Answer:
y=-1/2x+5
Step-by-step explanation:
Calculus 2 master needed; stuck on evaluating the integral please show steps [tex]\int {sec(x/2)tan^5(x/2)} \, dx[/tex] I am thinking that we want to split up the tan^5, making [tex]\int {sec(x/2)tan^2 tan^3(x/2)} \, dx[/tex] and then [tex]\int {sec(x/2)*sec^2x-1* tan^3(x/2)} \, dx[/tex] but I am not sure this is correct. Can anyone help? The thing I am unsure of is that tan^3 is still odd, so would we do the same thing again and factor so we will be left with just tanx?
Answer:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]
Step-by-step explanation:
We want to find the integral:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left({\frac{x}{2}\right)dx[/tex]
First, perform the substitution y = x / 2. This yields:
[tex]\displaystyle dy = \frac{1}{2} \, dx \Rightarrow dx = 2\, dy[/tex]
Hence, the integral becomes;
[tex]\displaystyle =2\int \sec y\tan^5 y \, dy[/tex]
Next, as you had done, let's expand the tangent term but to the fourth:
[tex]\displaystyle =2\int \sec y\tan^4 y\tan y\, dy[/tex]
Recall that:
[tex]\tan^2(y)=\sec^2(y)-1[/tex]
Hence:
[tex]\displaystyle =2\int \sec y(\sec^2 y-1)^2\tan y\, dy[/tex]
We can use substitution once more. This time, let u = sec(y). Hence:
[tex]\displaystyle du = \sec y \tan y \, dy[/tex]
Rewrite:
[tex]\displaystyle =2\int \left((\sec^2y-1)^2\right)\left(\sec y \tan y\right)dy[/tex]
Therefore:
[tex]\displaystyle = 2\int (u^2 - 1)^2\, du[/tex]
Expand:
[tex]\displaystyle =2\int u^4-2u^2+1\, du[/tex]
Reverse Power Rule:
[tex]\displaystyle = 2\left(\frac{u^5}{5} - \frac{2u^3}{3} + u\right) + C[/tex]
Simplify:
[tex]\displaystyle = \frac{2u^5}{5} - \frac{4u^3}{3} + 2u + C[/tex]
Back-substitute:
[tex]\displaystyle = \frac{2\sec^5 y }{5}-\frac{4\sec^3 y}{3}+2\sec y+C[/tex]
Back-substitute:
[tex]\displaystyle =\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec \left(\frac{x}{2}\right)+C[/tex]
Therefore:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]
Answer:
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) ) + C
3 5
Step-by-step explanation:
∫sec(x/2) tan⁵(x/2) dx
apply u substitute u = x/2
= ∫sec(u) tan⁵(u) * 2du
= 2 * ∫sec(u) tan⁴(u) tan(u) du
= 2 * ∫sec(u) (tan²(u))² tan(u) du
= 2 * ∫sec(u) (-1 + sec²(u))² tan(u) du
apply u substitute v = sec(u)
= 2 * ∫(-1 + v²)² dv
expand
= 2 * ∫1 - 2v² + v⁴ dv
sum
= 2 (v - 2v³ + v⁵ )
3 5
substitute it back
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) )
3 5
add constant to the solution.
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) ) + C
3 5
Show that the equation represents a circle and find its center and radius.
x2 + y2 +6y + 2 = 0
Answer:
Step-by-step explanation:
The general equation of a circle can be expressed as (x-a)²+(y-b)² = r² where (a,b) is the centre of the circle and r is the radius.
To show that the equation x² + y² +6y + 2 = 0 represents a circle, we need to write it in the format above using the completing the square method.
Given x² + (y² +6y) + 2 = 0
First we need to complete the square of the square in parenthesis by adding the square of half of the coefficient of y i.e [tex](\frac{1}{2}*6) ^2[/tex] to the equation and adding the constant to the other side of the equation as well.
x² + (y² +6y) + 2 = 0
[tex]x^2+(y^2+6y+(\frac{1}{2}*6) ^2)+2 = 0+(\frac{1}{2}*6) ^2\\x^2+(y^2+6y+(3) ^2)+2 = 0+3 ^2\\x^2+(y^2+6y+9)+2 = 0+9\\x^2+(y+3)^2+2 = 9\\x^2+(y+3)^2+2-2 = 9-2\\x^2+(y+3)^2 = 7\\(x-0)^2+(y+3)^2 = 7\\[/tex]
Hence the equation represents a circle with centre C at (0, -3) and radius of √7
You are going shopping for some new sweaters, t-shirts, and pants. Sweaters (s) cost $29, t-shirts (t) cost $16, and pants (p)
cost $25. What algebraic expression models the total cost of clothes that you buy?
Suppose you bought 28 sweaters, 7 t-shirts, and 17 pairs of pants. How much did you spend?
Answer:
You spent $1349
Step-by-step explanation:
sweaters s = $29
t-shirts t = $16
pants p = $25
Cost = C
28s + 7t + 17p = C
28 ($29) + 7 ($16) + 17 ($25) = C
$812 + $112 + $425 = C
$1349 = C
the sum of 5x and 8x is less than the sum of 4x and -7
Answer:
false or not true
Step-by-step explanation:
5x + 8x < 4x + -7
combine like terms
13x<4x+-7
4x divided by 4 -7 divided by 4
x= -7/4
13x<-7/4
Jack is running back on his football team. The first play he gained 12 yards, second play loss 15 yards, third play gained 25 yards, and fourth play loss 2 yards. What was his total gains or losses?
Answer:
20
Step-by-step explanation:
The total gains of Jack if, In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards is 20 yards.
What is Subtraction?The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards.
Assume the gains can be denoted by positive and loss by negative,
Gains = 12 yards, 25 yards.
Total gain = 12 + 25 = 37 yards
Loss = -15 yards, -2 yards
Total loss = -15 + (-2) = -17 yards
Calculate the total gain as shown below,
Total gain = total gain + total loss
Total gain = 37 + (-17)
Total gain = 20 yards.
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In Texas, the coldest temperature ever recorded is -23 F. That's a lot chillier than in Florida, where the coldest recorded temperature is -2 F. How many degrees warmer is Florida's coldest recorded temperature than Texas's?
Answer:
21
Step-by-step explanation:
The answer is negitive 21 becuase it you sub and
After conducting some mathematical operations, we can conclude that Florida is warmer than Texas by 21°F.
What exactly are mathematical operations?In mathematics, an operation is a function that converts zero or more input values into a discrete output value. The number of operands in the operation determines how difficult it is. The order of operations refers to the rules that outline the sequence in which certain operations should be carried out in order to solve an expression. The following is the order of operations: parentheses, exponents, multiplication, division (from left to right), addition, and subtraction. PEMDAS (from left to right) (from left to right).
So, Florida is warmer than Texas by:
Florida's coldest temperature is -2°F.Texas's coldest temperature is -23°F.Now, calculate as follows:
23 - 221°FTherefore, after conducting some mathematical operations, we can conclude that Florida is warmer than Texas by 21°F.
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cleveland has 64 fl Oz of orange juice how many pints of orange juice does cleveland have??
Answer:
4 pints
Step-by-step explanation:
16 oz in a pint
224 fl oz equals how many gallons
Consider the strength data for beams given below :5.7 7.2 7.3 6.2 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.08.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.5 11.8 10.6Required:a. Construct a stem-and-leaf display of the data. What appears to be a representative strength value? Do the observations appear to be highly concentrated about the representative value or rather spread out?b. Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way?c. Do there appear to be any outlying strength values?d. What proportion of strength observations in this sample exceed 10 MPa?
Answer:
(a) Shown below
(b) Positively Skewed
(c) No Outlier
(d) 15%
Step-by-step explanation:
Arrange the data set in ascending order as follows:
S = {5.7 , 6.2 , 6.3 , 6.5 , 6.8 , 6.8 , 7 .0, 7 .0, 7.2 , 7.3 , 7.4 , 7.6 , 7.7 , 7.7 , 7.8 , 7.8 , 7.9 , 8.1 , 8.2 , 8.7 , 9 .0, 9.7 , 9.7 , 10.6 , 11.5 , 11.6 , 11.8}
(a)
Construct a stem-and-leaf display of the data as follows:
5 | 7
6 | 2 3 5 8 8
7 | 0 0 2 3 4 6 7 7 8 8 9
8 | 1 2 7
9 | 0 7 7
10 | 6
11 | 5 6 8
The representative strength value is the mid-value.
The mid-value is: 7.7
Thus, the representative strength value is 7.7.
(b)
No, the data does not appear to be highly concentrated about the representative value or rather spread out.
As we take the stem-and-leaf plot into consideration we observe that most of the observations are concentrated towards the right of the graph.
So, the data is right or positively skewed.
(c)
No, there doesn't appear to be any outlying strength values.
This is because all the values are closer to each other and none of the observations are too extreme.
(d)
The number of observations more than 10 MPa is, 4.
Total number of observations, 27.
Compute the proportion of strength observations that exceed 10 MPa as follows:
[tex]P(>10\ \text{MPa})=\frac{4}{27}=0.14815\approx 0.15[/tex]
Thus, the proportion of strength observations that exceed 10 MPa is 15%.
Question 3 (1 point)
(03.06)
Choose the point slope form of the equation below that represents the line that passes through the point (-1, 6) and has a slope of -3.
Answer:
Step-by-step explanation:
y -6 = -3(x + 1)
y - 6 = -3x - 3
y = -3x + 3
What is the estimate sum of 709, 645, 798, 704 and 658
⇔·⇔
Answer:
3550
Step-by-step explanation:
Round each number: 709 ⇒ 700, 645 ⇒ 650, 798 ⇒ 800, 704 ⇒ 700, 658 ⇒ 700Add the rounded numbers: 700 + 650 + 800 + 700 + 700 Start slow: 700 + 650 = 13501350 + 800 = 21502150 + 700 = 28502850 + 700 = 3550I hope this helps!
Answer:
3550
Step-by-step explanation:
Round each number: 709 ⇒ 700, 645 ⇒ 650, 798 ⇒ 800, 704 ⇒ 700, 658 ⇒ 700
Add the rounded numbers: 700 + 650 + 800 + 700 + 700
Start slow: 700 + 650 = 1350
1350 + 800 = 2150
2150 + 700 = 2850
2850 + 700 = 3550
Which of the following is a solution to the equation. X^2
x^2 -6x+5=0
A: -5
B: -1
C: =1/5
D: = 5
Answer:
x=1 or x=5
Step-by-step explanation:
x2−6x+5=0
Step 1: Factor left side of equation.
(x−1)(x−5)=0
Step 2: Set factors equal to 0.
x=1 or x=5
Sally works as an estimator for G&J Electric. She has determined that 550 feet of electrical cable will be needed to wire a new house. Later, Sally is told that the
homeowner has decide to cut back from a three-car garage to a two-car garage, which will eliminate two branch circuits, one of 23 feet and the other of 34 feet. How
many feet of wire will be needed now?
Answer:34
Step-by-step explanation:
i just did it
Answer: the number of feet needed after the change is 493 Feet
Step-by-step explanation:
you’re welcome
1.
Adrienne and Michelle are two hairstylists at a new age salon. They pay two different monthly
fees to rent a station at the salon.
The graph below represents Adrienne's profit she makes each month based on the number of
haircuts she performs.
Answer:
$50 is profit because every $50 it intersects.
X would be the $50 so 10x50=500-150=which would be $350.
I think this is right hope this helps!
TRUE OR FALSE: When two lines intersect then they create 4 linear pairs
Jens purchased a new ski jacked for $91. The Jacket was marked down 35%. What was the original price of the jacket?
Answer:
1.00-.35=.65
.65×140.00=$91.00
Can some body check my math on this one(question #6) I think it’s n=26 am I right?
Answer:
[tex]n=26[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-413.4=-15.9n[/tex]
To figure out the value of n, divide both sides by -15.9. The right will cancel. Thus:
[tex]n=(-413.4)/(-15.9)[/tex]
Use a calculator:
[tex]n=26[/tex]
So, the answer is 26.
So, yes, you are very correct!
Answer:
n=26
Step-by-step explanation:
We are given the equation:
[tex]-413.4=-15.9n[/tex]
We want to solve for the unknown variable, which is n. Therefore, we must isolate n on one side of the equation.
n is being multiplied by -15.9. The inverse of multiplication is division. Divide both sides of the equation by -15.9
[tex]\frac{-413.4}{-15.9} =\frac{-15.9n}{-15.9}[/tex]
[tex]\frac{-413.4}{-15.9}=n[/tex]
[tex]26=n[/tex]
Let's check our solution. Plug 26 in for n and solve.
[tex]-413.4=-15.9n[/tex]
[tex]-413.4=-15.9(26)[/tex]
Multiply -15.9 and 26.
[tex]-413.4=-413.4[/tex]
This checks out, so we know our solution is correct.
The solution to this equation is n=26 and you are correct!
By switching service providers, a family’s telephone bill decrease from about $50 a month to about $46. What was the percent of decrease?
Answer:
92%
Step-by-step explanation:
2+3+4+3+3+3x3x3x3x3x3x3x3x3x3x3x3x3x3
Answer:4782984
Step-by-step explanation:
Answer:4782984
Step-by-step explanation:
the product of 9 and the sum of a number x and 12
Answer:
X * 12 = 9
Step-by-step explanation:
The required model of the given situation is given as y = 9 (x + 12).
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
the product of 9 and the sum of the number x and 12 is given as
Let the product is equal to y
y = 9 (x + 12)
Thus, the required model of the given situation is given as y = 9 (x + 12).
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9+(-3)=______________
Answer:
6
Step-by-step explanation:
9-3=6
Since -3 is in (), you can just do 9-3 easily
Answer:
My answer to the question is 6.
9+(-3)=9-3=6.
Give a picture about real- life situation illustration percentage and decimals
Step-by-step explanation:
A good example that comes to find is the fuel gauge found on a car, this gauge allows the driver to monitor the percentage of fuel left in the car.
Let's assume the car fuel tank has a capacity of 100 liters. if the indicator is showing half-filled, to illustrate this in percentage it is written as 50% while decimal it will be 0.5.
what is the answer to: (4x)(7y) + (x)(3y)=
Answer:
31xy
Step-by-step explanation:
28xy + 3xy = 31xy
In need of some major help!!
The answer to your question is 4.8 kilometers. Brainliest?
Answer:
1.86
Step-by-step explanation:
What number is 23 percent of 556?
Answer:
127.88
Step-by-step explanation:
=>23/100*556
=>127.88
Answer:
127.88
Step-by-step explanation:
23 x 556 = 127.88
100
can you find two fractions that multiply together to make 12/20 can you find two fractions that multiply together to make 12/35
Answer:
4/5*3/4&6/7*2/5
Step-by-step explanation:
4/5*3/4=12/20
6/7*2/5=12/35
1 Point P(-12. 7) is reflected over the x-axis. What are the coordinates of P'?
Answer:
P prime would be (-12, -7)
Natalie has 1/2 gallon of milk. She pours an equal amount of milk each of 8 glasses.
Answer:
there are 4 quarts in a gallon so therefore the glasses are half a quart
Step-by-step explanation:
yes
1.46 x 10^-7 in standard form
Answer:
0.00000014 x
Step-by-step explanation:
The product of two whole numbers is 650 and their sum is 51. What are the two numbers?
Answer:
The numbers are 25 and 26.
Step-by-step explanation:
When you multiply 25 with 26 you get their product, 650. And when you add them you get the answer 51.