Evaluate the indefinite integral. ft-53 at 1250 + c 5 - + 2 - 125t + c 312 - 30t + 75 + 6 O r4 - 15+ 7512 - 125t + c
Answers
Given:
[tex]∫(t-5)^3\text{ dt}[/tex]Let's evaluate the integral:
[tex]\begin{gathered} ∫(t-5)^3\text{ dt} \\ \\ =\frac{1}{4}(t-5)^4+c \\ \\ ^{} \end{gathered}[/tex]Thus, we have:
[tex]\frac{1}{4}(t^4-20t^3+150t^2-500t+625)+C[/tex]Expand using distributive property:
[tex]\begin{gathered} (\frac{t^4}{4}-\frac{20t^3}{4}+\frac{150t^2}{4}-\frac{500t}{4}+\frac{625}{4})+C \\ \\ \\ =\frac{t^4}{4}-5t^3+\frac{75t^2}{2}-125t+C \end{gathered}[/tex]ANSWER:
[tex]=\frac{t^4}{4}-5t^3+\frac{75}{2}t^2-125t+C[/tex]Related Questions
Write a mathematical model that estimates the average cost of tuition and fees, T, at public 4 years college for the school year ending x years after 2000
Answers
The mathematical model that estimates the average cost of tuition and fees, T, at public 4 years college for the school year ending x years after 2000 is T = 3349 + 379x.
We can use the data in Figure from 2000 and 2016 to estimate the
yearly increase in tuition and fees.
Yearly increase in tuition and fees is approximately = change in tuition and fees from 2000 to 2016 / change in time from 2000 to 2016
⇒ ≈ 9410 - 3349 / 2016 - 2000
⇒ 6061/16
= 378.8125
= 379
Each year the average cost of tuition and fees for public four-year
colleges is increasing by approximately $379.
Now we can use variables to obtain a mathematical model that estimates the average cost of tuition and fees, T, for the school year ending x years after 2000.
⇒ The average cost of tuition and fees is:
⇒ T = 3349 + 379x
The mathematical model T = 3349 + 379x estimates the average cost
of tuition and fees, T, at public four-year colleges for the school year
ending x years after 2000.
Hence we get the mathematical model as T = 3349 + 379x
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Suppose that the age of all of a country's vice presidents when they took office was recorded. The collection of the ages of all the country's vice presidents when they took office is a A. PopulationB. ParameterC. Sample D. Statistic
Answers
Answer:
Population
Explanation:
A population is a complete group that has a common feature. A Sample is a part of that population and a statistic or parameter are measures of the sample or population.
In this case, we have the ages of all the country's vice presidents, so it is a population.
15 decreased by -7 is 22true or false why?explain
Answers
Given -
15 decreased by -7 is 22
To Find -
True or false
Step-by-Step Explaation -
15 decreased by -7 is 22
can be written as -
= 15 - (-7)
[as -(-a) = +a]
= 15 + 7
= 22
Final Answer -
Statement is True
Use the quadratic formula to solve for x.5x? - 7x=2Round your answer to the nearest hundredth.If there is more than one solution, separate them with commas.X == 0DO...Х5?
Answers
Given equation:
[tex]5x^2-7x\text{ = 2}[/tex]Re-arranging:
[tex]5x^2-7x\text{ -2 = 0}[/tex]Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]a = 5, b = -7, c= -2
Substituting into the formula:
[tex]\begin{gathered} x\text{ = }\frac{-(-7)\pm\text{ }\sqrt[]{(-7)^2-4(5)(-2)}}{2\times5} \\ =\text{ }\frac{7\pm\sqrt[]{89}}{10} \end{gathered}[/tex]Writing as a decimal:
[tex]x\text{ = }-0.24\text{ or 1.64 (nearest hundredth)}[/tex]Answer:
x = -0.24, 1.64
How many y-values are there for each x-value in the function represent by the graph
Answers
Answer: 1
Step-by-step explanation:
If the equation is a function there is one y-value for every x-value
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 6 ft high? (Round your answer to two decimal places.)
Answers
The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)
Define Volume of cone?
A pyramid having a circular cross section is called a cone. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly get the volume of a cone. Formula is , V = 1/3 πr²h
We have, dV/dt = 40 ft³/min
h = diameter where, h = 2r
so r = 1/2h
The formula for regular circular cone is,
V = 1/3 πr²h
put the value of r,
V = 1/ 3 * π * (1/2h)² * h
= 1/12 * π * h³
differentiate it, we get
dV/dt = 3/12 * π * h² * dh/dt
dh/dt = (dV/dt)/(3/12*π*h²)
we have, dV/dt = 40 ft³/min and h = 6
Put these values,
dh/dt = 40 / (3/12 * 22/7 * 6²) (∵ π = 22/7)
After solving, we get
dh/dt = 1.41 ft/min
Therefore, The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)
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Look at this graph: 70 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 What is the slope?
Answers
EXPLANATION
As we can see in the graph, we need to take two ordered pairs in order to calculate the slope with the following equation:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Let's consider either one ordered pair, as (x1,y1)=(60,0) and (x2,y2)=(100,100), then the slope will be:
[tex]\text{Slope}=\frac{(100-0)}{(100-60)}=\frac{5}{2}[/tex]Answer: the slope is equal to 5/2.
Solve the inequality and graph the solution on the number line. 3 + 8x < 67
Answers
Answer:
The solution to the inequality is
x < 8
Explanation:
Given the inequality:
3 + 8x < 67
Subtract 3 from both sides of the inequality:
3 + 8x - 3 < 67 - 3
8x < 64
Divide both sides by 8
8x/8 < 64/8
x < 8
The solution to the inequality is
x < 8
The graph is shown below:
use the zero product to find the solutions to the equation x^2 + 12 = 7x 1. x = -4 or x =3 2. x= -4 or x= -3 3. x= -3 or x =4 4. x=3 or x=4
Answers
Given the equation :
[tex]x^2+12=7x[/tex]Make all terms at one side:
[tex]x^2-7x+12=0[/tex]Factor the equation :
( x - 4 ) ( x - 3 ) = 0
Using the zero product to find x
So,
x - 4 = 0 OR x - 3 = 0
x = 4 OR x = 3
so, the answer is option 4. x = 3 or x = 4
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 19 people are combined. What is the probability that
the combined sample tests positive for the virus? ls it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least or person has the virus.
The probabilty that the combined sample wil test posiltive is 1.
(Round to three decimal places as needed.)
Answers
Answer: there is a 0.095% chance that one of the adults tests positive
Step-by-step explanation:
What is the area of the shaded region?____ square miles.
Answers
Finding the area of the shaded part means finding the area of the yellow triangle,
The exercise provide us the base and the height of the triangle, so we must replace these values in the next equation
[tex]A_{triangle}=\frac{b\cdot h}{2}[/tex]Where, b is the base and h is the height
[tex]A=\frac{5\text{ mi}\cdot4\text{ mi}}{2}=\frac{20\text{ mi}}{2}=10\text{ mi}[/tex]So, the area of the shaded region is 10 mi.
For a circle of radius 7 feet, find the arc length of a central angle of 6°.
Answers
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r = 7\\ \theta = 6 \end{cases}\implies s=\cfrac{(6)\pi (7)}{180}\implies s=\cfrac{7\pi }{30}\implies \underset{\textit{about 9 inches}}{s\approx \stackrel{ft}{0.73}}[/tex]
true or false√3^(3√2) =(108)^1/6
Answers
False
Explanations:For the Left Hand side of the expression:
[tex]\sqrt[]{3}^{(3\sqrt[]{2})}[/tex]This can be simplified as:
[tex]\begin{gathered} 3^{\frac{1}{2}(3\sqrt[]{2})} \\ =3^{1.5\sqrt[]{2}} \\ =3^{2.12} \\ =\text{ }10.27 \end{gathered}[/tex]For the Right Hand Side of the expression:
[tex]\begin{gathered} (108)^{\frac{1}{6}} \\ =(108)^{0.167} \\ =\text{ }2.19 \end{gathered}[/tex]Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true
solve for the following system by using Elimination4x-2y=86x+6y=30
Answers
System
[tex]\begin{gathered} 4x-2y=8 \\ 6x+6y=30 \end{gathered}[/tex][tex]\begin{gathered} 3(4x-2y)=8 \\ 6x+6y=30 \\ \\ 12x-6y=24 \\ + \\ 6x+6y=30 \\ \\ 12x+6x-6y+6y=24+30 \\ 18x=54 \\ x=3 \end{gathered}[/tex]Now, for y
[tex]\begin{gathered} 4x-2y=8 \\ -2y=8-4x \\ 2y=4x-8 \\ y=\frac{4x-8}{2} \\ y=\frac{4\cdot3-8}{2} \\ y=\frac{12-8}{2} \\ y=\frac{4}{2} \\ y=2 \end{gathered}[/tex]A group of 15 people are ordering pizza.each person want 2 slices and each pizza has 15 slices.how many pizzas should they order
Answers
15x2=30
Which are the foci of the hyperbola represented by… Thanks!
Answers
The equation is given to be:
[tex]x^2-3y^2+12=0[/tex]We can write the equation in the standard form of the equation of a hyperbola to be:
[tex]\frac{\left(y-0\right)^2}{2^2}-\frac{\left(x-0\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]Therefore, we have the following parameters:
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:a=2,\:b=2\sqrt{3}[/tex]Recall the hyperbola foci definition:
[tex]\begin{gathered} \mathrm{For\:an\:up-down\:facing\:hyperbola,\:the\:Foci\:\left(focus\:points\right)\:are\:defined\:as}\:\left(h,\:k+c\right),\:\left(h,\:k-c\right),\: \\ \mathrm{where\:}c=\sqrt{a^2+b^2}\mathrm{\:is\:the\:distance\:from\:the\:center}\:\left(h,\:k\right)\:\mathrm{to\:a\:focus} \end{gathered}[/tex]Therefore, the value of c will be:
[tex]\begin{gathered} c=\sqrt{2^2+(2\sqrt{3})^2} \\ c=4 \end{gathered}[/tex]Therefore, the foci will be:
[tex]\begin{gathered} \left(h,\:k+c\right),\:\left(h,\:k-c\right)=\left(0,\:0+4\right),\:\left(0,\:0-4\right) \\ Foci=\left(0,\:4\right),\:\left(0,\:-4\right) \end{gathered}[/tex]The correct option is the FIRST OPTION.
Point O is on line segment NP . Given NO =5 and NP =20, determine the length OP .
Answers
If the point O is on the line segment NP, then:
[tex]NO+OP=NP[/tex]Replace for the given values and find the length of OP:
[tex]\begin{gathered} 5+OP=20 \\ OP=20-5 \\ OP=15 \end{gathered}[/tex]The length of OP is 15.
I'm willing to give out 30 points so please this one is the most annoying one.
Match the example on the left with the corresponding property on the right.
3(x + 3) = 3x +9
2+3+4= 4+3 +2
4(2 x 3) = (4 x 2)3
6+ (7 + x) = (6 + 7) + x
those four up there you have to match with these three down here
Commutative Property
Associative Property
Distributive Property
Answers
Answer:
Commutative Property: 2 + 3 + 4 = 4 + 3 + 2
Associative Property: 4(2 x 3) = (4 x 2)3
Distributive Property: 3(x + 3) = 3x +9
Step-by-step explanation:
Hello, no worries!
These are just basic definitions that you need to remember, and then you'll be on track. The commutative property is when you change the order of the numbers you're either adding or multiplying.
For example, 2 + 3 = 3 + 2.
The associative property is when you simply have just three terms that when you switch the order in a way, the answer will be the same.
For example, 2(5 x 4) = 5(4 x 2).
Last, but not least, the distributive property is when you distribute a term in the parentheses and multiply them.
Hope this helped, and best of luck with the rest of your assignment. (:
Solve x/2 -3 =71. 52.403.104.20
Answers
We have the expression:
[tex]\frac{x}{2}-3=7[/tex]We solve as follows:
[tex]\Rightarrow\frac{x}{2}=10\Rightarrow x=20[/tex]From this, we have that the solution is option 4, x = 20.
How do you write 6.01 × 10^2 in standard form?
Answers
Solve each proportion.
4/5 = n/2
5/b = 9/5
Answers
The value of the first proportion is 1.6 and the value of the second proportion is 2.78.
What is a proportion?A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. A formula or claim shows that two ratios or fractions are equivalent.
According to the question,
The first proportion will be :
4/5 = n/2
n = 8/5
n = 1.6
The second proportion will be :
5/b = 9/5
b = 25/9
b = 2.78
Hence, the value of n will be 1.6 and the value of b will be 2.78 respectively.
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Maria made $161 for 7 hours of work.
At the same rate, how many hours would she have to work to make $115?
Answers
Answer: 5 hours
Step-by-step explanation: 161$/7h= 23 per hour, therefore, 115$/23 per hour= 5 hours.
What is the solution to the following system of equations?x+y=5Ix-y=1
Answers
the initial equation is:
[tex]\begin{gathered} x+y=5 \\ x-y=1 \end{gathered}[/tex]So we can add bout of the equation so:
[tex](x+y)+(x-y)=5+1[/tex]and we simplify it so:
[tex]\begin{gathered} x+x+y-y=6 \\ 2x=6 \end{gathered}[/tex]now we solve for x so:
[tex]\begin{gathered} x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]and with the value of x we can replace it in the first equation so:
[tex]3+y=5[/tex]and we solve for y:
[tex]\begin{gathered} y=5-3 \\ y=2 \end{gathered}[/tex]So the solution is x equal to 3 an y equal to 2
if n (A)=4, n (B) =9, and n(A ∩ B) =2; what is n( A U B)?
Answers
Given:
[tex]\begin{gathered} n(A)=4 \\ n(B)_{}=9 \\ n\mleft(A\cap B\mright)=2 \end{gathered}[/tex]To find:
[tex]n(A\cup B)[/tex]Using the formula,
[tex]\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ =4+9-2_{} \\ =11 \end{gathered}[/tex]Hence the answer is 11.
Find the slope of the line that passes through (97, 21) and (54, -17).
Answers
Given data:
The first point given is (97, 21).
The second point given is (54, -17).
The slope of the line passing through the given points is,
m=(-17-21)/(54-97)
=-38/-43
=38/43
Thus, the slope of the line passing through the given points is 38/43.
1. An Uber driver charges a $3 boarding rate in addition to $2 for every mile. What is the equation of the
line that represents this driver's rate? How much is the rate for 5 miles? For 7 miles? What is the x axis?
What is the y axis? What is the y-intercept?
2. An office has an envelope stuffing machines. The machine can stuff a batch of envelopes in 5 hours.
How long would it take the machines to stuff 10 batches of envelopes? 14 batches of envelopes? What
is the x axis? What is the y axis?
3. Sarah has a job working for Boeing constructing plane wings. She earns a Salary of $67,500.00 a year,
with an overtime flat rate of $20.00 an hour. How much money did she make before taxes if she worked
88 hours of overtime last year? What is the x axis? What is the y axis? What is the y-intercept?
Answers
For 5 miles ride uber driver charges $13and for 7 miles ride uber driver charges $17.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
The y-intercept is the point where the graph intersects the y-axis.
2- For 10 batches of envelopes machine take 50 hours and for 14 batches of envelopes machine take 70 hours.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
3-Sarah makes $1760 money if she worked 88 hours of overtime last year.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
Solution 1 -
What is linear equation?
A linear equation is an algebraic equation where each term has an exponent of 1, it always results in a straight line.
uber driver charges a $3 and for every mile charge $2
let assume driver complete x miles ride and charge y $.
so, 3 + 2x = $y
For 5 miles, put the value of x = 5
3 + 2(5) = y$
y=$13
For 7 miles, put the value of x = 7
3 + 2(7) =$ y
y=$17
Therefore, for 5 miles ride uber driver charges $13and for 7 miles ride uber driver charges $17
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
The y-intercept is the point where the graph intersects the y-axis.
solution 2-
given information a batch of envelopes machine stuff in 5 hours.
so, for 10 batches of envelopes machine take 10 x 5 = 50 hours.
given information a batch of envelopes machine stuff in 5 hours.
so, for 14 batches of envelopes machine take 14 x 5 = 70 hours.
Therefore, for 10 batches of envelopes machine take 50 hours and for 14 batches of envelopes machine take 70 hours.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
Solution 3 -
given - Sarah earns a salary of $67,500 a year.
Boeing company pay her for per hour overtime =$20.00
if Sarah worked 88 hours, then company will pay her = 88 ($20.00)
= $1760
Therefore, Sarah makes $1760 money if she worked 88 hours of overtime last year.
The x-axis is a horizontal number line, and the y-axis is a vertical number line.
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What is the answer to 2 tokens + 2 tokens
Answers
Answer: 4 tokens
Step-by-step explanation: 2+2=4
Answer:
4
Step-by-step explanation:
We can figure this out by counting. Using our fingers, we start with two, then when we add two more we have four fingers, or in this case tokens.
Help please I did them and got all wrong LOL..............
Answers
Answer:
1. Choice (2) 13
2. Choice (3) 8.1
3. Choice (3) 95 to 105 ft
4. Choice (3) 96 in
Step-by-step explanation:
All the problems use the Pythagorean theorem
The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
[tex]c^{2} = a^{2} + b^{2}[/tex]
or
[tex]c = \sqrt{a^{2} + b^{2}}[/tex]
where c is the hypotenuse and a, b the shorter sides.
This means that given any two of the three sides of a right triangle we can compute the length of the third side
For example if we were given the hypotenuse c and side b, we can solve for side a by:
[tex]a = \sqrt{c^{2} - b^{2}}[/tex]
If we were given side a and asked to solve for side b then
b = \sqrt{c^{2} - a^{2}}
Frankly it does not matter which you choose as side a and side b.
Question 1
The distance from the foot of the ladder to the wall can be taken to be side a and is equal to 8ft
So b = 8ft
The length of the ladder is the hypotenuse c = 15 feet
[tex]a = \sqrt{c^{2} - b^{2}} \\\\a = \sqrt{15^{2} - 8^{2}}\\\\a = \sqrt{225 - 64}\\\\a = \sqrt{161}\\\\a = 12.68857754045 \\\\[/tex]
Rounded to nearest foot, that would be 13 feet So choice (2)
Question 2
The points J and K have the following coordinates as indicated on the graph.
J(-3, 2)
K (1, -5)
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
For:
(X1, Y1) = (-3, 2)
(X2, Y2) = (1, -5)
[tex]d = \sqrt {(1 - (-3))^2 + (-5 - 2)^2}\\\\d = \sqrt {(4)^2 + (-7)^2}\\\\d = \sqrt {{16} + {49}}\\\\d = \sqrt {65}\\\\d = 8.062258\\\\\text{Rounded to the nearest 10th it would be \boldsymbol{8.1}}\\\\[/tex] So choice (3)
Question 3
This again involves a right triangle as shown in the figure
The sides are a = AC = 60 and b = BC = 80 and we are asked to find the length of AC which is the hypotenuse of ΔABC
Use the Pythagorean Theorem directly
[tex]c = \sqrt{a^{2} + b^{2}}}\\\\a = \sqrt{60^{2} + 80^{2}}\\\\c = \sqrt{3600 + 6400}}\\\\c = \sqrt{10000}}\\\\c = 100}\\\\[/tex]
Answer 100 feet so choice (3): from 95 to 105 ft
Question 4
The brace is one of the shorter sides, with the platform top as the hypotenuse.
Let's use a for the brace, b for the 40 in side and c for the hypotenuse = 104 in
So we have to compute for b using the formula:
[tex]b = \sqrt{c^{2} - a^{2}}[/tex]
Using the given values, this would be:
[tex]b = \sqrt{104^{2} - 40^{2}}\\\\b = \sqrt{10816 - 1600}\\\\b = \sqrt{9216}\\\\b = 96\\\\[/tex]
which would be choice (3)
I need to know the following steps to find the range and domain.
Answers
In a radical function as given the domain is any x-value for which the radical (value under the radical sing) is not negative:
[tex]\begin{gathered} x^2+1\ge0 \\ x^2\ge-1 \\ \end{gathered}[/tex]As any value of x makes x squared be possitive or 0, the domain is:
[tex]\begin{gathered} x\in\R \\ Interval\text{ notation:} \\ (-\infty,\infty) \end{gathered}[/tex]Any value of x makes x squared greater than or equal to zero the range is:
[tex]\begin{gathered} x^2\ge0 \\ \\ \text{Range stars in x=0:} \\ f(0)=\sqrt[]{0+1} \\ f(0)=\sqrt[]{1} \\ f(0)=1 \\ \\ Range\colon \\ y\ge1 \\ \\ \text{Interval notation;} \\ \lbrack1,\infty) \end{gathered}[/tex]Find the standard form of the equation of the ellipse satisfying the given conditions.Endpoints of major axis: (4,12) and (4,0)Endpoints of minor axis: (8,6) and (0,6)
Answers
The Standard form of the ellipse is given as,
[tex]\frac{(x-a)^2}{a^2}+\text{ }\frac{(y-b)^2}{b^2}\text{ = 1}[/tex]The length of the major axis is given as,
[tex]\begin{gathered} 2a\text{ = 8} \\ a\text{ = }\frac{8}{2} \\ a\text{ = 4} \end{gathered}[/tex]The length of the minor axis is given as,
[tex]\begin{gathered} 2b\text{ = 12} \\ b\text{ = }\frac{12}{2} \\ b\text{ = 6} \end{gathered}[/tex]Therefore the required equation is calculated as,
[tex]\begin{gathered} \frac{(x-4)^2}{4^2}\text{ + }\frac{(y-6)^2}{6^2}\text{ = 1} \\ \frac{(x-4)^2}{16^{}}\text{ + }\frac{(y-6)^2}{36^{}}\text{ = 1} \end{gathered}[/tex]