Answer:
Step-by-step explanation:
In the first part, we are given the function:
[tex]\int \dfrac{x^6}{\sqrt{1+x}^2} \ dx[/tex]
Suppose we make x = tan θ
Then dx = sec² θ.dθ
[tex]= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* dx[/tex]
[tex]= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* sec ^2 (\theta) * d\theta[/tex]
Since; sec² θ - tan² θ = 1
sec² θ = 1+ tan² θ
[tex]sec \ \theta = \sqrt{1 + tan^2 \ \theta}[/tex]
∴
[tex]= \int \dfrac{tan^6 (\theta)}{sec \ \theta}* sec ^2 (\theta) * d\theta[/tex]
[tex]= \int tan^6 (\theta)* sec (\theta) * d\theta[/tex]
Thus; In the first part, Use x = tan θ, where [tex]- \dfrac{\pi}{2} < \theta <\dfrac{\pi}{2}[/tex], since the integrand comprise the expression [tex]\sqrt{1+x^2}[/tex]
From the second part by using substitution method;
[tex]\int \dfrac{x^6}{\sqrt{1+x^2}} \ dx = \int \mathbf{tan^6(\theta) * sec ( \theta) } \ d \theta[/tex]
Quick. What is the product of the LCM and the GCD of 6 and 9? ANSWER FAST
I need a answer solved, WITH the explanation done well.
The question is:
What percentage of students chose hockey or softball?
Answer:
16%+26%= 42%
Answer: 32% is the answer
Step-by-step explanation: since the question says What percentage of students chose hockey or softball? add the presentage of hockey and softball and you will get 32% hope it helps
What is an equation of the line that passes through the points (-4, -4) and (4, 6)?
Answer:
y = (5/4)x+1
Step-by-step explanation:
[tex]\frac{y+4}{x+4} =\frac{-4-6}{-4-4}[/tex]
[tex]\frac{y+4}{x+4} = \frac{-10}{-8} \\or, 4(y+4) = 5(x+4)\\or, 4y= 5x+20-16\\or, y= \frac{5}{4}x+1[/tex]
Quickly Need help ASAP
Answer:
It's (B), using L'Hopital's Rule.
An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9. Is there sufficient evidence at the 0.1 level to support the testing firm's claim?
Answer:
The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.
Step-by-step explanation:
An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:
At the null hypothesis, we test if the mean is the same, that is:
[tex]H_0: \mu = 59.5[/tex]
At the alternate hypothesis, we test that it is different, that is:
[tex]H_a: \mu \neq 59.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
59.5 is tested at the null hypothesis:
This means that [tex]\mu = 59.5[/tex]
After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.
This means that [tex]n = 250, X = 59.2, \sigma = 1.9[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{59.2 - 59.5}{\frac{1.9}{\sqrt{250}}}[/tex]
[tex]z = -2.5[/tex]
Pvalue of the test and decision:
The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.
Looking at the z-table, Z = -2.5 has a pvalue of 0.0062
2*0.0062 = 0.0124
The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.
Please help me it’s simple but I just have forgotten
9514 1404 393
Answer:
y = -3x
Step-by-step explanation:
Your solution will be in the form ...
y = (something)
In order to get the y-term by itself, you need to add the opposite of everything else*:
3x +y +(-3x) = 0 +(-3x)
y = -3x . . . . . simplify
_____
* Anything you do to one side of the equation must also be done to the other side. Here, we added -3x to both sides.
Ashas age is twice the age of Roman. After how many years will Roman be two third of Ashas age?
Answer:
5
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEE
Answer:
The perimeter of rectangle JKLM is 16 units.
Step-by-step explanation:
Perimeter is the area around the shape, so if you look at the space between K and J, the units there are 7. Multiply 7 by 2 (since there are two sides), and then add 2. 2 + 14 = 16.
Answer:
17 units
Step-by-step explanation:
can u mark me as brainliest?
what 2 number multiply to be -12 and add to be -1
Write the absolute value equation that is represented by the graph
Answer:
Step-by-step explanation:
g(x) = -|x-3| +4
What is the system of linear equations to represent the situation?
Answer:
x+y= 30
8x+7.5y=234
you need to work 18 hours as a dog walker and 12 hours at the carwash
Step-by-step explanation:
x is the number of hours spent dog walking
y is the number of hours spent at the car wash
x+y is to total number of hours work (30)
8x is the amount made dog walking
7.5y is the amount made working at the carwash
234 is the total amount made by working 30 hours
x+y= 30
8x+7.5y=234
to solve:
x+y=30 (isolate the variable x) x=30-y
8(30-y)=234 (substitute in the 30-y for x)
240-8y+7.5y=234 (distribute the 8)
240-.5y=234 (combine like terms)
-.5y=-6 (subtract 240 from each side)
y=12 (divide by .5)
x+12=30 (put 12 in for y)
x=18 (subtract 12 from both sides)
you need to work 18 hours as a dog walker and 12 hours at the carwash
What are the values of a, b, and c in the quadratic equation –2x2 + 4x – 3 = 0?
a = 2, b = 4, c = 3
a = 2, b = 4, c = –3
a = –2, b = 4, c = 3
a = –2, b = 4, c = – 3
Answer:
a = –2, b = 4, c = – 3
Step-by-step explanation:
We are given the following quadratic equation in the question:
-2x^2 + 4x - 3 = 0−2x
2
+4x−3=0
General form of quadratic equation:
ax^2 + bx + c = 0ax
2
+bx+c=0
Comparing the given equation to general quadratic equation, we get,
a = -2, b = 4, c = -3a=−2,b=4,c=−3
Thus, the correct answer is
Option D) a = –2, b = 4, c = – 3
The values of a, b, and c in the given quadratic equation are a = -2, b = 4, c = -3
What is a quadratic equation?The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Given is a quadratic equation -2x²+4x-3 = 0, we need to find the values of a, b, and c in the given quadratic equation.
The standard equation of a quadratic equation is ax²+bx+c = 0,
Comparing the given equation with the standard equation,
We get, a = -2, b = 4, c = -3
Hence, the values of a, b, and c in the given quadratic equation are a = -2, b = 4, c = -3
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I would like help thanks!
Answer:
B
Step-by-step explanation:
if you connect and extend to points it forms a line with a y-intercept of 2 when x is zero
y = mx + b m the slope equals 1
y = x +2
What does x have to equal to make the statement true (solve for x)
a. 2x =10
b. -3x = 21
c. 1/3(x) = 6
d. -1/2(x) = -7
Answer:
See below
Step-by-step explanation:
2x = 10
Divide by 2.
x = 5
x has to equal 5 to make the first statement true.
Proof:
2x = 10
2(5) = 10
10 = 10
-3x = 21
Divide by -3.
x = -7
x has to equal -7 to make the second statement true.
Proof:
-3x = 21
-3(-7) = 21
21 = 21
1/3(x) = 6
Multiply by 3 to cancel the fraction.
x = 18
x has to equal 18 to make the third statement true.
Proof:
1/3(x) = 6
1/3(18) = 6
6 = 6
-1/2(x) = -7
Multiply by -2 to cancel the fraction.
x = 14
x has to equal 14 to make the fourth statement true.
Proof:
-1/2(x) = -7
-1/2(14) = -7
-7 = -7
A jar contains 4 marbles marked with the numbers 1 through 4. You pick a marble at random. What is the
probability of not picking the marble marked with the number 3? Enter your answer as a simplified
fraction.
The probability of not picking the marble marked with the number 3 is
Answer:
p =favorable outcome/possible outcome
p(not 3)=3/4
Find the measure of angle BAC. (The figure is not drawn to scale.)
A. 22
B. 34
C. 68
D. 136
If angle BOC in circle is 68° then the measure of angle BAC is 34°.
Given that angle BOC in the circle is 68°.
We have to find the angle BAC.
We have that m∠BOC=arc BC ------by central angle.
we have m∠BOC=68°.
therefore arc BC=68°.
We know that the inscribed angle is half that of the arc it comprises so m∠BAC=1/2 *(arc BC)-----1
In geometry one of the theorem states states that angle at the center of a circle is twice angle at the circumference.
We have that arc BC=68°
substitute arc BC in equation 1 to get the measurement of ∠BAC.
m∠BAC=[tex]68/2[/tex]
=34°
Hence if angle BOC in circle is 68° then the measure of angle BAC is 34°.
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Suki named a fraction that was not a multiple of. Which fraction could she have
named?
A. 6/4
B. 9/4
с. 10/4
D.12/4
Paul is filling the rectangular prism shown with cubes that measure 14 inch along each edge.
Answer:
Step-by-step explanation:
Olive flipped a coin and rolled a number cube with the
numbers 1-6 on it. What is the probability that she flipped
heads and rolled an even number?
1
N
3
4
5
6
H
H1
H2
H3
H4
H5
H6
T
T1
T2
T3
T4
T 5
T6
3
3
Answer:
p
Step-by-step explanation:
2x-y=-5 x+y=8 elimination
Currently, the number of people entering a shopping mall is 109. It is estimated that the number of people entering the shopping mall will decrease by 3% each hour. Find the total number of people entering the shopping mall at the end of 4 hours. (Round your answer to the nearest whole number if necessary.)
Answer:
96 people.
Step-by-step explanation:
Exponential equation for a decreasing amount:
The exponential equation for a decreasing amount is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial rate and r is the decay rate, as a decimal.
Currently, the number of people entering a shopping mall is 109.
This means that [tex]A(0) = 109[/tex]
It is estimated that the number of people entering the shopping mall will decrease by 3% each hour.
This means that [tex]r = 0.03[/tex]
So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 109(1-0.03)^t[/tex]
[tex]A(t) = 109(0.97)^t[/tex]
Find the total number of people entering the shopping mall at the end of 4 hours.
This is A(4). So
[tex]A(4) = 109(0.97)^4 = 96.49[/tex]
Rounding to the nearest whole number, 96 people.
David inherited some land in 1960 that was valued at $25,000. The value of the land has increased 10% every 5 years. Which function will calculate the value of the land x years after 1960?
Answer:
f(x) = 25,000(0.1)^5x
Step-by-step explanation:
Solve t - 4 > 12
1. t > -12
2. t > 12
3. t > -16
4. t > 16
Answer:
4. t>16
hope it helps......
Automobile engineers wanted to check the effect of a new automatic transmission on mileage. They selected 50 cars of the same make and model. Twenty-five of the cars used the old transmission, while the other 25 cars used the new model of transmission. A hypothesis test on the difference between the means was conducted. Which one of the following is a condition necessary to conduct this test?
a. The standard deviation of each group should be different.
b. The sampling distribution of the difference between the sample means is bimodal.
c. Since the data were random, no linear regression was possible.
d. Twenty-five cars are randomly selected with the new transmission and 25 with the old transmission.
e. The difference between the means was within one standard deviation.
Answer:
d. Twenty-five cars are randomly selected with the new transmission and 25 with the old transmission.
Step-by-step explanation:
A hypothesis test on the difference between the means must satisfy the following conditions
1) the samples must be randomly selected
2) each sample must have a known standard deviation
3) the samples must be independent
4) the samples must be from normal distribution
Hence only part d gives the right answer.
DUE IN 3 MINUTES PLEASE HELP
Answer:
B. 12^3 - 12^2 - 11
Step-by-step explanation:
........
Approximately how many square inches of space are blank?
Answer:
blank area = 1.5π units²
Step-by-step explanation:
area of full circle = πr² = π6² = 36π units²
blank area = (15/360)(36π) = 1.5π units²
The area blank in a circular mosaic pattern is 4.71 square units.
What is a circle?A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.
For the given situation,
The diagram shows the circle with a central angle cutout.
The central angle, θ = 15°
Radius of the circle, r = 6 units
The formula of area blank in circle is
[tex]Area_{blank} = \frac{\theta}{360}\pi r^{2}[/tex]
⇒ [tex]Area_{blank} = \frac{15}{360}(3.14) (6)^{2}[/tex] [∵ π = 3.14 ]
⇒ [tex]Area_{blank} = 0.0416(3.14) (36)[/tex]
⇒ [tex]Area_{blank} = 4.71[/tex]
Hence we can conclude that the area blank in a circular mosaic pattern is 4.71 square units.
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Write an expression to show the sum of g and h reduced by 11.
Answer:
Required expression = (g+h) - 11
What is 3.4 million divided by 60
Answer:
[tex]56666\frac{2}{3}[/tex]
Step-by-step explanation:
Answer:56,666.666
Step-by-step explanation:
Respuesta
Which is the simplified form of the expression?
Answer:
[tex]\frac{1}{x^21y^12}[/tex]
Step-by-step explanation:
What is the the volume of the rectangular prism?
PLEASE HELP FAST! 15 POINTS!!
Answer:
540 in³
Step-by-step explanation:
v = lwh
v = 18 * 10 * 3
c = 540 in³
Answer:
v= length x width x height so 10x18x3= 540in cubed
Step-by-step explanation: