Mathematics College

Find the area of the region bounded by the given curves. y = 9x2 ln(x), y = 36 ln(x)

Answers

Answer 1
alrighty
find where they intersect

9x²ln(x)=36ln(x)
divide both sides by 9
x²ln(x)=4ln(x)
[tex]ln(x^{x^2})=ln(x^4)[/tex]
so
[tex]x^{x^2}=x^4[/tex]
so x=1 and and 2 (x can't be 0 or -2 because ln(0) and ln(-2) don't exist)

so intersect at x=1 and x=2
which is on top?

9(1.5)²ln(1.5)=20.25ln(1.5)
36ln(1.5)=36ln(1.5)
36ln(1.5) is on top
so

that will be
the area is
[tex] \int\limits^2_1 {36ln(x)-9x^2ln(x)} \, dx= [/tex]
[tex] [36x(ln(x)-1)-x^3(3ln(x)-1)]^2_1=[/tex]
[tex] 48ln(2)-29[/tex]

the area between the curves is 48ln(2)-29
Answer 2
Final answer:

The area of the region bounded by y = 9x2 ln(x) and y = 36 ln(x) is found by integrating the absolute difference of the two functions from x = 1 to x = 2, which yields ∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx.

Explanation:

To find the area of the region bounded by the curves y = 9x2 ln(x) and y = 36 ln(x), you first need to find the points where they intersect. This means setting the two functions equal to each other and solving for x, i.e., 9x2 ln(x) = 36 ln(x).

This simplifies to x2 = 4 which yields two solutions x = 2 and x = -2. However, since the natural logarithm ln(x) is not defined for x < 0, we discard x = -2. So, the two curves intersect at x = 2.

The area between the curves from x = 1 to x = 2 is then obtained by integrating the absolute difference of the two functions from x = 1 to x = 2, which gives:

∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx. You can evaluate this integral with standard calculus techniques.

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Related Questions

A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. 

Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.

Answers

Final answer:

Using the 45°-45°-90° triangle theorem in a right triangle, where 'a' represents the triangle's leg that is also the trapezoid's height, 'h' equals 'a' and the hypotenuse is 'a' times √2. Additional information would be needed to solve for a numerical value of 'h'.

Explanation:

In this problem, the wall's shape is a trapezoid, and we are using the 45°-45°-90° triangle theorem to find 'h', the height of the wall. We know in a 45°-45°-90° triangle, the two legs are congruent (same length), and the length of the hypotenuse is √2 times the length of a leg (based on Pythagorean theorem). In this case, if 'a' is the length of the triangle's leg connected to the rectangle, then 'h' would be equal to 'a' (since they are the legs in a 45-45-90 triangle), and the hypotenuse would be a√2.

Given an additional variable or measurement in this problem such as the length of the wall or the hypotenuse of the triangle, we could plug it in to solve for 'h'. Without additional information, the exact numerical height cannot be determined.

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if five notebooks cost $5.25, how much would three notebooks cost?

Answers

$5.25/5 notebooks= $1.05 each

$1.05*3 notebooks= $3.15 for 3 notebooks
The answer will be $3.15..

Steps to divide 125.00 by 7.75

Answers

            _____
    7.75 | 125

we want to get rid of that decimal....so we move it 2 spaces to the right....by doing that, we also have to move the decimal under the division sign by 2 spaces to the right....turning ur problem into :

                  16.1  R 225 <== ur answer
           ______
   775 |12500.0
             775
           ------- subtract
             4750
             4650
           ---------subtract
                1000
                  775
           -----------subtract
                225

Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 50 miles per hour and the other train travels at 60 miles per hour. How much time passes until the trains are 660 miles apart?

Answers

Let n =  the hours elapsed when the two trains are 660 miles apart.

Let the first train travel east and the second train travel west.
The distance traveled by the first train is
x = (50 mi/h)*(n h) = 50n mi

The distance traveled by the second train is
y = (60 mi/h)*(n h) = 60n h

The distance between the two trains after n hours is
x + y = 50 n + 60n = 110n mi

Because this distance is 660 miles, therefore
110n = 660
n = 6 hours

Answer: 6 hours

Select from the drop-down menu to correctly identify the property shown.

−4.8 + (3.2 + (−1.6)) = (3.2 + (−1.6)) + (−4.8)

A. Associative Property
B. Commutative Property
C. Opposite of a Sum Property

Answers

The answer is Commutative Property.

Answer:

Option B is correct.

Commutative property is used here.

Explanation:

Commutative Property states that we can add any number in any order, we will get the same result i.e, a+b = b+a.

let a = -4.8 and b = (3.2+(-1.6))

then, using commutative property we have;  

a+b=b+a then,

−4.8 + (3.2 + (−1.6)) = (3.2 + (−1.6)) + (−4.8).



For a Circle of radius is 5 feet, find the arc length s subtended by a central angle of 42 degrees

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{r\theta \pi }{180}\qquad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=5\\ \theta = 42 \end{cases}\implies s=\cfrac{5\cdot 42\cdot \pi }{180}[/tex]

The arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is  3.665 feet.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The formula for arc length is given by:

s = rθ

where s is the arc length, r is the radius of the circle, and θ is the central angle subtended by the arc in radians.

To use this formula, we first need to convert the central angle from degrees to radians:

θ = (π/180) × 42 = 0.733 radians

Now we can plug in the values of r and θ into the formula to get:

s = 5 × 0.733

= 3.665 feet

Therefore, the arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.

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What are all the positive integers that are in the solution set for
m < 3

Answers

1 and 2 because it’s not asking for negatives. 3<3 wouldn’t work because they are the same.

The price of gourmet coffee beans at the corner market has increased 10% per year over the past several years if the current cost is $40 per pound what did a pound of gourmet beans cost two years ago

Answers

$20 because 10% of 40 is 10 and the price now is 40 so 2 years before would have been 20

Answer: $32.4

Step-by-step explanation:

Given : The price of gourmet coffee beans at the corner market has increased 10% (0.1) per year over the past several years.

The current cost is $40 per pound .

The exponential decay equation is given by :-

[tex]y=A(1-r)^x[/tex], where r is the rate of decay and A is the initial amount and x is the time period.

Put A = 40 , r= 0.1 and t=2, we get

[tex]y=40(1-0.1)^2=\$32.4[/tex]

Hence, the cost of  a pound of gourmet beans two years ago= $32.4

Tony rounded each of the numbers 1,210 and 1,148 to the nearest hundred. Which choice correctly compares the rounded numbers?

Answers

1,200 is the correctly nearest . We round 1,210 to 1,200
Final answer:

The process of rounding numbers 1,210 and 1,148 to the nearest hundred results in 1,200 and 1,100, respectively. Therefore, 1,200 is greater than 1,100.

Explanation:

In Mathematics, rounding numbers is common practice for simplifying calculations. We are given the numbers 1,210 and 1,148, and we need to round them to the nearest hundred.

Let's round them:

1,210 rounded to the nearest hundred is 1,200.1,148 rounded to the nearest hundred is 1,100.

So, when comparing the rounded numbers, 1,200 is greater than 1,100.

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based on the census state A has 11 fewer electoral votes for president then state b. If the total number of electoral votes for these two states is 87 find the number for each state.

Answers

a + b = 87
a = b - 11

b - 11 + b = 87
2b - 11 = 87
2b = 87 + 11
2b = 98
b = 98/2
b = 49 <===

a = b - 11
a = 49 - 11
a = 38 <===

Which equation represents a line that passes through (5, 1) and has a slope of ?

A. y – 5 = (x –1)
B. y – = 5(x –1)
C. y – 1 = (x –5)
D. y – 1 = 5

Answers

the answer is c  because
 when you y -1 = ( x - 5)
                 1- 1 = 5 -5
                   0 = 0
where  A    y - 5 = ( x - 1)
                  1 - 5 =  ( 5 - 1 )
                    -4 dosenot equal 4
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ &({{ 5}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{1}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=\cfrac{1}{2}(x-5)\implies y-1=\cfrac{1}{2}x-\cfrac{5}{2} \\\\\\ y=\cfrac{1}{2}x-\cfrac{5}{2}+1\implies y=\cfrac{1}{2}x-\cfrac{3}{2}[/tex]

A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 32 square feet. Find the lengths of the sides of the poster and the sign?

Answers

Area of square one = [tex](x-2)(x-2)[/tex] = [tex]x^2-4x+4[/tex]
Area of square two = [tex]x^2[/tex]

The difference of the area of two squares = 32
[tex]x^2-(x^2-4x+4)=32[/tex]
[tex]x^2-x^2+4x-4=32[/tex]
[tex]4x-4=32[/tex]
[tex]4x=32+4[/tex]
[tex]4x=36[/tex]
[tex]x=36/4[/tex]
[tex]x=9[/tex]

The side length of the poster = [tex]x-2 = 9-2 = 7 feet[/tex]
The side length of the sign = [tex]x=9[/tex]

Jonah is playing a video racing game called Checkpoint. The speed of Jonah’s car is recorded four times during one lap. At the first checkpoint, his speed is 80 miles per hour. At the second checkpoint, his speed has reduced by 5%. At the third checkpoint, Jonah’s speed has increased by the speed from the previous checkpoint. At the fourth checkpoint, his speed decreased by 20% compared with the third checkpoint. What is Jonah’s net change in speed between the first and fourth checkpoints?

Answers

Answer:

negative 15 is your answer

Step-by-step explanation:

the last number was negative so it would be negative 15

Answer:

-15

Step-by-step explanation:

yes

I need help on and c plz

Answers

Wouldn't you just multiply 3/4 (the height) by 2 1/4 (the width) l x w = a if it's flat so 27/4 simplified to be 6 3/4 (hopefully i'm right)

Create a process that will calculate the series 1 + x + x2 + x3 + x4 .......... + xn where x is a floating point number and n is a positive number. you process should be designed so exponentiation (or the pow function in c++) is not needed.

Answers

Assumptions
   
1. n is an integer.
   
2. Language is c++
       
double expr(double x, int n)
   
{
   
double sum = 0.0;
   
double power = 1.0; // Will have the value x^y where y ranges from 0 to n
   
int i;
       
for(i=0; i <= n; ++i) {
   
sum += power;
   
power *= x;
   
}
   
return sum;
   
}

Jeff prepares meals in the home of his customers. His fixed cost for transportation and supplies is $14.50. The labor and groceries needed for each family meal is $8.80, so the expense function is E=5.7q+8.8. T or F

Answers

The expense function is:E ( q ) = m q + b,where b stays for Fixed costs.In this case:m = 8.8 ( the labor and groceries for each family meal ) and b = 14.5So E = 8.8 q + 14.5,  not E = 5.7 q + 8.8Answer: False

Answer:

The given equation is false

Step-by-step explanation:

Given equation : E= 5.7q+8.8

To show : It is true or false

Solution : Cost of transportation and supplies is fixed = $14.50

Cost of labor and groceries for each family meal =$8.80

Let x is the number of meals

so, according to the question Expense function for x number of meals is

Expense function = x(cost of labor and groceries for 1 family meal)+ cost of  transportation and supplies(fixed)

E= 8.80x+14.50  which is the required equation.

Therefore, given equation is false.

if the perimeter of a rectangle is 318 inches, find the width and length. what's the answer?

Answers

If those Length and Width are consecutive integers then we can calculate the answer by following:

let's consider that Length is n
Then width will be n+1

Perimeter of rectangle is equal to 2*(L+W) in this case
P = 2*(n + [n+ 1]) = 2*(n + n + 1) = 2(2n + 1)

P = 318

318 = 2(2n+1)
159 = 2n+1
159 - 1 = 2n
158 = 2n
79 = n

So this means that Length is 79 and Width is 80
or vice versa, Length is 80 and Width is 79

Soon after taking an aspirin, a patient has absorbed 320 mg of the drug. After 2 hours, only 80 mg remain. Find an exponential model for the amount of aspirin in the bloodstream after t hours.

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ \textit{at 0 seconds, t = 0, the patient has 320mg in its blood} \\\\\\ 320=I(1-r)^0\implies 320=I\cdot 1\implies 320=I \\\\\\ A=320(1-r)^t\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{2 hours later, t = 2, the patient has 80mg in its blood} \\\\\\ 80=320(1-r)^2\implies \cfrac{80}{320}=(1-r)^2\implies \cfrac{1}{4}=(1-r)^2 \\\\\\ \sqrt{\cfrac{1}{4}}=1-r\implies \cfrac{\sqrt{1}}{\sqrt{4}}=1-r\implies \cfrac{1}{2}=1-r\implies r=1-\cfrac{1}{2} \\\\\\ r=\cfrac{1}{2}\implies r=0.5\qquad A=320(1-0.5)^t\implies \boxed{A=320(0.5)^t}[/tex]

What are the factors of 27

Answers

Factors of 27: 1, 3, 9, 27

Note that two negative factors such as -3 and -9 can also multiply to equal 27.

HELP PLEASE,

Part a of the question was posted earlier on.

Answers

[tex]\bf \lim\limits_{x\to 6}~\cfrac{x^2+x+42}{x-6}\implies \lim\limits_{x\to 6}~\cfrac{(x+7)(x-6)}{(x-6)}\implies \lim\limits_{x\to 6}~x+7 \\\\\\ \lim\limits_{x\to 6}~(6)+7=13 \\\\\\ \textit{since the original equation holds for all, }x\ne 6,\textit{ then it approaches}\\ \textit{the same limit as }x+7[/tex]

805 tens in standard form

Answers

Hey! Hope that I can help.

Y + z — 2y

If y=4 and z= 2
(Simplify)

Answers

Substitute y for 4 and z for 2
4+2-2y
Then add like terms
6-2y
That is as simplified as it gets.

Order square root of three, 2pi, and 1.5 from least to greatest

Answers

Be more specific please
1.5, square root of 3, and 2pi

Answer to both of these?

Answers

14a³ /a = 14a²

9b/3b = 3

hope this helps

Solve for x. 4−(2x+4)=5
A x=6
B x=−10
C x=−52

Answers

4 - (2x + 4) = 5
4 - 2x - 4 = 5
-2x = 5
x = - 5/2 <==

The solution for x in the equation 4 - (2x + 4) = 5 is x = -5/2. So, the correct choice is x = -5/2. Option c is the correct choice.

To solve for x in the equation 4 - (2x + 4) = 5, follow these steps:

1. First, simplify the equation by combining like terms. Start by removing the parentheses by distributing the negative sign:

  4 - 2x - 4 = 5

2. Now, simplify further by combining the constants on the left side of the equation:

  (4 - 4) - 2x = 5

  0 - 2x = 5

3. Next, isolate the variable x by getting rid of the -2 coefficient. To do this, divide both sides of the equation by -2:

  (0 - 2x) / -2 = 5 / -2

  0 / -2 - (2x / -2) = -5/2

  0 + x = -5/2

4. Finally, simplify:

  x = -5/2

So, the solution for x is:

x = -5/2

So,  Option c is the correct choice.

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Que. Solve for x. 4−(2x+4)=5

A x=6

B x=−10

C x=−5/2

Write a number sentence that demonstrates each property.
Commutative property of addition
Associative property of addition
Identity property of addition

Answers

they are usually represented like this

commutative property of addition
a+b=b+a

associative property of additon
(a+b)+c=a+(b+c)

identity property of addition
a+0=a




so number sentatnces

lets say a=1,b=2,c=3




commutative property of addition
1+2=2+1

associative property of addition
(1+2)+3=1+(2+3)

identity property of addition
1+0=1

Answer:

a + b = b + a

(a + b) + c = c + (b + a)

0 + a = a

I hope this helps, have an amazing day!

The length and width of a rectangle whose length is 8 centimeters more than its width

Answers

What is the question? Please give more details.

Identify the triangles that are right triangles.

Answers

Right triangles have a 90 degree corner.
triangles often have a small box in the corner and are 90 degrees

Tyron is making 52 cookies fi a party. Some will be pecan cookies. Some will be honey ginger cookies . The ratio of pecan to honey ginger cookies will be 7:6 . Suppose you use systematic guess and check to find the number of each type of cookie

Answers

There will be  28 pecan cookies and 24 honey ginger cookies

Where did the Maya's lived?

Thanks,
-Laura B

Answers

The ancient Mayans lived in what is now known as southern Mexico and northern Central America including Guatemala, Belize, Honduras, Yucatán Peninsula and El Salvador

The Mayans lived, hmm, where is now know as Southern Mexico and northen Central America, including lots of countrys in their. etc, Guatemala, Belize, El Salvador
The ancient Mayans lived in what is now known as southern Mexico and Northern Central America, including Guatemala, Belize, Honduras, Yucatán Peninsula, and El Salvador.

I hope this helps! :>
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