====standard form
degree is 3 (this is the largest exponent) and there is three terms
discuss three strengths of the linear regression. identify a peer-reviewed study that uses linear regression in its analysis. explain why linear regression was used and discuss one challenge in interpreting the results. include the permalink with your citation.
Answers
Linear Regression analysis has three key applications:
(1) evaluating predictor strength, (2) anticipating an effect, and as well (3) trend forecasting.
Define the term linear regression?Linear regression is a fundamental and widely used method of predictive analysis. The overall goal of regression is to investigate two things:
How well does a set of predictor factors predict an outcome (dependent) variable? Which variables, in particular, are significantly predictive of both the outcome variable, and how do they influence it?Regression analysis has three key applications:
evaluating predictor strength,anticipating an effect, trend forecasting.The formula y = c + b*x defines the simplest form of the regression equation with one dependent so one independent variable,
where,
y = approximately dependent variable score, c = constant, b = regression coefficient, and x = independent variable score.To know more about the linear regression, here
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A supermarket has bags of red grapes for 22.96 for 7 bags
They also had bags of green grapes priced 9.60 for 3 bags
Which type was most expensive?
Answers
Answer:
The bag of red grapes costs more.
Step-by-step explanation:
We can do proportions.
A supermarket has bags of red grapes for 22.96 for 7 bags:
\( \frac{22.96 \: dollars}{7 \: bags} = \frac{x}{1 \: bag} \\ \frac{7x}{7 } = \frac{22.96}{7} \\ x = 3.28\)
For one bag of red grapes, its costs $3.28.
They also had bags of green grapes priced 9.60 for 3 bags:
\( \frac{9.60 \: dollars}{3 \: bags} = \frac{x}{1} \\ \frac{3x}{3} = \frac{9.60}{3} \\ x = 3.2 \: \: \: - > 3.20\)
One bag of green grapes costs $3.20.
The bag of red grapes costs more.
The cost of Mr. Patten’s car insurance increased by 5% to $86.82 per month. What was the cost of his insurance before it increased?
Show the work in answer.
Answers
The cost of the insurance bought by Patten is $82.69.
How to calculate the value?From the information, the cos of Mr. Patten’s car insurance increased by 5% to $86.82 per month.
It should be noted that the increase can be illustrated as:
= 100% + 5%
= 105%
Therefore, 105% of x is $86.82
where x = old cost
This will be:
105% of x is $86.82
1.05x = 86.82
Divide
x = 86.82 / 1.05
x = 82.69
The insurance was $82.69.
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