Answer:
[tex]\mathbf{\int \dfrac{x^3}{\sqrt{9x^4+ 6x^2 -1}} dx \ \ is \ \ equivalent \ \ to \ \ \dfrac{1}{18} \int ( \sqrt{2}* sec^2 \theta - sec \theta) d\theta}[/tex]
Step-by-step explanation:
[tex]\int \dfrac{x^3}{\sqrt{9x^4+ 6x^2 -1}} dx = \int \dfrac{x^3 \ dx}{\sqrt{(3x^22)^2 + 2(3x^2) (1) + 1-2}}[/tex]
[tex]\implies \int\dfrac{x^3 \ dx}{\sqrt{(3x^2 +1)^2-2}}[/tex]
let;
[tex]3x^2 + 1 = \sqrt{2}\ sec \theta[/tex]
[tex]6xdx = \sqrt{2} sec \theta tan \theta \ d \theta[/tex]
[tex]xdx = \dfrac{\sqrt{2}}{6} sec \theta tan \theta \ d \theta[/tex]
[tex]\implies \int\dfrac{x^2*x \ dx}{\sqrt{2 \sec^2 \theta -2}}[/tex]
[tex]\implies \int\dfrac{\dfrac{1}{3}(\sqrt{2} \ sec \theta - 1)*\dfrac{\sqrt{2}}{6} sec \theta tan \theta \ d\theta }{\sqrt{2 } \ tan \theta }[/tex]
[tex]\implies \dfrac{1}{18} \int ( \sqrt{2}* sec \theta - 1) \ sec \theta d \theta[/tex]
[tex]\implies \dfrac{1}{18} \int ( \sqrt{2}* sec^2 \theta - sec \theta) d\theta[/tex]
∴
[tex]\mathbf{\int \dfrac{x^3}{\sqrt{9x^4+ 6x^2 -1}} dx \ \ is \ \ equivalent \ \ to \ \ \dfrac{1}{18} \int ( \sqrt{2}* sec^2 \theta - sec \theta) d\theta}[/tex]
Find x of the triangle within the circle (geometry) :).
?=44
Bananas are curved because they grow towards the sun ☀️
A baker owns a small business. He produces bread in bags. Each bag needs 2.6 oz of dough. The baker purchased 10.4 lb of dough. How many bags of bread can be produced?
Answer:
4 bags of bread can be produced
Step-by-step explanation:
Hope this is right I'm still new to all this if not please critique me.
Thomas invests $50,000 in an account that compounds interest continuously and earns 15%. How long will it take for his money to triple? Round to the nearest tenth of a year.
Answer:
7.3 years
Step-by-step explanation:
Simplify the expression by removing symbols of grouping and combining like terms.
3(r − 4s) − 5(3r − 5s)
Step-by-step explanation:
the answer is -12r+13s
if u need the explanation I gotchuu just lemme know or need work shown
hope it helps<33
Which equation describes the same line asy- 3 =-1(x+ 5)?
OA. y=-1x- 2
O B. y= -1x-1
O C. y=-1x+8
O D. y=-1x-5
If the minute hand of a clock rotates 6 degrees every minute. Determine how minutes does it take to rotate 2160
degrees. (1 point)
Ot=360
Ot= 340
Ot=180
Ot = 2160
Answer:
Yo wassup. To your question it will be 360 degrees.
Step-by-step explanation:
Now bro can you mark as brainlest?
4.) Anoki wants to determine the height of a vertical lighthouse, shown below. He measures the angle of
elevation to the top of the lighthouse at a point 103 feet along level ground from the center of the base of the
lighthouse. The angle of elevation is 31º. Which of the following expressions gives the best approximation
of the height of the lighthouse, in feet?
D. 103 cos 31°
cos 31°
A.
103
tan 31°
B.
103
C. 103 sin 31°
E. 103 tan 31°
310
103
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the lighthouse is 103×tan 31°.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given that the distance between the Anoki and the lighthouse is 103 feet, while the angle between Anoki and the top of the lighthouse is 31°. Therefore, using the tangent function of the trigonometry we can write the height of the lighthouse as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
[tex]\rm tan(31^o) = \dfrac{\text{Height of the lighthouse}}{103\ feet}\\\\\text{Height of the lighthouse} = 103 \times tan(31^o)\\\\[/tex]
Hence, the height of the lighthouse is 103×tan 31°.
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the length of a rectangle is twice the width. the perimeter is 90 inches. what is the rectangles area? you write the equation 2w+2w+w+w=90 for the word problem. you solve and get 15. what is the answer to the problem?
A) The area is 450 in^2
B) The width is 15 inches.
C) The area is 112.5 in^2
D) The length is 30 inches.
One width and one length is half the perimeter.
90/2 = 45
Let the width = X
the length is 2 times the width so 2X
The sum of the two equals 45"
2X + X = 45
Simplify:
3x = 45
Divide both sides by 3:
x = 15
The width is 15 inches
Length = 30 inches.
Area = Length x width = 15 x 30 = 450 in^2
The area 450 in^2
Which of the following equations could be used to show the relationship between number of days and amount of soda consumed? Select all that apply. Prove your answer is correct using points on the graph.
Answer:
b and e
Step-by-step explanation:
Number of days = x
Amount of soda = y
An equation that can represent the relationship between amount of soda and number of days can be represented in the form of y = mx
Where slope (m) = y/x
Using any point on the line, say (1, 40),
m = 40/1
m = 40
Plug the value of m into y = mx
Thus, we have:
y = 40x
This can also be rewritten as:
y/x = 40
Therefore, the equations that can be used to represent the relationship are:
y = 40x or y/x = 40
1. Which of the following expressions is equal to m3?
m. 3
m + m + m
3
m. m. m
Answer:
m +m+m is equal to M3. hope it helps
Answer:
m.m.m
Step-by-step explanation:
I'm going to assume m3 signifies m³. If this be the case, then;
m.3 = m×3 = 3mwhere as
m+m+m = 3mbut
m.m.m = m×m×m = m³Addison rae i need bad bleep
Answer:
please get help
Step-by-step explanation:
Sleep
wake up
repeat
Answer:
Hate to break it to you
Step-by-step explanation:
Addison died two weeks ago
What is the volume of the following rectangular prism? 3 1/3 units^2
1 2/5 units
The volume of the given rectangular prism is 14/3 units³ or approximately 4 2/3 units³.
Given:
Rectangular base area = 3 1/3 units²
Height = 1 2/5 units
Convert the mixed number to improper fractions.
The rectangular base area can be written as:
= 3 + 1/3
= 3/1 + 1/3
= 10/3 units².
The height can be written as:
= 1 + 2/5
= 1/1 + 2/5
= 7/5 units.
Multiply the area of the base by the height.
Volume = Base area × Height
Volume = (10/3 units²) × (7/5 units)
Multiply the numerators and denominators separately.
Volume = (10 × 7) / (3 × 5) units³
Volume = 70 / 15 units³
Volume = 14/3 units³
Therefore, the volume of the given rectangular prism is 14/3 units³ or approximately 4 2/3 units³.
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Consider the population consisting of all computers of a certain brand and model, and focus on whether a computer needs service while under warranty.
a. Pose several probability questions based on selecting a sample of 100 such computers.
b. What inferential statistics question might be answered by determining the number of such computers in a sample of size 100 that need warranty service?
a. The probability questions are given below.
b. The inferential statistics question is:
"What is the estimated proportion of computers in the population that need warranty service based on the observed proportion in the sample?"
We have,
a.
Probability questions based on selecting a sample of 100 computers:
- What is the probability that exactly 5 computers in the sample need warranty service?
- What is the probability that more than 10 computers in the sample need warranty service?
- What is the probability that at least 2 computers in the sample need warranty service?
- What is the probability that none of the computers in the sample need warranty service?
- What is the probability that the proportion of computers needing warranty service in the sample is greater than 0.3?
These questions can provide insights into the likelihood of certain outcomes within the sample of 100 computers.
b.
Inferential statistics question that can be answered by determining the number of computers needing warranty service in a sample of size 100:
"What is the estimated proportion of computers in the population that need warranty service based on the observed proportion in the sample?"
By determining the number of computers in the sample of 100 that need warranty service, we can use inferential statistics to make an estimate or inference about the proportion of the entire population of computers of that brand and model that may require warranty service.
This can help in understanding the warranty service needs of the entire population based on the information gathered from the sample.
Thus,
a. The probability questions are given above.
b. The inferential statistics question is:
"What is the estimated proportion of computers in the population that need warranty service based on the observed proportion in the sample?"
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2 of 2
X= 1
True
False
Answer:
of means to multiple so it would equal 4 so the answer is false
Does this graph represent a function? Why or why not?
Answer:
B. No, because it is not a straight line.
Have a nice day!!!
How many births occur among women under the age of 20?
Answer:
what do you mean?
Step-by-step explanation:
Arrange the numbers as they appear from left to right on a horizontal number line. -5/7, 2 5/7, 5/7, -1 5/7, 1 2/7, -1/7, -2 2/7
Plz be quick will give Brainiest!
Answer:
-2 2/7, -1 5/7, -5/7, -1/7, 5/7, 1 2/7, 2 5/7
Answer:
the answer is on the image below, hope this helps!
|
v
Iron can exist as a solid or liquid. Which statement best comparison solid iron and liquid iron?
A. Solid iron and liquid iron have the same type of atoms.
B. Solid iron and liquid iron have different types of atoms.
C. Solid iron is an element, and liquid iron is a compound.
D. Liquid iron is an element, and solid iron is a compound.
Answer: Iron, a solid at room temperature, becomes a liquid at 2800 degrees Fahrenheit (really, REALLY hot) and a gas at 5182 degrees Fahrenheit (about half the temperature of the sun). When things are hot, the molecules and atoms move around more and faster, and when they are cold they are slower.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Identify the coefficient(s) and constant(s) in this expression. 9x - 8y + 6
Trolls will be reported have a right answer please
Answer:
the coefficient are 9 and -8
the constant is 6........
ILL GIVE A BRAINLEST!!!! TO THE FIRST ONE WHO ANSWERS THIS PLZ I NEED HELP ASAP!!!
Answer:look at the picture for the answer
If f(x)=9−4 |x+1|, find f(−5). −15 −7 7 23
Answer:
If f(x) = 9–4 |+1|, find f(-5)?
Step-by-step explanation:
15
-7
7
23
ANSWER 23
The value of function f (- 5) will be;
⇒ f (-5) = - 7
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The function is,
⇒ f (x) = 9 - 4 |x + 1|
Now,
The function is,
⇒ f (x) = 9 - 4 |x + 1|
Substitute x = - 5, we get;
⇒ f (-5) = 9 - 4 |- 5 + 1|
⇒ f (-5) = 9 - 4 |- 4|
⇒ f (-5) = 9 - 4 × 4
⇒ f (-5) = 9 - 16
⇒ f (-5) = - 7
Thus, The value of function f (- 5) will be;
⇒ f (-5) = - 7
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xyz-qrs and the scale factor from xyz to qrs is 2/5. what is the length of side rs?
Answer:
RS = 10
Step-by-step explanation:
We are told that to get ∆QRS, the scale factor of ⅖ was used. To get side RS, we would multiply the side length of the side that corresponds to RS.
YZ corresponds to RS.
YZ = 25
Thus,
RS = 25*⅖
RS = 10
Please help me with this question
Answer:
I think it is 4×10^-2
DO NOT FORGET STAY SAFE AT HOME
Philip ran 438 miles yesterday. Michael ran 158 miles yesterday.
How much farther did Philip run than Michael?
A. 338 miles
B. 212 miles
C. 314 miles
D. 234 miles
Step-by-step explanation:
Distance ran by Philip=438 miles
Distance ran by Michael=158 miles
Distance Philip run farther than Michael=(Distance ran by Philip-Distance ran by Michael)
438 miles-138miles
=280miles
Hope it helps you
X
X
What is the value of x
Answer:
2x..................
Two parallel lines intersected by more than one transversal. Let x=45 find measure of angle 1,2 and 3
Answer: to me i think u ar missing the distance between the parallel lines
Step-by-step explanation:
8. Glass Garbage Generation A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds. 0.7135 Source: Michael D. Shook and Robert L. Shook, The Book of Odds. 9. College Costs The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for a recent academic year. Suppose
Answer:
.7147
Step-by-step explanation:
Let P be the probability of 55 families having mean more than 17
P { (17-17.2)/ (2.5/√55) }
P(- 0.5933 )
= - .2765 [ From the z table ]
P be the probability of 55 families having mean less than 18
P { (18 -17.2)/ (2.5/√55) }
P( 2.3732 )
= .9912 [ From the z table ]
Probability of mean between 17 and 18
= .9912 - .2765
= .7147
what is the length of ST?
Answer:
5 cm
Step-by-step explanation:
Let's assume this is a number line were given.
Distance of S from 0 = 4 units
Distance of T from 0 = 9 units
Length of ST = the difference between T and S
ST = |9 - 4| = 5 units = 5 cm
This means S and T are 5 cm apart.
Please help me with this anyone I beg
Answer:
A)336
B) In how many ways can you arrange 8 people in 3 different chairs?
C) 21
D) You want to buy 3 cartoon books from a book store that has 7 cartoon books. In how many ways can you select?
Step-by-step explanation:
A) P(n, r) = P(8, 3)
Formula for permutation is;
P(n, r) = n!/(n - r)!
P(8, 3) = 8!/(8 - 3)!
P(8, 3) = (8 × 7 × 6 × 5!)/5!
5! will cancel out to give;
P(8, 3) = (8 × 7 × 6)
P(8, 3) = 336
B) In how many ways can you arrange 8 people in 3 different chairs?
C) C(n, r) = C(7, 2)
Formula for combination is;
C(7, 2) = n!/(n - r)!r!
Thus;
C(7, 2) = 7!/(7 - 2)!2!
C(7, 2) = (7 × 6 × 5!)/(5! × 2 × 1)
5! will cancel out to give;
C(7, 2) = 7 × 6/2
C(7, 2) = 21
D) You want to buy 3 cartoon books from a book store that has 7 cartoon books. In how many ways can you select?
Grandma's Recipe for Sugar Cookies
1 cups kutter
2 cups sugar
4 eggs
12 teaspoon baking powder
1% cups flour
4 teaspoon salt
Your sister wants to make more cookies and decides to use 4 cups of sugar. She says that she
will need to use 3 cups of flour. Do you agree with her? Explain your reasoning.
