I have a question about the application of definite integrals. I came up with the following integral:
[tex] \int\limits^5_0 {62.5 * 6 * 2 * x} \, dx [/tex]
This is equal to 9780. Unfortunately, 9780 ft-lb is not an answer, but 9375.0 ft-lb is! Can someone tell me what is wrong with my integral and if 9375.0 ft-lb is the answer to my question?
![I Have A Question About The Application Of Definite Integrals. I Came Up With The Following Integral:[tex]](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/W8exWihGJLKNdT8hrLgigcw8Dt64TTLZ.png)
Answers
The volume of each slice is 6*2*DeltaX cubic feet. So the force pulling down on each slice is 62.5*6*2*DeltaX pounds as this is the weight of the slice.
The work done to move that slice x feet upward is 62.5*6*2*DeltaX*x or 62.5*6*2x*DeltaX as you wrote for your integrand.
Integrating with respect to x will effectively add up all the horizontal slices to get the total work done
See the attached image for the integral and steps leading to the answer of 9375
![I Have A Question About The Application Of Definite Integrals. I Came Up With The Following Integral:[tex]](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/tJdymOwTIsSaS1wIgohQ3QlAZTGbQAvs.png)
Related Questions
WILL GIVE BRAINLIEST OF YOU ANSWET ALL
50 points plus 49 with brainliest
Answers
Lateral Surface Area = 2π×2×15 = 188.49555921539 feet2
Total Surface Area = 213.62830044411 feet2
(Figure A)
Base Surface Area = 2π×52 = 157.07963267949 feet2
Lateral Surface Area = 2π×5×17 = 534.07075111026 feet2
Total Surface Area = 691.15038378975 feet2
(Figure B)
Base Surface Area = 2π×82 = 402.12385965949 feet2
Lateral Surface Area = 2π×8×22 = 1105.8406140636 feet2
Total Surface Area = 1507.9644737231 feet2
(Figure C)
Answer:
his answer is right.
Suppose the diameter of a circle is \color{green}{10}10 start color green, 10, end color green. what is its radius
Answers
The diameter is always the twice of radius. If d represents the diameter and r represents the radius, we can write:
d = 2r
or
r = d/2
For d=10,
r = 10/2 = 5 units
So, the radius of the circle will be 5 units
4+3x-ax=9-7x+bx
PLEASE HELP
Answers
a=−bx+10x−5x
Answer:
[tex]x=\frac{5}{(10-a-b)}[/tex]
Step-by-step explanation:
4+3x-ax=9-7x+bx
take all variable terms at one side and all constant terms at one side,
3x+7x-bx-ax=9-4
10x-ax-bx=5
x(10-a-b)=5
[tex]x=\frac{5}{(10-a-b)}[/tex]
Which polar coordinates represent the point plotted on the graph? Select all that apply. (2 answers)
a. (-4, 90 degrees)
b. (4, 90 degrees)
c. (4, -90 degrees)
d. (-4, 270 degrees)
e. (-4, -270 degrees)
Answers
Answer: The correct options are (b) and (d).
Explanation:
It the polar form [tex]r^2=x^2+y^2[/tex], where
[tex]x=r\cos \theta,y=r\sin \theta[/tex]
The polar coordinate are in the form of [tex](r,\theta)[/tex].
From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .
So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.
The value,
[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]
Check the each option if we get the same value then that option is correct.
For option a.
[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]
Therefore option (a) is incorrect.
For option c.
[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]
Therefore option (c) is incorrect.
For option d.
[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]
Therefore option (d) is correct.
For option (e).
[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]
Therefore option (e) is incorrect.
Answer:
1. A
2. B, D
3. A, D, E
4. C
5. A
Step-by-step explanation:
A number x, rounded to 1 decimal place is 12.3 write down the error interval for x
Answers
The error interval for a number x rounded to 12.3 is 12.25 ≤ x < 12.35, indicating the range that x could be before rounding to one decimal place.
Explanation:If a number x, rounded to 1 decimal place, is 12.3, the error interval for x defines the range of values that x could be in order to round to 12.3. Since the value is rounded to one decimal place, we consider half of a tenth (0.05) on either side of 12.3 to find the error interval. Hence, the lower bound of the error interval would be just below 12.3 (12.25), and the upper bound would be just before it would round up to the next tenth (12.35).
The error interval for x can be written as: 12.25 ≤ x < 12.35.
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Error interval for [tex]\( x \)[/tex] rounded to 1 decimal place as 12.3 is from 12.25 to 12.35.
To find the error interval for the number [tex]\( x[/tex], rounded to 1 decimal place as 12.3, we need to consider the possible range of values that [tex]\( x \)[/tex] could have been before rounding.
1. Lower Bound: To find the lower bound, we need to consider the smallest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The smallest value that would round up to 12.3 is 12.25.
2. Upper Bound: Similarly, to find the upper bound, we need to consider the largest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The largest value that would round down to 12.3 is 12.35.
So, the error interval for [tex]\( x \)[/tex] is from 12.25 to 12.35.
A fish tank contains 18 goldfish and 22 guppies. If you randomly select 2 fish, what is the probability that they are both goldfish?
Answers
Answer:
b
Step-by-step explanation:
I really need help with these questions:
Use basic identities to find the simplified expression-
1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
2. cosine θ^2 / sine θ^2 + csc θ sin θ
Explanations would be greatly appreciated
Answers
(cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
The numerator becomes 1 since addition order matters not.
1 / (cot^2 x - csc^2 x)
If we factor the denominator out a negative
1 / -(csc^2 x - cot^2 x)
Consider sin^2 x + cos^2 x = 1. Divide both sides by sin^2 x to get
1 + cot^2 x = csc^2 x
Subtract both sides by cot^2 x to get 1 = csc^2 x - cot^2 x.
Replace the denominator
1 / -(1) = -1
For cos^2 θ / sin^2 θ + csc θ sin θ, we use cscθ = 1/sinθ and cosθ/sinθ = cotθ so
= cos^2 θ / sin^2 θ + 1
= cot^2 θ + 1
We use 1 + cot^2 θ = csc^2 θ to simplify this to
= csc^2 θ
Answers: -1
csc^2 θ
[tex]\bf sin^2(\theta)+cos^2(\theta)=1 \qquad \qquad cot(\theta)=\cfrac{cos(\theta )}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -------------------------------\\\\ \cfrac{cos^2(x)+sin^2(x)}{cot^2(x)-csc^2(x)}\implies \cfrac{1}{\frac{cos^2(x)}{sin^2(x)}-\frac{1}{sin^2(x)}}\implies \cfrac{1}{\frac{cos^2(x)-1}{sin^2(x)}} \\\\\\ \cfrac{1}{\frac{-[1-cos^2(x)]}{sin^2(x)}}\implies \cfrac{1}{\frac{-[\underline{sin^2(x)}]}{\underline{sin^2(x)}}}\implies \cfrac{1}{-1}\implies -1[/tex]
2)
[tex]\bf \cfrac{cos^2(\theta )}{sin^2(\theta )}+csc(\theta )sin(\theta )\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{1}{sin(\theta )}\cdot sin(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+1\implies \cfrac{cos^2(\theta )+sin^2(\theta )}{sin^2(\theta )}\implies \cfrac{1}{sin^2(\theta )}\implies csc^2(\theta )[/tex]
The relative locations of a swing set, a garden, and a sandbox in Gina's backyard are shown in the diagram.
What is the distance between the sandbox and garden?
Enter your answer as a decimal in the box. Round only your final answer to the nearest foot.
Answers
Let us suppose the distance between the sandbox and garden is x feet.
Apply the sine law in the given triangle, we have
[tex]\frac{x}{\sin 65^{\circ}}=\frac{36}{\sin 104^{\circ}}\\ \\ \text{On coss multiplying, we get}\\ x\sin 104^{\circ}=36\sin 65^{\circ}\\ \\ x=\frac{36\sin 65^{\circ}}{\sin 104^{\circ}}\\ \\ x\approx 33.6[/tex]
Therefore, in the nearest foot, the distance between the sandbox and garden is 34 foot.
Answer:
Hello! The correct answer is 34 ft.
Step-by-step explanation:
I am just confirming!
A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.
Answers
The radius of the circle that includes the footbridge, given the bridge's arc length and height, is 14.1 ft.
Explanation:The problem relates to the geometry of a circle, specifically the concept of the arc length and radius. Given the arc length (L) and the height of the arc (h), we can use these to find the radius (r) of the circle using the formula r = L²/(8h) + h/2.
Here, the arc length is the horizontal length of the footbridge, which is 27 ft and the height h is the height of the bridge, 10 ft.
Substituting these values into the formula we get:
r = (27² ft)/(8*10 ft) + 10 ft/2 = 729/80 + 5 = 14.1 ft
So, to the nearest tenth of a foot, the radius of the circle that includes the footbridge is 14.1 ft.
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If the pattern below follows the rule "Starting with four, every consecutive line has a number one more than the previous line," how many marbles must be in the seventh line?
Answers
3 x 1 = 3.
Basically you have to add 3 to the number that is in the 4th row. This should be 10, because 7 + 3 = 10
The number of balls in 7th line would be 10.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a pattern as shown in the image.
An arithmetic sequence is of the form -a, a + d, a + 2d, a + 3d, ......,
{d} is common difference and {a} is first term.We can write the pattern as -
4, 5, 6, 7, .....
This is a arithmetic progression. We can write the nth term as -
a{n} = a + (n - 1)d
a{7} = 4 + (7 - 1) x 1
a{7} = 4 + 6
a{7} = 10
Therefore, the number of balls in 7th line would be 10.
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An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other?
Answers
Plane 1(625): Took 23 hours to arrive.
Plane 2(575): Took 25 hours to arrive.
Therefore, the answer should be from 23-25 hours to arrive or if looking for middle number, 24 hours exactly.
Hope this helps.
Which is least expensive per oz rounded to the nearest cent: 20 oz for $1.79 or 2 lb 2 oz for $2.59?
A.) 20 oz
B.) 2 lb 2 oz
C.) Neither
Answers
11.17 = 11.2
2 lb 2 oz / 2.59 = 0.82
0.82 = 0.8
So the answer is B) 2 lb 2 oz.
Hope this Helps!
Answer:
B.) 2 lb 2 oz
Step-by-step explanation:
$1.79 for 20 ounces gives us
1.79/20 = $0.0895 ≈ $0.09 per ounce.
1 lb = 16 oz.; this means that 2 lb = 2(16) = 32 oz.
$2.59 for 2 lb 2 oz then gives us
2.59/34 = $0.07617647059 ≈ $0.08 per ounce.
The second choice is cheaper by 1 cent.
If f(x) = 1000(3)x and g(x) = 8x. Which statement is true? A) None are true. B) as x → ∞, f(x) < g(x). C) as x → ∞, f(x) = g(x). D) as x → ∞, f(x) > g(x).
Answers
Answer: f(x) > g(x).
If f(x) = 1000(3)x and g(x)=8x
fx=3000x
f=3000x/x
f=3000
g(x)=8x
g=8x/x
g=8
For whatever amount of X (positive), the statement f(x) > g(x) is true.
On a 10 item test, three students in prof. miller's advanced chemistry seminar received scores of two, five, and eight, respectively. for this distribution of test scores, standard deviation is equal to the square root of
Answers
In order to calculate the standard deviation, first, you need to calculate the mean of the scores:
m = (2 + 5 + 8) / 3
= 15 / 3
= 5
Then, find the variance: subtract the mean from each value, square the results, sum them up and divide it by the number of scores.
(2 - 5)² = 9
(5 - 5)² = 0
(8 - 5)² = 9
Therefore:
v = (9 + 0 + 9) / 3
= 18 / 3
= 6
The standard deviation is the square root of the variance:
σ = √6
= 2.45
In conclusion, the standard deviation can be calculated by the formula:
[tex]\sigma = \sqrt{ \frac{\sum(v - m)^{2} }{n} } [/tex]
The standard deviation for the given test scores can be calculated by finding the mean, computing the squared differences from the mean, averaging those squared differences to get the variance, and then taking the square root of that variance. The standard deviation for the scores is approximately 2.449.
The student is likely seeking assistance with the concept of standard deviation, which is a measure of dispersion or distribution around the mean in a set of data. The question at hand requires calculating the standard deviation for a small dataset consisting of three scores from a chemistry seminar. To find the standard deviation, one would first need to calculate the mean of the test scores, then find the variance by averaging the squared differences between each score and the mean, and finally, take the square root of the variance.
Step-by-step Calculation:
Calculate the mean (average) of the scores: (2 + 5 + 8) / 3 = 15 / 3 = 5.Find the squared differences from the mean: (2 - 5)² + (5 - 5)² + (8 - 5)² = 3² + 0² + 3² = 9 + 0 + 9.Calculate the variance: (9 + 0 + 9) / 3 = 18 / 3 = 6.The standard deviation is the square root of the variance: √(6) = 2.449The standard deviation of the test scores in Prof. Miller's advanced chemistry seminar is approximately 2.449.
In Miami the number of accidents increased by 20% over a four year period.how many accidents were there in 2013 if there were 5120 in 2009
Answers
The measure of an angle is 27°. what is the measure of a complementary angle?
Answers
Because 27 + 63 = 90
The measure of a complementary angle to a 27 degree angle is 63 degrees because two angles are complementary if their measures add up to 90 degrees. This is calculated by subtracting the given angle from 90.
Explanation:The measure of an angle is given as 27°, and you are asked to find the measure of a complementary angle. In mathematics, two angles are considered complementary if their measures add up to 90 degrees. Therefore, to find the measure of a complementary angle, you subtract the given angle from 90 degrees.
So, to solve this problem, you would simply subtract 27 from 90.
The calculation would look like this:
90-27 = 63. Therefore, the measure of the complementary angle is 63°.
Write the equation in standard form using integers y=4x+5
Answers
On two examinations, you have grades of 83 and 89. there is an optional final examination, which counts as one grade. you decide to take the final in order to get a course grade of a, meaning a final average of at least 90
Answers
The average of all three examinations must be at least 90 to get an A.
[tex] \dfrac{x + 83 + 89}{3} \ge 90 [/tex]
[tex] x + 172 \ge 270 [/tex]
[tex] x \ge 98 [/tex]
In order to get an A, you must get at least a 98 on the third examination.
Find the surface area of a sphere with radius, r = 11 in.
Surface Area = ________ in^2
(Type an exact answer in terms of pi.)
Answers
Sphere Surface Area = 484 PI
what is the value of x, if the volume of the cone is 12piem^3
Answers
12π=πx²h/3
12=x²h/3
36=x²h
36/h=x²
x=6/√h=(6√h)/h
Two lighthouses are located 40 miles from each other. A boat is spotted at an angle of 37 degrees northeast of the western lighthouse. At this point, the boat is 28 miles from the eastern lighthouse. How far is the boat from the western lighthouse?
A. 46.27 miles
B. 17.43 miles
C. Either 46.27 miles or 17.43 miles
D. There is no possible solution.
Answers
Using sine rule,
28/Sin 37 = 40/Sin B => Sin B = (40 Sin 37)/28 = 0.8597 => B = Sin ^-1(0.8597) = 59.287°
Therefore,
Angle E = 180 - (37+59.287) = 83.713°
Using the sine rule again;
BW/Sin E = 28/Sin 37 => BW = (28 Sin 83.713)/Sin 37 = 46.246 ≈ 46.27 miles.
The boat is 46.27 miles from the western lighthouse. The correct answer is A.
Answer:
C. Either 46.27 miles or 17.43 miles
If a person uses $700 in credit with an interest of 14%,what is that person going to owe after three billing cycles with simple interest
Answers
14%
This boils down to ----------- interest per month: a monthly rate of 0.0117.
12 mo
Thus, after 3 months, the amount owed, including the original $700, would be $700 + 3($700)(0.0117) = $724.57.
Find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches, and a length of 13 inches. A) 338 in2 B) 422 in2 C) 520 in2 D) 1364 in2
If you can, please explain. Thank you vv much! :D
Answers
Answer:
422 in.2
Step-by-step explanation:
Substitute the measurements of the rectangular prism into the formula SA = 2(lw) + 2 (lw) + 2(lh): 2(13)(7) + 2(6)(7) + 2(13)(6) = 422 in2.
PLZ help
which inequality does the graph represent
Answers
For -2 on the number line, we can see a hollow circle. This means that -2 is not included in the interval, eliminating the possibilities of greater and equal than or less and equal than (≥ and ≤).
The graph will have to use the original greater than symbol (>) or less than symbol (<).
The graph represents all numbers less than -2. Thus, the final inequality will be
x < -2.
The inequality the graph represent is y > x - 2.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.
We are given that;
The number line
Now,
The slope of the line is 1 and the y-intercept is -2,
so we can write y = x - 2 for the equation of the line.
The line is dashed, so we know that y is not equal to x - 2.
The region above the line is shaded, so we know that y is greater than x - 2.
Therefore, by the inequality the answer will be y > x - 2.
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YOOO!!!!NEEED IMMEDIATE HELP!!!!!!!!!!!!
Answers
Transformations:
1) Reflect the graph across the x-axis: f(x) changes sign:
h(x)=-f(x)→h(x)=-sqrt(x)
2) and shift it upward 3 units: We must add 3 units to the function:
g(x)=h(x)+3→g(x)=-sqrt(x)+3
Answer: Option C. g(x)=-sqrt(x)+3
Write an expression for the total Surface Area (SA) of a rectangular prism whose base is a square with side of length x and height of y.
Answers
S.A = 2x ^ 2 + 2x *y + 2x * y
Rewriting we have:
S.A = 2x ^ 2 + 4x *y
S.A = 2 (x ^ 2 + 2x * y)
Where,
x: side length of a square base
y: height of the prism
Answer:
an expression for the total Surface Area (SA) of a rectangular prism is:
S.A = 2 (x ^ 2 + 2x * y)
What is the end behavior of the polynomial function? PLEASE HELP!!!
Answers
We have then that:
x ---> - inf then,
y -----> - inf
Answer:
option 4
Here is the explanation:
x ---> - inf then,
y -----> - inf
So in the graph, the choices given will give this answer and it is the 4th option.
Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?
Answers
Total money earned:
[tex]10x + 15y = 1800[/tex]
Sum of hourly rates:
[tex]x + y = 155[/tex]
To solve this, you solve for one equation first, substitute it in the second, then input it back into the first equation. I will first be solving for x.
[tex]x + y = 155 \\ x = 155 - y[/tex]
Input this into the other equation to find y:
[tex]10(155 - y) + 15y = 1800 \\ 1550 - 10y + 15y = 1800 \\ 5y = 250 \\ y = 50[/tex]
Input y into the first equation:
[tex]x + 50 = 155 \\ x = 105[/tex]
The first mechanic charges $105 per hour and the second mechanic charges $50 per hour.
The rates charged per hour by the first and second mechanics will be $105 and $50.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that two mechanics worked on a car, the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800.
Suppose x is the hourly rate for the first mechanic and y is the hourly rate of the second.
If the total money earned is 1800.
10x + 15 y = 1800 ---- (1)
If both have their individual rates the sum of the hourly rate is,
x+ y = 15 -------- (2)
Rearrange the equation,
x = 155- y
Substitute the value of x in equation 1 we get,
10x + 15 y = 1800
10(155-y) + 15y = 1800
1150 - 10y + 15y = 1800
5y = 250
y = 50
Substitute the value of y in equation 2 we get,
x = 155- y
x= 155 - 50
x = 105
Thus, the rates charged per hour by the first and second mechanics will be $105 and $50.
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The table below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often?
Options:
20%
31%
43% is wrong
57%
(I already did my other questions, this is the only one I needed help with)
Answers
For the white car we have:
Male = 0.11
Female = 0.20
Total = 0.31
The percentage is given by:
(0.31) * (100) = 31%
Answer:
The percentage that represents the car bought most often is:
31%
A cruise ship can cover 17 nautical miles in 374 minutes. How many nautical miles will it travel in 330 minutes?
Answers
330/22= 15 nautical miles in 10 minutes
To check your work:
17/374=.04545 nautical miles per minute
.04545*330= 14.999 or 15.
So your answer is that the cruise ship covered 15 nautical miles in 330 minutes. I hope that helped!
The ship's speed in deep water is 0.045 nautical miles per minute. In shallow water, the ship's maximum speed typically decreases due to increased drag and turbulence.
To find the speed of the ship in very deep water:
Calculate speed = Distance / Time = 17 nmi / 374 min = 0.045 nautical miles per minute.For the ship's speed in shallow water:It depends on the water resistance; usually, in shallow water, the ship's maximum speed decreases due to increased drag and turbulence.