Answer:
[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx \approx \boxed{0.862854}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Methods: U-Substitution and U-Solve
Special Integrals:
Sine Integral:Step-by-step explanation:
*Note:
The problem is too big to fit all work. I will assume that you know how to do basic calculus.
Step 1: Define
Identify given.
[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite:Step 3: Integrate Pt. 2
Identify variables for u-substitution.
Set u:Step 4: Integrate Pt. 3
[Integral] Apply Integration Method [U-Substitution]:Step 5: Integrate Pt. 4
Identify variables for u-substitution for the 1st integral.
Use another variable besides u to avoid confusion with earlier substitutions.
Set v:Step 6: Integrate Pt. 5
Solve the 1st integral using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int\limits^{x = 1}_{x = 4} {\cos (u - e)} \, du & = \int\limits^{x = 1}_{x = 4} {\cos v} \, dv \\& = \sin v \bigg| \limits^{x = 1}_{x = 4} \\& = \sin (u - e) \bigg| \limits^{x = 1}_{x = 4} \\& = \sin (x) \bigg| \limits^{x = 1}_{x = 4} \\& = \sin 1 - \sin 4\end{aligned}[/tex]
Step 7: Integrate Pt. 6
To solve the 2nd integral, we use the same methods as "Step 6":
[tex]\displaystyle\begin{aligned}\int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du & = \int\limits^{x = 1}_{x = 4} {\frac{\sin e \sin u + \cos e \cos u}{u}} \, du \\& = \sin e \int\limits^{x = 1}_{x = 4} {\frac{\sin u}{u}} \, du + \cos e \int\limits^{x = 1}_{x = 4} {\frac{\cos u}{u}} \, du \\& = \sin (e) \text{Si} (u) \bigg| \limits^{x = 1}_{x = 4} + \cos (e) \text{Ci} (u) \bigg| \limits^{x = 1}_{x = 4} \\\end{aligned}[/tex]
[tex]\displaystyle\begin{aligned}\int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du & = \sin (e) \text{Si} (x + e) \bigg| \limits^{x = 1}_{x = 4} + \cos (e) \text{Ci} (x + e) \bigg| \limits^{x = 1}_{x = 4} \\& = \bigg[ \sin (e) \text{Si} (1 + e) - \sin (e) \text{Si} (4 + e) \bigg] + \bigg[ \cos (e) \text{Ci} (1 + e) - \cos (e) \text{Ci} (4 + e) \bigg] \\\end{aligned}[/tex]
Step 8: Integrate Pt. 7
Combine our 2 integral values to obtain a final answer:
[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^{x = 1}_{x = 4} {\cos ( u - e)} \, du - e \int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du \\\begin{aligned}& = \sin 1 - \sin 4 - e \bigg[ \sin (e) \text{Si} (1 + e) - \sin (e) \text{Si} (4 + e) + \cos (e) \text{Ci} (1 + e) - \cos (e) \text{Ci} (4 + e) \bigg] \\& \approx \boxed{0862854} \\\end{aligned}[/tex]
∴ we have evaluated the given special definite integral.
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Topic: Calculus
35. Cindy walks at a constant rate of 2 miles per hour. She leaves home to walk to her friend Jenny's house at 9 am. When she is halfway there, she thinks that she left her phone at home. She turns around and begins to walk back home, but when she is halfway home (from where she turned around), she finds her phone. She turns back around to walk to Jenny's and arrives there at 10 am. How far apart are Cindy's house and Jenny's house?
Hint: Draw a diagram!
Answer:
you're screwed
Step-by-step explanation:
don't forget your phone so anyon doesn't ever have to do this
Cindy's house and Jenny's house are 1.33 miles distant from each other.
What is speed?Speed is defined as the rate at which an object is moving (covering a particular distance). It is a scalar quantity as it defines only the magnitude and not direction.
The SI derived unit for speed is meter per second (m/s).
Given,
Cindy leaves house at 9 am and reaches to jenny house at 10 am
Let the distance between Cindy and Jenny house is x
First, Cindy walks half way to jenny house = x/2
then Cindy take U-turn and walks half way to home = x/4
again Cindy take U-turn and reaches jenny house = 3x/4
Total distance walked by Cindy = x/2 + x/4+ 3x/4
= x/2 + x
= 3x/2
Speed of jenny is 2 miles per hour
She walks 3x/2 distance and reaches Jenny house in one hour
⇒ 3x/2 = 2
⇒ 3x = 4
⇒ x = 4/3
⇒ x = 1.33 miles
Hence, distance between Cindy's and jenny's house is 1.33 miles.
Learn more about speed here:
https://brainly.com/question/6280317
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Simplify The Expression
5x-4y+2(y+x)
Answer:
5x-2y
Step-by-step explanation:
5x-4y+2y+2x=
7x-2y
Pls help
Due pretty soon
Answer:
I think the area is 25 im unsure of the perimeter amd sorry if I'm wrong.
For which distributions is the median the best measure of center?
Select each correct answer.
Answer:
d
Step-by-step explanation:
d has similar ones from the middle to the right and the left
PLSS help
Elsa used 23 of a cup of sugar in chocolate cupcakes and 34 of a cup of sugar in vanilla cupcakes. Which choice is the MOST reasonable for how much more sugar Elsa used in the vanilla cupcakes?
A)7/12 cup
B) 1/2 cup
C) 1/6 cup
D)1/12 cup
Answer:
1/2 cup
Step-by-step explanation:
Subtract 34 - 23 = 11 AND the closed number is 12 which is 1/12.
Hope this helps!
PLS HELP!
Give three real-world examples of rectangular prisms. Then give two real-world examples of triangular prisms. Explain how you know the object you chose represents a prism.
Answer:
A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent.?
Step-by-step explanation:
Is that what you wanted?? sorry if its not
A game show has a contestant pick one of five doors to reveal the prize the contestant wins. A photo of a new boat is behind one of the doors, and joke prizes are behind the others. Which BEST describes the probability of winning the new boat?
Hi,
It is unlikely that the game show contestant will win the boat.
To be exact it is 20% chance that the game show contestant will win the boat.
XD
PLS HELP!! GIVING BRAINLIEST TO FIRST CORRECT ANSWER!!+50 POINTS
Answer:
is there any question?
so I can answer
Answer:
See below
Step-by-step explanation:
7) a rectangle 12 x 8 = 96
plus semi-circle 1/2 pi r^2 = 1/2 pi 4^2 = 25.132
total = 121.132 m^2
8) Circle area = pi r^2
large circle pi * 2^2 = 4pi
MINUS the smaller one pi 1.5^2 = 2.25 pi
total = 1.75 pi = 5.498 in^2
9) Square area = 10 x 10 = 100
minus circle pi r^2 = 25pi total = 21.46 ft^2
What is the circumstance of the circle? (3.14 for pi)
Answer:
131.88in
Step-by-step explanation:
C = 2πr
The radius of the circle is from center to the perimeter.
In this case the radius is 21in.
3.14 for pi
C = 2(21)(3.14)
C = 42(3.14)
C = 131.88in
Answer:
the answer for this question should be 131.88 because 21 is the radius and the radius is half of the diameter which is 42 because you need to multiply 21 times 2 getting an answer for the diameter but we use the formulas.
C=2 times 3.14 times 21= 131.88
C= 3.14 times 42=131.88
Step-by-step explanation:
You pick two of the cards below at random. What is the probability that the card is an even number greater than 5?
The Cards: 3, 4, 5, 6, 7, 8
Answer:
2 in six chance or 1:3 simplified
Step-by-step explanation:
Answer:
1/3.
Step-by-step explanation:
The 2 numbers whcih are even and > 5 are 6 and 8.
So the Required Probability
= 2/6 = 1/3.
the answer to this, i don’t understand it
Answer: the answer should be 9.22
Step-by-step explanation:
the formula is a^2 +b^=c ^
So 49 plus 36 equals 85
And the square root of 85 is 9.22
somebody had a seizure while making this question, please help
Check the picture below.
[tex]\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}asn ~~ \begin{cases} a=apothem\\ n=\stackrel{side's}{number}\\ s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ a=7\\ s=8.1\\ n=6 \end{cases}\implies \stackrel{\textit{area of the hexagonal base}}{A=\cfrac{1}{2}(7)(8.1)(6)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{volume of a prism}\\\\ V=Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(7)(8.1)(6)\\ V=3572.1 \end{cases}\implies 3572.1=\cfrac{1}{2}(7)(8.1)(6)h \\\\\\ 3572.1=170.1h\implies \cfrac{3572.1}{170.1}=h\implies \boxed{21=h}[/tex]
well, the length of the tunnel is "h", now two 8 meters cars, that's 8+8=16 meters plus a 3 meter connector between them, that's 16 + 3 = 19 meters, can those two cars connected like so fit inside the tunnel? sure thing, "h" can fit 19 meters just fine.
The figure below shows a rectangular prism with a height of h inches.
Answer:
the answer is d
Step-by-step explanation:
your welcome
10 < 3 (r-3) + 1
Round Decimals to the nearest hundredth place
Answer:
r>6
Step-by-step explanation:
10<3r+3 x -3+1
Solve by distributing:
10<3r-9+1
Simplify the arithmetic:
10<3r-8
Simplify the arithmetic:
3r-8>10
Add 8 to both sides:
3r-8+8>10+8
Simplify the arithmetic:
3r>10+8
Simplify the arithmetic:
3r>18
Divide both sides by 3:
3r/3 > 18/3
Simplify the fraction:
r>18/3
Find the greatest common factor of the numerator and denominator:
r> 6x3/1x3
Factor out and cancel the greatest common factor:
r>6
I need help I have been stuck on it FOREVER!!!
Answer:
22.
Step 1: Find area of inner square = 4 ft × 12 ft = 48ft2
Step 2: Find area of outer shape =
25 ft +11 ft = 36 cm2
Step 3: Area of shaded region = area of outer shape – area of inner square
= 36 ft2 – 48 ft2
= 12 ft2
Write and solve a proportion to answer the question. (Skills Review Handbook) 21. 70% of what number is 98?
Answer:
451.61
Step-by-step explanation:
1) Set a linear equaion
[tex] \frac{98}{x} = \frac{21.70}{100} [/tex]
2) Cross multiply
[tex]21.70x = 98 \times 100[/tex]
3) Multiple the right side
[tex]21.70x = 9800[/tex]
4) Divide both side by 21.70
[tex] \frac{21.70x}{21.70} = \frac{9800}{21.70} [/tex]
5) Solve the linear equation
[tex]x = 451.6129032[/tex]
[tex]x≈451.61[/tex]
Then 21.70% of 451.61 is 98
27. The fifth and thirteenth terms of an arithmetic sequence are 5 and 77 , respectively. Find the first term and the tenth term.
Answer:
if the first term is 13, the second will be 13+x, the third 13+2x and so on, the tenth term will be 13+9x=40 9x = 27 x = 3 so the difference between the terms is 3 the sum of the first 10 terms is 13*10 + (x+2x+…+9x) = 130 + 45x = 130 + 45*3 = 130 + 135 = 265
Step-by-step explanation:
hope this helps you!
PLEASE HELLLP i will give you brainiest points and everything!!!!
Answer:
A = 8cm
B = 11cm
C = 4cm
D = 4cm
(b)
11x4=32
11x4=32
8x11=88
8x11=88
88+88+32+32=240 (i think)
(c)
240
8x4=32
8x4=32
240+32+32=302
Step-by-step explanation:
What is the measure of x? Image below
Answer:
Angle x= 76
Step-by-step explanation:
angle DIJ = 180-107
=73
angle x =angle DJI =180-31-73
=76
both angles x and DJI are equal because they both intersect with each other.
Find the areas of the figures below.
Answer:
4. 42yds squared 5. 95 m squared 6. 152.5 m squared 7. 252cm squared 8. 310’ squared 9. 23cm squared
Step-by-step explanation:
BRAINLIESTT again, lol, i have no life.
Answer:
3/5+1/10=7/10
Step-by-step explanation:
Multiplying both sides of 3/5, we get a common denominator (6/10)
The adding the two together, we get 7/10.
Good luck! Hope this helps!
Answer:
LCD = 5
3/5 *2 because the denominators must be equal so 6/10 + 1/10
Then the full answer is 7/10
Hope this helps!
The dot plots below show the scores for a group of students for two rounds of a quiz:
Which of the following inferences can be made using the dot plots?
A. The range of each round is the same.
B. There is no overlap between the data.
C. Round 1 scores were higher than round 2 scores.
D. Round 2 scores were lower than round 1 scores.
Answer: A. The range of each round is the same.
Step-by-step explanation:
Below shows the total score for both rounds. As you can see the totals for both rounds are very close so their range is most likely the same.
Round 1
(2 x 2) + (3 x 3) + (4 x 2) + 5 = 26
4 9 8
Round 2
(3 x 2) + (4 x 3) + (5 x 2) + 2 = 30
6 12 10
-(-9)_l-9l is it grater than or less than or eqaul to?
Answer:
Equal to
Step-by-step explanation:
Hello!
Let's simplify the left side:
- ( -9 ) 9Remember that the negative sign also means opposite, so the opposite of negative 9 is positive 9.
Let's simplfy the right side:
| - 9 |9Remember that in an absolute value bracket, any positive value stays positive, but any negative value turns to the positive value.
So the inequality is 9 _ 9
Therefore the sign should be "=" as 9 is equal to 9.
Select the correct answer. What is 10 1/2 divided by 2 1/4 ? A. 23 5/8 B. 4 2/3 C. 2 3/4 D. 1 1/2
Answer:
The answer is B. 4_2/3
Step-by-step explanation:
21/2 / 9/4 =21/2 * 4/9 =42/9 =4 6/9 =4 2/3
Answer: B) 4 2/3
Step-by-step explanation:
10 1/2= 21/2
2 1/4= 9/4
21/2 divided by 9/4=
21/2 x 4/9= 84/18=
4 2/3
What is 26% of 600?
Enter your answer in the box.
Answer: 156
Step-by-step explanation: do 600 x 0.26 since 0.26 = 26%, 0.26 x 600 is 156.
Answer:
156
Step-by-step explanation:
600/x=100%/26%
[tex]\frac{x}{600}[/tex] [tex]\frac{26}{100}[/tex]
x=156
Explain the difference between center and shape of a data set.
The center is the median and/or mean of the data. And, the shape describes the type of graph.
There are many shapes data sets could show. One example would be asymmetric data set. In this case, both sides of the picture would look almost exactly or could be exactly (rarely) alike. In this case, the mean could be used as a measure of center.
When the data is skewed right or left, the pictorial representation of the data will show fewer data points on the side where it is skewed and more data on the opposite side. The tail will be longer on the right if it is skewed right and vice versa.
In skewed right data, the mean will be greater than the median, and if the data is skewed left, the mean will be less than the median. The mean is not the measure of the center when the data is skewed.
Blue whales eat an average of 5,000 pounds of fish daily, with a standard deviation of 850 pounds. Approximately what percentage of blue whales eat more than 6,700 pounds of fish?
A. 2.5%
B. 5%
C. 15.87%
D. 31.74%
Answer:
it is C 15.87%
Step-by-step explanation:
can i get brainlyliest
Answer:
2.5%
Step-by-step explanation:
I did the math, it might be wrong but i looked up a chart and yeah, still the only one that makes sense out of all of these anyways.
which graph represent the liner function y= 1/3 x -4?
Answer:
Graph 3
Step-by-step explanation:
equation: y = mx + b → y = 1/3x - 4
- m is the slope (slope = rise / run):
- b is the y intercept (when x = 0): -4
Graph 1 is incorrect because the y-intercept is 1.5 on this graph when the equation is -4
Graph 2 is incorrect because the slope is 3 / 1, the rise is 3 and the run is 1
the correct equation for this graph is y = 3x - 4
Graph 3 is correct because the slope is 1/3, the rise is 1 and the run is 3
and the y intercept is -4
Graph 4 is incorrect because the y-intercept is not even shown
(PLS HELP HURRY MY TEACHER NEEDS ME TO PASS THIS!)
What is the rate for the function shown?
PLEAAAAAAAAAAAASEEEEEEEEEEEEE HELP!!!!!!!!! | In your own words, describe when you should use area, and when you should use volume in calculating the amount of space an object occupies.