Use the Trapezoidal Rule to approximate ∫43ln(x2+9) dx using n=3. Round your answer to the nearest hundredth.
Answers
The Trapezoidal rule formula is given to be:
[tex]\begin{gathered} \int_a^bf(x)dx\approx\frac{\triangle x}{2}(f(x_o)+2f(x_1)+2f(x_2)+2f(x_3)+...+2f(x_{n-1})+f(x_n) \\ where \\ \triangle x=\frac{b-a}{n} \end{gathered}[/tex]The question gives:
[tex]\begin{gathered} f(x)=\ln(x^2+9) \\ a=3 \\ b=4 \\ n=3 \\ \therefore \\ \triangle x=\frac{1}{3} \end{gathered}[/tex]Therefore, divide the interval into n = 3 subintervals of length 1/3 with the following endpoints:
[tex]a=3,\frac{10}{3},\frac{11}{3},4[/tex]Evaluate the function at the endpoints:
[tex]\begin{gathered} f(x_0)=f(3)=2.89 \\ 2f(x_1)=2f(\frac{10}{3})=6.00 \\ 2f(x_2)=2f(\frac{11}{3})=6.22 \\ f(x_3)=f(4)=3.22 \end{gathered}[/tex]Sum up the calculated values and multiply by Δx/2:
[tex]\Rightarrow\frac{1}{3\times2}(2.89+6.00+6.22+3.22)=3.06[/tex]Therefore, the answer will be:
[tex]\int_3^4\ln(x^2+9)dx\approx3.06[/tex]Related Questions
Using the graph of f(x)=x^2 as a guide describe the transformations and then sketch a graph of each function g(x)=(x-5)^2
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1) In comparison to that parent function y =x², in g(x) = (x-5)² we have a horizontal translation to the right. in 5 units.
2) As we can see below:
Note that the Potting tool expands the (x-5)².
[tex]y = \frac{1}{3} x + 15[/tex]what is the answer
Answers
The slope of the given equation is ,
[tex]m=\frac{1}{3}[/tex]Slope of perellel line will also be same = 1/3 ,
The equation of perellel line is ,
[tex]\begin{gathered} y-0=\frac{1}{3}(x-6) \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]The graph below shows the relationship between the amount of time a ferris wheel has been moving and the height above ground of a seat on the ferris wheel. based on the graph. Which statement best describes why height is a function of time in the relationship?
Answers
ANSWER
b. Each value of time has exactly 1 value for height associated with it.
EXPLANATION
A function is a relationship where each value of the function has only one value of the variable associated with that value. In this problem, the function is height and the variable is time, therefore the answer is option b.
Working together, Sarah and Heidi can clean the garage in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?
Answers
Given the rates:
[tex]\begin{gathered} \frac{1}{t}=Sarah^{\prime}s\text{ }Rate \\ \\ \frac{1}{t+3}=Heidi^{\prime}s\text{ }Rate \\ \\ \frac{1}{2}=Rate\text{ }working\text{ }together \end{gathered}[/tex]Add their rates of cleaning to get rate working together:
[tex]\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}[/tex]Solving for t:
[tex]\begin{gathered} \frac{2(t+3)+2t-t(t+3)}{2t(t+3)}=0 \\ \\ \frac{2t+6+2t-t^2-3t}{2t(t+3)}=0 \\ \\ \frac{t+6-t^2}{2t(t+3)}=0 \\ \\ -t^2+t+6=0 \\ \\ (t+2)(t-3)=0 \end{gathered}[/tex]Hence:
t = -2
t = 3
Time can't be negative; then:
Heidi's time: t + 3
3 + 3 = 9
ANSWER
It will take Heidi 9 hrs to clean garage working alone
A pie shop bakes a certain amount of pies each week. 150 of those pies are apple pies. These apple pies makes up 40 percent of the total pies. How many pies does the shop make each week?
Answers
The number of apple pies made each week is 375
Here, we want to know the total number of pies made per week
Let the total number of pies be p
From the question, 40% of p is 150
Thus, we have it that;
[tex]\begin{gathered} 40\text{ \% of p = 150 } \\ \frac{40}{100}\times\text{ p = 150} \\ 40p\text{ = 100}\times150 \\ \\ p\text{ = }\frac{100\times150}{40} \\ p\text{ = 375} \end{gathered}[/tex]Evaluate. 3/4 - 1/2 × 7/8 Write your answer in simplest form.
Answers
we have the expression
3/4 - 1/2 × 7/8
so
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
First Multiplication
so
[tex]\frac{1}{2}\cdot\frac{7}{8}=\frac{7}{16}[/tex]substitute
[tex]\frac{3}{4}-\frac{7}{16}[/tex]Remember that
3/4 is equivalent to 12/16 (multiply by 4 both numerator and denominator)
substitute
[tex]\frac{12}{16}-\frac{7}{16}=\frac{5}{16}[/tex]therefore
the answer is 5/16Mary is 4 years older than Sue. If the sum of their ages is 16. How would you set up the equations?
Answers
Answer:
A. x=y-4, x+y=16
C. x=y-4, x+y=16
Explanation:
• Let Sue's age = x
Mary is 4 years older than Sue, therefore:
• Mary's age, y = x+4
[tex]\begin{gathered} y=x+4 \\ \implies x=y-4 \end{gathered}[/tex]Next, the sum of their ages is 16. This gives:
[tex]x+y=16[/tex]Therefore, the equation is:
[tex]\begin{gathered} x=y-4 \\ x+y=16 \end{gathered}[/tex]The correct choices are A and C.
What is the solution to 4x+6. A x<3 B x<6 C x<48 D x<96
Answers
we have the inequality
[tex]4x+6\leq18[/tex]solve for x
subtract 6 both sides
[tex]\begin{gathered} 4x\leq18-6 \\ 4x\leq12 \end{gathered}[/tex]step 2
Divide by 4 both sides
[tex]x\leq3[/tex]In the front of a building there are three doors each to be painted
a different color from 10 different available colors. How many color
arrangements for the doors are there?
Answers
In this case, the order doesn't matter and the colors cant be repeated.
Now, we need to use the permutation formula:
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]Where n represents the total different available colors and r is equal to
the number of doors.
Replacing on the permutation formula:
[tex]P(10,3)=\frac{10!}{(10-3)!}[/tex][tex]P(10,3)=\frac{10!}{7!}[/tex][tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=10x9x8![/tex]Then
[tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=720[/tex]Hence, there are 720 possible arrangements for the doors.
The formula is A=P(1+r/n)^nt8. Oswald Chesterfield Cobblepot invests $5,000 into an account that earns 2.5% interestcompounded monthly.a. How much money is in the account after two years? Use the formula above.Answer:b. How much money in interest was earned?Answer:
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given formula with definition of terms
Compounded Amount is gotten using:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]Where:
A =final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
STEP 2: Write the given parameters
[tex]P=5000,r=\frac{2.5}{100}=0.025,t=2,n=12\text{ since it is compounded monthly}[/tex]STEP 3: Calculate the Compounded Amount
[tex]\begin{gathered} A=5000(1+\frac{0.025}{12})^{2\times12} \\ A=5000(1+0.002083333333)^^{24} \\ A=5000\times1.0020833333^{24} \\ A=5000\times1.05121642 \\ A=5256.0821 \\ A\approx5256.08 \end{gathered}[/tex]STEP 4: Calculate the compounded interest
[tex]\begin{gathered} Interest=Amount-Principal \\ \text{By substitution,} \\ Interest=5256.08-5000 \\ Interest=256.08 \end{gathered}[/tex]Hence,
$5256.08 was in the account after 2 years
The interest earned was $256.08
Last weekend, 26, 675 tickets were sold at County Stadium. This weekend 24,567 tickets were sold at County Stadium. If you estimate the number of tickets County Stadium sold over the two weekends by rounding each number to the nearest thousand, then you will find there were about ____ tickets sold.
Answers
We have the tickets sold each weekend:
• Last weekend: 26,675
,• This weekend: 24,567
We have to find how many tickets where sold in both weekends by rounding each number to the nearest thousand units. This will let us do the math without a calculator.
Then, we can approximate 26,675 to 27,000 and 24,567 to 25,000.
NOTE: we round the numbers up because the next number is 5 or greater. Then 675 is and 567 are approximated as 1,000.
We then can add them as: 27,000+25,000 = 52,000.
Answer: the solution is about 52,000 tickets sold.
NOTE: the exact solution would have been 51,242
The square of the difference between a number n and eighty
Answers
Given the statement: The square of the difference between a number n and eighty.
we need to write the algebraic expression for the statement.
The difference between the number n and 80 will be:
[tex]n-80[/tex]The square of the difference will be:
[tex](n-80)^2[/tex]A farmer has 1,416 feet of fencing available to enclose a rectangle area bordering a river. No fencing is required along the river. Let x represent the length of the side of the rectangular enclosure that is perpendicular A(x)= Find the dimensions that will maximize the area. The length of the side rectangle perpendicular to the river is and the length of the side of the rectangle parallel to the river is.What is the maximum area?
Answers
The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 250632 ft²
Explanation:Given:
The length of the fencing = 1416 ft
The length of the side rectangle perpendicular to the river = x
To find:
The dimensions that will maximize the area
To determine the dimensions, we will make an illustration of the given information:
let the length o the rectangle parallel to the river = y
Length of the for the enclosed area = Perimeter of the enclosed area
Perimeter of the enclosed area = x + x = y = 2x + y
[tex]1416=2x+y\text{ . . .\lparen1\rparen}[/tex]Area of the rectangle = length × width
length = y, width = x
let the Area of the rectangle = A(x)
[tex]A(x)\text{ = xy . . . \lparen2\rparen}[/tex]To get the expression for A(x), we will make y the subject of the formula in equation (1):
y = 1416 - 2x
substitute for y in equation (2):
[tex]\begin{gathered} A(x)\text{ = x\lparen1416 - 2x\rparen} \\ \\ A(x)\text{ = 14166x - 2x}^2 \end{gathered}[/tex]To get the maximum dimension, we will differentiate with respect to x:
[tex]\begin{gathered} A^{\prime}(x)\text{ = 1416 - 4x} \\ \\ At\text{ maximum, A'\lparen x\rparen = 0:} \\ 1416\text{ - 4x = 0} \\ 1416\text{ = 4x} \\ x\text{ = }\frac{1416}{4} \\ x\text{ = 354} \end{gathered}[/tex]substitute for x in equation (1):
[tex]\begin{gathered} 1416\text{ = 2\lparen354\rparen + y} \\ 1416\text{ - 708 = y} \\ y\text{ = 708} \end{gathered}[/tex]The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 354 × 708
The maximum area = 250632 ft²
by noon the temperature in Buffalo had risen to 18 degrees farenheit what was the temperature there at noon Buffalo is a - 9
Answers
If the temperature of buffalo rised 18 degrees means that it is an addition between the 2 temperatures
[tex]-9+18=9[/tex]the temperature at noon is 9°F
Math Lab A - Section 203B Notebook Home Insert Draw View Class Notebook U abe А. = = A Styles ☆ ? The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Average Mass (kilograms) 1,354 1,985 Large Car Large Truck 2,460 Part A To the nearest hundred, how much greater is the mass of a large truck than the mass of a small car? Fill in the blanks to answer the question. To the nearest hundred, a large truck has a mass of kilograms, and a small car has a mass of kilograms. So, a large truck has a mass about kilograms greater than a small car.
Answers
Given:
Round the mass of the large car to the nearest thousand.
Because 1985 is between 1,000 and 2,000 and closer to 2,000 ,the number should round up to 2,000.
Option D is the correct answer.
Solve the inequality. Graph the solution.Z/4 is less than or equal to 12.
Answers
You have the following inequality:
z/4 ≤ 12
To solve the previous inequality you proceed as follow:
z/4 ≤ 12 multiply both sides by 4
z ≤ 48
Hence, the solution is z ≤ 48
when you want to graph a solution of the form "z lower or equal than", you draw a black point, that means the solution are all number lower than 48, including 48.
which of the following equations is a direct variation equation that has the ordered pairs 12.5, 5 as a solutiona. y=7.5xb. y=x-7.5c. x=y+7.5d. y=2.5x e. y= -2.5x f. (2/5)x
Answers
The ordered pair given is 12.5, 5
This means that
When x = 12.5, y = 5
Looking at the given equations, if we substitute the values of x and y, the correct option would be C
The equation is expressed as
x = y + 7.5
By substituting, it becomes
12.5 = 5 + 7.5
12.5 = 12.5
The correct option is C
Suppose that you want to buy 6 different books and the order that you buy them does not matter. Then thenumber of ways to choose 6 books from 44 available books is
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We have that the order doesn't matter without repetition, so should use combinations that are represented by the next formula:
[tex]C=\frac{n!}{r!(n-r)!}[/tex]Where n is the total of books and r the numbers of the group, in this case, 6 differents books.
Replace these values:
[tex]\frac{44!}{6!(44-6)!}[/tex][tex]C=\frac{44!}{6!(38)!}=7059052\text{ ways to choose 6 books from 44 available}[/tex]If f(5)=3, write an ordered pair that must be on the graph of y = f(x + 1) + 2
Answers
(4, 5)
Explanations:The given function is:
y = f(x + 1) + 2
There are many ordered pairs that can be on the graph of y = f(x + 1) + 2, but with the information given will can look for one of them.
Let x = 4
y = f(x + 1) + 2
y = f(4 + 1) + 2
y = f(5) + 2
Since it is given that f(5) = 3, the equation above can be simplified to get the value of y.
y = f(5) + 2
y = 3 + 2
y = 5
Therefore, an ordered pair that must be on the graph of y = f(x+1) + 2 is (4, 5)
I need help with this trigonometric function I will upload a photo
Answers
For us to be able to determine the distance along an arc on the surface of the earth, we will be using the following formula:
[tex]\text{ S = r}\theta[/tex]Where,
S = arc length
r = radius (radius of the earth)
θ = central angle (in radian)
Given:
r = 3960 miles
θ = 48 mins.
a.) Let's convert the given measure of the central angle to radian.
[tex]\theta=48mins.\text{ = (48 mins.) x }\frac{1^{\circ}}{(60\text{ mins.})}\text{ = }\frac{48}{60}(1^{\circ})[/tex][tex]\theta\text{ = }\frac{4}{5}^{\circ}[/tex][tex]\text{ }\theta_{radian}\text{ = }\theta_{degrees}\text{ x }\frac{\pi}{180^{\circ}}[/tex][tex]\text{ }\theta_{radian}\text{ = }\frac{4}{5}\text{ x }\frac{\pi}{180}\text{ = }\frac{4\pi}{900}\text{ = }\frac{\pi}{225}\text{ radians}[/tex]b.) Let's now determine the distance (arc length).
[tex]\text{ S = r}\theta[/tex][tex]\text{ S = (3960)(}\frac{\pi}{225}\text{ ) = }\frac{3960\pi}{225}\text{ miles = 17.6}\pi\text{ miles = 55.2920307 }\approx\text{ 55.292 miles}[/tex]Therefore, the answer is 55.292 miles.
Max exercise 4 hrs during each 7 day week. At this rate, how many hours do he exercise in 35 days?
Answers
We know that Max exercises 4 hours during each 7-day-week.
After 35 days (5 weeks), the number of hours would be
[tex]4\cdot5=20[/tex]Max would exercise 20 hours after 35 days.450 students are graduating. 68% are going to college. 14% are working. How many students are unsure about what to do?
Answers
ANSWER
81 students
EXPLANATION
We have that 450 students are graduating.
68% (out of 100%) are going to college while 14% (out of 100%) are working.
To find the percentage of the studetns that are unsure about what to do, we have to subtract the percentages of those that know what to do from 100%.
That is:
100 - (68 + 14)
=> 100 - 82
=> 18%
Therefore, 18% of people are unsure about what to do.
Now, to find the number of students, we multiply this percent by the total number of students (450):
[tex]\begin{gathered} \frac{18}{100}\cdot450 \\ =\text{ 81} \end{gathered}[/tex]81 students are unsure about what to do.
question 15:A new webpage received 5,000 page views on the first day. The number of page views decreased by 10% every day. How many total page views did the webpage have after seven days? Round to the nearest whole number.
Answers
Explanation
This question wants us to compute the depreciation formula and also get the value of the total page views did the webpage have after seven days.
The general formula is given by
[tex]A=P(1-\frac{r}{100})^n[/tex]In our case
[tex]\begin{gathered} A=? \\ P=5000 \\ r=10 \\ n=n \end{gathered}[/tex]Thus, we will have
[tex]A=5000(1-\frac{10}{100})^n[/tex]We will now have to write the first three terms of the expression to get the required equation
[tex]\begin{gathered} when\text{ n=1} \\ A_1=5000(0.9)^1=4500 \end{gathered}[/tex][tex]\begin{gathered} when\text{ n=2} \\ A_2=5000(0.9)^2=4050 \end{gathered}[/tex]Now, we can list the first three terms as
[tex]5000,4500,4050[/tex]With the above, we can now compute the total web pages after 7 days using the sum of the geometric sequence:
We will get the common ratio
[tex]ratio=r=\frac{4500}{5000}=0.9[/tex][tex]\begin{gathered} S=\frac{a(1-r^n)}{1-r} \\ \\ a=5000 \\ r=0.9 \\ n=7 \end{gathered}[/tex][tex]S=\frac{5000(1-0.9^7)}{1-0.9}=26085[/tex]
Thus, we can see that the answer is option C
[tex]\frac{5000(1-0.9^7)}{1-0.9}=26,085[/tex]Find the distance of a wheel where the radius is 10 feet and it gives 15 rotations. How many inches did the wheel travel in those 15 rotations?
Answers
We will find the distance after 15 rotations by multiplying the perimeter of the circumference by 15, that is:
[tex]d=15(2\pi r)\Rightarrow d=30\pi(10)\Rightarrow d=300\pi\Rightarrow d\approx941.48[/tex]From this, we have that the wheel traveled approximately 941.48 feet.
Pleasr help fast it's due today 1. Consider the surface area of the following pyramid.224 am4 am4 am2.24 cm4 cm3 cm4 cm4 cm3 cm13 cm4 cm4 cm3 cm4 cm4 cm3 cm(a) Calculate the total surface area of the pyramid. Show your work.
Answers
Given data:
The given figure of square pyramid.
The expresssion for the total surface area is,
[tex]\begin{gathered} \text{TSA}=(3\text{ cm)(3 cm)+4}\times\frac{1}{2}(3\text{ cm)(}2.24\text{ cm)} \\ =9cm^2+2(3\text{ cm)(2.24 cm)} \\ =22.44cm^2 \end{gathered}[/tex]Thus, the total surface area of the given pyramid is 22.44 sq-cm.
Study 8 22,29,36 Which expression could be used to find the missing number in the pattern? A. (8 +36) - 2 C. (29-22) + 8 B. (8 x 22) - 2 D. (22 - 7) + 8
Answers
8,22,29,36
between 22 - 8 = 14
divide by 2 ,14/2= 7
now add 8+7 = 15
Then anwer is
Option C) (29-22) + 8 = 7 + 8
(Score for Question 3: of 6 points)3. Felipe is ordering new carpet for his bedroom floor. (The floor is represented in the picture below asrectangle JKLM). He knows the base edge, ML, measures 18 ft. And the distance of diagonal KMmeasures 25 ft. What is the area of Felipe's bedroom floor? Show all work and round your answer tothe nearest tenth.JKM
Answers
Solution:
Given:
[tex]\begin{gathered} The\text{ length of the room floor is 18 ft} \\ The\text{ width of the room floor is }x \end{gathered}[/tex]
Considering the right triangle KLM,
To get the width (x), we use the Pythagoras theorem.
[tex]\begin{gathered} 18^2+x^2=25^2 \\ x^2=25^2-18^2 \\ x^2=625-324 \\ x^2=301 \\ x=\sqrt{301} \\ x=17.35ft \\ \\ Hence,\text{ the width is 17.35ft} \end{gathered}[/tex]
The area of the bedroom floor is;
[tex]\begin{gathered} A=l\times w \\ A=18\times17.35 \\ A=312.3ft^2 \end{gathered}[/tex]
Therefore, the area of Felipe's bedroom floor to the nearest tenth is 312.3 square feet.
Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.Interval notation for the above graph in inequality is______
Answers
Answer:
[tex](-∞,4)[/tex]Step-by-step explanation:
To solve the following inequality, use inverse operations.
[tex]\begin{gathered} -8x-4>-36 \\ -8x>-32 \\ x<\frac{-32}{-8} \\ x<4 \\ \text{ Interval notation:} \\ (-∞,4) \end{gathered}[/tex]Now, for the number line representing this inequality:
The United States Pentagon building is modeled on the coordinate plane as regular pentagon ABThe vertices of the pentagon are A(-7.42,2.42), B(0,7.88),C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35) what is the approximate perimeter in feet of the us pentagon building
Answers
Given,
The coordinates of the vertices of the pentagon is,
A(-7.42,2.42), B(0,7.88), C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35)
Required
The approximate perimeter of the pentagon.
The perimeter of the pentagon is calculated as,
The length of side AB is,
[tex]AB=\sqrt{(-7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side BC is,
[tex]AB=\sqrt{(7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side CD is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The length of DE is,
[tex]DE=9.21[/tex]The length of AE is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The perimeter of the pentagon is,
[tex]Perimeter=9.2124+9.2124+9.211+9.211+9.21=46.0568[/tex]Hence, the perimeter of the pantagon is 46.0568.
Hello! I need help in answering question number 3 which I will attach. Geometry 3 D shapes. It reads To make one order you need to fill the cone with ice cream first, and then add the scoop on top. How many total cubic inches of ice cream are in one order?
Answers
The ice-cream is made up of of a sugar cone and a scoop in the shape of half a sphere
Hence, the formula for the volume V of the total cubic inches of ice cream is:
[tex]\begin{gathered} V\text{ = Volume of cone + half a volume of a sphere} \\ V\text{ = }\frac{1}{3}\pi r^2h\text{ + }\frac{2}{3}\pi r^3 \end{gathered}[/tex]Given:
height of cone = 4.6 inches
radius of cone = 1.7 inches
radius of sphere = 1.7 inches
Substituting the given values:
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^2\text{ }\times\text{ 4.6 + }\frac{2}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^3 \\ =\text{ 24.211 in}^3 \\ \approx\text{ 24.21 in}^3 \end{gathered}[/tex]Answer:
24.21 cubic inches