Find the area between the graph of y= -12x^3 and the x-axis on the interval [-1, 1]. Write the exact answer. Do not round.
![Find The Area Between The Graph Of Y= -12x^3 And The X-axis On The Interval [-1, 1]. Write The Exact](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/AmiWztAUyBJWt81tbioERzroQ4c6ZrVc.jpeg)
Answers
Recall that the integral of the area between the graph of two functions, in an interval [a,b] is:
[tex]\int ^b_a|f(x)-h(x)|dx\text{.}[/tex]Now, if f(x) is an odd function, we can use the following property:
[tex]\int ^a_{-a}|f(x)|dx=2\int ^a_0|f(x)|dx\text{.}[/tex]Now, notice that the function y=-12x³ is an odd function, therefore:
[tex]\int ^1_{-1}|y-0|dx=2\int ^1_0|-12x^3|dx=2\int ^1_012x^3dx\text{.}[/tex]Applying the linearity of the integral we get:
[tex]24\int ^1_0x^3dx=24\frac{x^4}{4}|^1_0=24(\frac{1}{4}-0)=\frac{24}{4}=6.[/tex]Answer: 6.
Related Questions
Complete the table of values for 2 x - 5 y =10
Answers
ANSWER
x y
0 -2
1 -8/5
-2 -14/5
2 -6/5
EXPLANATION
We can solve the equation for y. First add 5y to both sides of the equation:
[tex]\begin{gathered} 2x-5y+5y=10+5y \\ 2x=10+5y \end{gathered}[/tex]Then subtract 10 from both sides:
[tex]\begin{gathered} 2x-10=10-10+5y \\ 2x-10=5y \end{gathered}[/tex]And divide both sides by 5:
[tex]\frac{2}{5}x-2=y[/tex]And we can flip the equation so we read the y first:
[tex]y=\frac{2}{5}x-2[/tex]Now, to complete the table we have to replace x by each of its values in the equation above and solve to find the y-value:
[tex]y=\frac{2}{5}0-2=0-2=-2[/tex][tex]y=\frac{2}{5}\cdot1-2=\frac{2}{5}-2=-\frac{8}{5}[/tex][tex]y=\frac{2}{5}\cdot(-2)-2=-\frac{4}{5}-2=-\frac{14}{5}[/tex][tex]y=\frac{2}{5}\cdot2-2=\frac{4}{5}-2=-\frac{6}{5}[/tex]An 8-lb cut of roast beef is to be medium roasted at 350 Fahrenheit. Total roasting time is determined by allowing 15 minutes roasting time for every pound of beef . If the roast is placed in a preheated oven at 2:00 pm., what time should it be removed ?
Answers
Given:
15 minutes roasting time for every pound of beef.
Total amount of beef is 8-lb
[tex]\begin{gathered} \text{Total time taken to roast 8-lb of beef}=15\times8 \\ \text{Total time taken to roast 8-lb of beef}=120\min utes\text{ } \\ \text{Total time taken to roast 8-lb of beef}=2\text{ hours} \end{gathered}[/tex][tex]\begin{gathered} \text{Time to remove from the over =2:00 pm +2 hours } \\ \text{Time to remove from the over =}4\colon00pm \end{gathered}[/tex]David can paint 3 rooms in 7 hours. At the same pace how long would it take him to paint 8 rooms?
Answers
Answer
It will take David 18.67 hours or 18 hours, 40 minutes to paint 8 rooms.
Explanation
We are asked to calculate the number of hours it'll take David to paint 8 rooms.
Let the number of hours David will take to paint 8 rooms be x
David can paint 3 rooms in 7 hours.
3 rooms = 7 hours
8 rooms = x hours
We can form a mathematical relationship by cross multiplying
3 × x = 8 × 7
3x = 56
Divide both sides 3
(3x/3) = (56/3)
x = 18.67 hours = 18 hours, 40 mins
Hope this Helps!!!
11. A map is drawn so that 2 inches represents 700 miles. If the distance betweentwo cities is 3850 miles, how far apart are they on the map?a. 5.5 inchesb. 11 inchesc. 22 inchesd. 6 inchese. 12 inches
Answers
Given:
• 2 inches represents 700 miles on the map.
,• Actual distance between two cities = 3850 miles
Let's find the distance on the map.
Let's first find how many miles 1 inch represent.
We have:
[tex]\frac{700}{2}=350\text{ miles}[/tex]This means on the map, 1 inch represent 350 miles.
Now, to find the distance between the two cities on the map, we have:
[tex]\frac{3850}{350}=11\text{ inches}[/tex]Therefore, the distance between the two cities on the map is 11 inches.
ANSWER:
b. 11 inches
Find the value of x. (Hint: The sum of the angle measures of a quadrilateral is 360°)
X= (simplify your answer)
Answers
Answer: The value of x is 26
In the given quadrilateral, it is given that, two angles have measurements
And two have measurement
And sum of measurement of angles of a quadrilateral is 360 degree, that is
SO for the given quadrilateral, the value of x is 26 .
Step-by-step explanation:
Answer:
x = 30
Step-by-step explanation:
You want the value of x given that adjacent angles in a parallelogram are (3x+30)° and (2x)°.
Supplementary anglesAdjacent angles in a parallelogram total 180°, so ...
(3x +30)° +2x° = 180°
5x +30 = 180 . . . . . . . . . divide by °, simplify
x +6 = 36 . . . . . . . . . divide by 5
x = 30 . . . . . . . . . subtract 6
The value of x is 30.
__
Additional comment
The angles are (3·30 +30)° = 120°, and 2·30° = 60°.
how do you get the answer to the following problem?... "Ben has two pencils, one that is 8 cm long, and one that is 15 cm long. If he uses these to create the legs of a right triangle on his desk, what length should the third pencil be to close out the right triangle? Round your answer to the nearest hundredth, if necessary."
Answers
If ben uses these to create the legs of a right triangle on his desk the shape he will get will be the following.
And we need to find the length of the triangle with the QUESTION MARK (the length L).
The Pythagoras's theorem comes in handy here, which says
[tex](8cm)^2+(15cm)^2=l^2[/tex][tex]l^2=289[/tex][tex]l=\sqrt[]{289}[/tex][tex]\textcolor{#FF7968}{\therefore l=17\operatorname{cm}}\text{\textcolor{#FF7968}{.}}[/tex]What is the surface area of the following composite figure?The figure below is a cone “topped” withhemisphere. Calculate the total surface area if theradius of the cone and hemisphere is 10 cm andthe height of the cone is 24 cm.
Answers
ANSWER
[tex]A=1445.133cm^2[/tex]EXPLANATION
We have to find the surface area of the composite figure made of a hemisphere and a cone.
To do that, we have to find the curved surface area of the hemisphere and the curved surface of the cone and add them together.
We are using curved surface area since the area of the flat surfaces of the cone and hemisphere are not relevant since they are covered.
The curved surface area of a hemisphere is given as:
[tex]\begin{gathered} 2\text{ }\pi r^2 \\ \text{where r = radius = 10 cm} \\ \Rightarrow\text{ A = 2 }\cdot\text{ }\pi\cdot10^2 \\ A=628.319cm^2 \end{gathered}[/tex]The curved surface area of a cone is given as:
[tex]\begin{gathered} \pi\cdot\text{ r }\cdot\text{ l} \\ where\text{ r = radius = 10 cm} \\ l\text{ = slant height of cone} \end{gathered}[/tex]We can get the slant height of the cone by using Pythagoras rule:
So, we have:
[tex]\begin{gathered} l^2=10^2+24^2\text{ = 100 + 576} \\ l^2\text{ = 676} \\ l\text{ = }\sqrt[]{676} \\ l\text{ = 26 cm} \end{gathered}[/tex]So, the curved surface area of the cone is:
[tex]\begin{gathered} A\text{ = }\pi\cdot\text{ 10 }\cdot\text{ 26} \\ A\text{ =8}16.814cm^2 \end{gathered}[/tex]Now, adding them together, the surface area of the composite figure is:
[tex]\begin{gathered} A\text{ = 628.319 + 816.814} \\ A=1445.133cm^2 \end{gathered}[/tex]That is the answer.
Question: The diameter of the handle of a softball bat is 1 3/4 inches of the diameters of 8 of the bat handles?
Answers
The answer is 14 inches
On Monday 92 students brought their lunch to school, which represents 46% of the total number of students that ate. How many total students ate on Monday ?
Answers
92 students represent 46%. To find how many students represent 100%, we can use the next proportion:
[tex]\frac{92\text{ students}}{x\text{ students}}=\frac{46\text{ \%}}{100\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 92\cdot100=46\cdot x \\ \frac{9200}{46}=x \\ 200=x \end{gathered}[/tex]200 students ate on Monday
A landscape architect uses molds for castingrectangular pyramids and rectangular prisms to makegarden statues. He plans to place each finishedpyramid on top of a prism. If one batch of concretemix makes one prism or three pyramids, how doesthe volume of one pyramid compare to the volume ofone prism? Explain.
Answers
Volume of a rectangular pyramid:
[tex]V=\frac{1}{3}(L\cdot W)\cdot h[/tex]Volume of a rectangular prism:
[tex]V=L\cdot W\cdot h[/tex]As you can see the volume of a rectangular pyramid (y) is a thrid part of the volume of a rectangular prism (x). Then, if the length, width and height of both molds is the same the volume of the rectangular prism (x) is three times the volume of the volume of the rectangular pyramid (y).
[tex]\begin{gathered} x=3y \\ y=\frac{1}{3}x \end{gathered}[/tex]what is the lcm of 25 and 37
Answers
SOLUTION:
Step 1:
In this question, we are given the question:
What is the lcm of 25 and 37?
Step 2:
From the question, we need to know the definition of LCM:
The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b
Step 3:
The details of the solution are as follows:
CONCLUSION:
The LCM of 25 and 37 =925
What input value produces the same output value for the two functions on the graph ? X=-1X= 0 X= 3X= 4
Answers
At x = 4 both f(x) and g(x) are qual to 3
Hi, can you help me, based with the data that is in the pic, to find the “Mean , Medium, Mode, and Range” . please !!
Answers
Step 1: Write out the set
[tex]\mleft\lbrace12,12,18,19,19,21,23,23,23,23,32,32,41,50,50,50,82,82\mright\rbrace[/tex]Step 2: Compute the mean
[tex]\text{Mean }=\frac{\text{ Sum of all the elements}}{\text{ the total number of the elements}}[/tex][tex]\text{the sum }=612[/tex][tex]the\text{ number of the elements }=18[/tex]Hence, the mean is given by
[tex]\operatorname{mean}\text{ = }\frac{612}{18}=34[/tex]The mean is 34
Step 3: Find the median
Median = [(n+1)/2]th element, if n is odd.
Median = mean of (n/2)th element and [(n/2)+1]th element, if n is even.
Where n is the number of elements in the set
In this case, n = 1 is even.
Therefore, the (n/2)th element is the 9th element, which is 23
and
the [(n/2)+1]th element is the 10th element, which is 23
[tex]\operatorname{median}\text{ }=\frac{23+23}{2}=\frac{46}{2}=23[/tex]Thus, the median is 23
Step 4: Find the mode
The mode is the value that appears most frequently in a data set.
In this case, 23 appears the most often in the data set.
Therefore, the mode is 23
Step 5: Find the range.
The range is the positive difference between the largest element of the set and the smallest element.
The largest element is 82, and
the smallest element is 12
Hence, the range is given by
[tex]\text{range = }82-12=70[/tex]The range is 70
How long will it take for a $2500 investment to grow to $4000 at an annual rate of 7.5%, compounded quarterly? Assume that no withdrawals are made. Donot round any intermediate computations, and round your answer to the nearest hundredth.If necessary, refer to the list of financial formulas.years I need help with this math problem
Answers
Answer:
6.33 years
Explanation:
The formula for investment at compound interest is given below::
[tex]A(t)=P\left(1+\frac{r}{k}\right)^{tk}\text{ where }\begin{cases}P=\text{Principal Invested} \\ r=\text{Interest Rate} \\ k=\text{Number of compounding periods}\end{cases}[/tex]From the statement of the problem:
• The initial investment, P = $2500
,• Annual Interest Rate, r = 7.5% = 0.075
,• Compounding Period (Quarterly), k = 4
,• Amount after t years, A(t) = $4000
,• Time, t = ?
Substitute these values into the compound interest formula above:
[tex]4000=2500\left(1+\frac{0.075}{4}\right)^{4t}[/tex]We then solve the equation for the value of t.
[tex]\begin{gathered} \begin{equation*} 4000=2500\left(1+\frac{0.075}{4}\right)^{4t} \end{equation*} \\ \text{ Divide both sides by 2500} \\ \frac{4000}{2500}=\left(1+0.01875\right)^{4t} \\ 1.6=\left(1.01875\right)^{4t} \\ \text{ Take the log of both sides} \\ \log(1.6)=\log(1.01875)^{4t} \\ \text{ By the power law of logs, }\log a^n=n\log a \\ \log(1.6)=4t\log(1.01875) \\ \text{ Divide both sides by 4}\log(1.01875) \\ \frac{\operatorname{\log}(1.6)}{4\operatorname{\log}(1.01875)}=\frac{4t\operatorname{\log}(1.01875)}{4\operatorname{\log}(1.01875)} \\ t\approx6.33\text{ years} \end{gathered}[/tex]It will take approximately 6.33 years for a $2500 investment to grow to $4000.
A man starts his job with a certain monthlysalary and earns a fixed increment every year. If his salary was$7500 after 4 years of service and $9000 after 10 years ofservice, what was his starting salary and what is the annualincrement? Do you consider it a fair increment according to ourpresent cost of life and infletion?
Answers
Let starting salary = x
Increment every year = y
Therefore:
Salary after 4 years of service = x+4y
Salary after 10 years of service = x+10y
We have the equations:
[tex]\begin{gathered} x+4y=7500 \\ x+10y=9000 \end{gathered}[/tex]Substracting equation 1 from equation 2, we get:
[tex]x+10y-(x+4y)=9000-7500[/tex]Simplify:
[tex]\begin{gathered} x+10y-x-4y=1500 \\ 6y=1500 \\ Solve\text{ for y} \\ \frac{6y}{6}=\frac{1500}{6} \\ y=250 \end{gathered}[/tex]Next, substitute y = 250 in the equation 1:
[tex]x+4(250)=7500[/tex]And solve for x:
[tex]\begin{gathered} x+1000=7500 \\ x+1000-1000=7500-1000 \\ x=6500 \end{gathered}[/tex]Answer:
Starting salary = $6500
Annual increment = $250
The following chart below represents the bedtimes of 100 students at Waller Junior High in a recent survey Number of Students Bedtime 8:00 PM 22 8.30 PM 17 9:00 PM 36 9:30 PM 25 If all 750 students at WJH were surveyed, what is the best prediction of the number of students who would have a bedtime of 9:00 PM in
Answers
Answer
The predicted number of students with bedtime of 9:00 PM
= 270 students
Explanation
For surveying and sampling, the fraction of a particular case in the sample is generalized for the entire population to predict that case for the population.
So, if we want the number of students who would have a bedtime of 9:00 PM, we first find the percentage of students with bedtime of 9:00 PM in the sample.
Number of students with bedtime of 9:00 PM in the survey = 36
Total number of students in the survey = 22 + 17 + 36 + 25 = 100
Percentage of students with bedtime of 9:00 PM in the survey = (36/100) = 0.36
So, in the population of 750 students,
The predicted number of students with bedtime of 9:00 PM = (0.36) (750) = 270 students
Hope this Helps!!!
What is the distance length between point a being located at 3 and point b being located at 7
Answers
Answer
The distance length between point a at 3 to point b at 7 is 4 units.
Step-by-step Explanation
The question wants us to find the distance between a point a located at 3 and another point b located at 7.
To solve this, we would visualize the question using the number line. The number line is one horizontal line whose markings represent integer numbers (whole numbers). So, if we want to find the distance from point 3 to point 7 on the number line, we simply move along the number line from 3 to 7.
To move this way we take it in steps of 1
3 to 4 (1 unit)
4 to 5 (1 unit)
5 to 6 (1 unit)
6 to 7 (1 unit)
So,
3 to 7 (1+1+1+1 = 4 units)
It is easy to see that the distance from point a at 3 to point b at 7 is simply
7 - 3 = 4
Hence, the distance length between point a at 3 to point b at 7 is 4 units.
Hope this Helps!!!
8. On a map with a scale of 1cm - 15km, two towns are 7.5 cm apart. How far apart are they in real life? I
Answers
ANSWER:
112.5 km
EXPLANATION:
Given that the map has a scale of 1cm : 15 km.
This means that 1 cm represents 15 km.
Since 1cm represents 50km, and the towns are 7.5 cm, the distance between both towns in real life will be:
[tex]\frac{15}{1\text{ }}\text{ }\ast\text{ 7.5 = }112.5\text{ km}[/tex]The distance between the two towns in real life will be 112.5 km
the measure of an interior angle of an equilateral triangle is given as 3n-6. solve for the value of nA. 22B. 60C.6D. 2
Answers
Perform the operation. Write your answer in scientific notation. 7.86×10^9________3×10^4
Answers
Answer:
2.62 * 10^ 5
Explanation:
To perform the operation given we rewrite it as
[tex]\frac{7.86}{3}\times\frac{10^9}{10^4}^{}[/tex]Now,
[tex]\frac{7.86}{3}=2.62[/tex]and
[tex]\frac{10^9}{10^4}^{}=10^{9-4}=10^5[/tex]therefore,
[tex]\frac{7.86}{3}\times\frac{10^9}{10^4}^{}=2.62\times10^5[/tex]which is our answer!
Which of the qqq-values satisfy the following inequality?6−3q≤16−3q≤16, minus, 3, q, is less than or equal to, 1Choose all answers that apply:Choose all answers that apply:(Choice A)Aq=0q=0q, equals, 0(Choice B)Bq=1q=1q, equals, 1(Choice C)Cq=2q=2q, equals, 2
Answers
Given -
6 - 3q ≤ 1
To Find -
The q-values that satisfy inequality =??w
Step-by-Step Explanation - ion
We will check for each of the given values;
A) q = 0
Putting q = 0, we get:
6 - 3(0) ≤ 1
6 ≤ 1
But, Six is greaterr than onee
So, this is the incorrect option.
B) q = 1
Putting q = 1, we get:
6 - 3(1) ≤ 1
3 ≤ 1
But, three is greater than one
So, this is the incorrect option.
C) q = 2
Putting q = 2, we get:
6 - 3(2) ≤ 1
0 ≤ 1
zero is less than one.
So, this is the correct option.
Final Answer -
Option (C) q = 2
Given the function g(x) = x2 – 2, find the range when the domain is {-2, -1, 1, 3} A. {-1, 2, 7} B. {-6, -3, 3, 11} C. {-7, -2, -1, 1} D. {-11, -3,3, 6}
Answers
The domain of the function is the values of x
Domain = {-2, -1, 1, 3}
We will substitute x by these values to find g(x)
g(x) is the range of the function
x = -2
[tex]g(-2)=(-2)^2-2=4-2=2[/tex]x = -1
[tex]g(-1)=(-1)^2-2=1-2=-1[/tex]x = 1
[tex]g(1)=(1)^2-2=1-2=-1[/tex]x = 3
[tex]g(3)=(3)^2-2=9-2=7[/tex]The range of the function is the values of g(x)
Range = {-1, 2, 7}
The answer is A
the scale of a map say that 4 cm represents 5km what distance on the map in cm represents an actual distance of 10 km
Answers
We can do as follow s
centimeters km
4 5
x 10
which is the same as saying that 4 centimeters are 5km, so x centimeters are 10 km. We want to find the value of x. To do so, we use the fact that this is a proportion, so it must happen that
[tex]\frac{4}{5}\text{ = }\frac{x}{10}[/tex]So if we multiply on both sides by 10, we get
[tex]x\text{ = }\frac{4_{}\cdot10}{5}\text{ = }\frac{40}{5}=8[/tex]So 8 cm represent 10 km.
write a ratio that is equivalent to 12:36 using the collums for 2 and 6
Answers
The given ratio is 12:36, which can be expressed as a fraction 12/36. An equivalent expression to this one can be obtained by simplifying
[tex]\frac{12}{36}=\frac{6}{18}[/tex]Therefore, the answer is 6/18.- x - 8 = -4x - 23 Solve for x
Answers
x=-5
Explanation
[tex]-x-8=-4x-23[/tex]Step 1
solve for x means we have to find the value for x that makes the equality true, to do that we need to isolate x
then
to isolate x we can apply the addition property of equality,it states that If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.
hence
Add 4x in both sides
[tex]\begin{gathered} -x-8=-4x-23 \\ -x-8+4x=-4x-23+4x \\ 3x-8=-23 \end{gathered}[/tex]Now, add 8 in both sides
[tex]\begin{gathered} 3x-8=-23 \\ 3x-8+8=-23+8 \\ 3x=-15 \end{gathered}[/tex]Step 2
now, we have a multiplication ( 3 multiplied by x), to isolate x we can apply the multiplication property,it says when you divide or multiply both sides of an equation by the same quantity, you still have equality
hence
divide both sides by 3
[tex]\begin{gathered} 3x=-15 \\ \frac{3x}{3}=\frac{-15}{3} \\ x=-5 \end{gathered}[/tex]therefore, the answer is
x=-5
I hope this helps you
Jim is cutting up apples to serve at a meeting.He is planning to serve 1/3ofvan apple to each of the 8 people at the meeting
How many apples does Jim need to serve
Answers
Jim needs three apples.
Step-by-step explanation:
1/3 x 8 =
8/3 =
2 and 2/3
Round up to three apples.
can you please help me
Answers
The relation between arcs AB and CD and angle x is:
[tex]m\angle x=\frac{1}{2}(m\hat{AB}+m\hat{CD})[/tex]Substituting with data, we get:
[tex]\begin{gathered} m\angle x=\frac{1}{2}(110+160) \\ m\angle x=\frac{1}{2}\cdot270 \\ m\angle x=135\text{ \degree} \end{gathered}[/tex]Identify the underlined place and 27.3856. Then round the number to that place.
Answers
Based on the positiion of the underlined decimal places, the underlined number is in the hundredths place.
Rounding it off, next to 8 in the hundredths place is 5 in the thousandths place.
If the number is 5 or greater, we add 1 to the previous decimal place therefore it is rounded to 27.39
For each measurement in the first column, write the equivalent number of inches in the second column. MeasurementMeasurement in Inches5 feet 2 inches627 feet 3 inches6 feet 4 inches4 feet 8 inches4 yards
Answers
You are required to provide the measurement in inches for each measurement given on the left column. The first one is solved thus;
[tex]\begin{gathered} 5ft,2in \\ \text{Where 1 foot=12 inches, then} \\ (5ft\times12)+2in=60in+2in \\ (5ft\times12)+2in=62in \end{gathered}[/tex]Therefore we shall use the same conversion rate of 12 inches equals 1 foot to solve the others as follows;
[tex]\begin{gathered} (1) \\ (7ft\times12)+3in=84in+3in \\ (7ft\times12)+3in=87in \end{gathered}[/tex][tex]\begin{gathered} (2) \\ (6ft\times12)+^{}4in=72in+4in \\ (6ft\times12)+4in=76in \end{gathered}[/tex][tex]\begin{gathered} (3) \\ (4ft\times12)+8in=48in+8in \\ (4ft\times12)+8in=56in \end{gathered}[/tex][tex]\begin{gathered} (4) \\ \text{Note that 1 yard=3 feet, which means} \\ 4\text{yards}=(4yd\times3)ft \\ 4\text{yards}=12ft \\ \text{Therefore,} \\ 12ft\times12=144in \\ \text{hence,} \\ 4\text{yards}=144in \end{gathered}[/tex]how do i solve for scale factor from smaller to larger?
Answers
Answer:
1) k = 3
2) k = 2
Explanation:
To find the scale factor from the smaller to the larger figure, we need to divide the length of the larger figure by the length of the smaller figure.
The figures are similar, so we will use corresponding sides. Then:
[tex]\begin{gathered} k=\frac{\text{ larger length}}{\text{ smaller length}} \\ \text{ For the first figure:} \\ k=\frac{21}{7}=3 \\ \text{For the second figure:} \\ k=\frac{8}{4}=2 \end{gathered}[/tex]Therefore, the answers are:
1) k = 3
2) k = 2