Mathematics College

How would I solve this

Answers

Answer 1

$A=\frac{1}{2}\ln17 = 1.417$

Step-by-step explanation:

The area A under the curve can be written as

$\displaystyle A = \int_0^2\!\dfrac{4x\:dx}{1+4x^2}$

To evaluate the integral, let

$u = 1+4x^2 \Rightarrow du = 8xdx\:\text{or}\:\frac{1}{2}du = 4xdx$

so the integral becomes

$\displaystyle \int\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\int\!\dfrac{du}{u} = \dfrac{1}{2}\ln |u|$

$\displaystyle \int\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\ln |1+4x^2|$

Putting in the limits of integration, our area becomes

$\displaystyle A = \int_0^2\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\left.\ln |1+4x^2|\right|_0^2$

$\;\;\;\;= \frac{1}{2}[\ln (1+16) - \ln (1)]$

$\;\;\;\;=\frac{1}{2}\ln17$

Note: $\ln 1 = 0$

Related Questions

Betsy, a recent retiree, requires $6,000 per year in extra income. She has $60,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?

Answers

$37,500 should be invested in B-rated bonds and $22,500 should be invested in a certificate of deposit in order to realize exactly $6,000 in interest per year.

The total amount to be invested is $60,000. We are given two options for investing the money.The money can be invested either in B-rated bonds, which pays 13% interest per year, or in a certificate of deposit (CD), which pays 5% interest per year.Let the amount to be invested in B-rated bonds be 'x'. The amount to be invested in a certificate of deposit equals 60,000-x. The requirement is to get an exact amount of interest that equals $6000. The total interest per year = 13% of 'x' + 5% of (60,000-x).6,000 = 13x/100 + 5(60,000-x)/100.6,00,000 = 13x + 5(60,000-x)6,00,000 = 13x + 300,000-5x6,00,000 = 8x + 300,0008x = 300,000x = 300,000/8x = 37,500Now calculate the value of 60,000-x.60,000-x = 60,000-37,50060,000-x = 22,500Thus, the amount to be invested in B-rated bonds is $37,500 and the amount to be invested in a certificate of deposit is $22,500.

To learn more about interest, visit :

https://brainly.com/question/13324776

#SPJ9

There are 6 triangles and 2 circles. What is the simplest ratio of circles to total shapes?
Answer 1:4

Answers

There is no simpler ratio then 1:4. So the answer is 1:4.

what is the factored form of polynomial? x^2-16x + 48

Answers

The answer is (x-4)(x-12)

A force of 90 Newtons is applied to a 20 cm2 surface.

The force applied is then increased by 5 Newton’s and the surface area is increased by 5 cm^2

Answers

The given question is incomplete. The complete question is:

A force of 90 Newton's is applied to a $20cm^2$ surface. The force applied is then increased by 5 Newton's and the surface is increased by $5cm^2$. What percentage does the outcome decrease by

Answer: The outcome decreases by 15.5 %

Step-by-step explanation:

Pressure is defined as the ratio of force per unit area.

$Pressure=\frac{Force}{Area}$

Case 1: $P_1=\frac{90N}{20cm^2}=4.5Ncm^{-2}$

Case 2: $P_2=\frac{95N}{25cm^2}=3.8Ncm^{-2}$

Decrease in pressure = $P_1-P_2$ = $(4.5-3.8) Ncm^{-2}=0.7Ncm^{-2}$

Percentage decrease = $\frac{0.7}{4.5}\times 100\%=15.5\%$

Thus the outcome decreases by 15.5 %

10x^2+4=0 solve using quadratic formula

Answers

Answer:

x=−

Step-by-step explanation:

(10x)

+4=0

Expande (10x)

+4=0

Calcula 10 a la potencia de 2 y obtiene 100.

100x

+4=0

Resta 4 en los dos lados. Cualquier valor restado de cero da como resultado su valor negativo.

100x

=−4

Divide los dos lados por 100.

100

−4

Reduzca la fracción

100

−4

a su mínima expresión extrayendo y anulando 4.

=−

La ecuación ahora está resuelta.

x=−

Help me with both questions please please help!

Answers

Answer:

we need to know whats given above can you show us a picture of the table above?

Step-by-step explanation:

Find the indicated side of the triangle.
b
45°
28
а
[?]
a =

Please help :)

Find the indicated side of the triangle.b4528[?]a =Please help :)

Answers

Answer:

Step-by-step explanation:

Use equivalent ratios to find the unknown vaule step by step 7/11= 28/44

Answers

Answer:

7:11

28:44

Step-by-step explanation:

Multiply both sides by 4.

question a newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. the editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. which of the following methods will achieve the desired sampling design?

Answers

Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

The correct option is (B).

Now, According to the question:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)

Learn more about Proportion at:

https://brainly.com/question/14936272

#SPJ4

The complete question is this:

A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?

(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.

(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.

(E) Select the first 500 city residents who attend the next high school football game.

hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)

Answers

The function with the steepest slope is $y = 7x - 3$.

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

$y = -8x + 5$

Slope: -8

$y - 9 = -2(x + 1)$

Simplifying, we get $y - 9 = -2x - 2$

Rearranging, we have $y = -2x + 7$

Slope: -2

$y = 7x - 3$

Slope: 7

$y + 2 = 6(x + 10)$

Simplifying, we get $y + 2 = 6x + 60$

Rearranging, we have $y = 6x + 58$

Slope: 6

Therefore, the steepest slope is the $y = 7x - 3$.

For such more questions on steepest slope

https://brainly.com/question/10726891

#SPJ8

The width of rectangle A is 2 feet and the length is 6 feet. The width of a similar rectangle is 3 feet. What is it length

Answers

9514 1404 393

Answer:

9 ft

Step-by-step explanation:

The length is 3 times the width, so in the larger rectangle it will be ...

length = 3×width = 3×(3 ft) = 9 ft

The length of the larger rectangle is 9 feet.

_____

Additional comment

We used the fact that the ratios of side lengths (length:width) are the same for similar figures.

You can also recognize that the larger rectangle's dimensions are 3/2 times those of the smaller rectangle. (3/2)(6 ft) = 9 ft . . . length of larger rectangle

Answer:

The answer is 9

I might be wrong....

Step-by-step explanation:

I got it because 2x3=6 so i multiplied 3x3 and 9

AGAIN I MIGHT BE WRONG!!!

A hybrid car can go 141 miles on 3 gallons how much miles can it go on 4 gallons

Answers

188

141 divided by 3 is 47 so 47 times 4 is 188

Given (x – 7)2 = 36, select the values of x.

Answers

Answer:

x = 25

Step-by-step explanation:

Solve by isolating x:
(x-7)2 = 36
x-7 = 18
x = 25

A full grown grizzly bear eats 60.5 pounds of fruits and vegetables each day. However, the zoo can only buy fruits and vegetables by the ounce. How many ounces of fruits and vegetables does the zoo need to buy for the bear each day? when converting _________ to _______, i need to __________. solve the problem:

Answers

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

KAKSKSKSKISKSSKSBSB OAOQISNWKENI WIKW

Express 83 kilometers per hour in miles per hour.
...
mi/hr
(Round to the nearest hundredth as needed.)

Answers

Answer:

83 kilometres per hour =

51.574 miles per hour

CAN SOMEONE HELP WITH THIS QUESTION?

Answers

We can use the given formula for the rate of change of the weight of the solid to estimate the amount of solid 1 second later.

If there is 6 grams of solid at time t, then f(t) = 6 g.

To estimate the amount of solid 1 second later, we can use the derivative formula:

f'(t) = −2f(t)(5+ f(t))

We want to estimate the value of f(t+1), which represents the weight of the solid 1 second later.

To do this, we can use Euler's method, which is an approximation method for solving differential equations.

Euler's method uses the formula:

f(t+1) ≈ f(t) + f'(t)Δt

where Δt is the time step (in minutes).

Since we want to estimate the amount of solid 1 second later, we can set Δt = 1 minute.

Plugging in the values for f(t) and f'(t), we get:

f(t+1) ≈ f(t) + f'(t)Δt

f(t+1) ≈ 6 - 2(6)(5+6)

f(t+1) ≈ -66

Therefore, the estimated weight of the solid 1 second later is -66 grams. However, this result does not make physical sense since weight cannot be negative.

It is possible that the given formula for f'(t) does not accurately describe the behavior of the solid, or that there was an error in the calculation.

or maybe im just bad at maths

Find the distance between a and b. a = −40, b = 50

Answers

Answer:

answer is 88 digits

Step-by-step explanation:

Quadrilateral MNPQ is rotated at 90 degrees counterclockwise about the origin and then rotated 270 degrees counterclockwise about the origin

Answers

After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

For more such questions on Quadrilateral:

https://brainly.com/question/27991573

#SPJ8

Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line

Answers

Answer is C) it is located between the numbers 2 and 3 on the number line

Explanation

The square root of a number is “what number times itself”

2 x 2 = 4

3 x 3 = 9

7 is between 4 and 9 so C is the correct answer

50 POINTS!
If (1,2) is a point in the graph of f(x), which ordered pair must also be on the graph of y=f(x−2)−3?

Write your answer as an ordered pair, like (a,b).

Answers

Answer:

(1,2) and (x-2)-3 should be on the graph

Step-by-step explanation:

Graphs. First correct answer will mark brainliest.
30 POINTS!!

Answers

The assumption in answering the question is that no student scored 0

The assumptions made in answering the question

From the question, we have the following parameters that can be used in our computation:

The bar chart

On the bar chart, we hae

Students that score more than 8 = 5

Students in the class = 33

The (b) is calculated by considering all students that score more than 0 from the histogram

This means that the assumption is that no student scored 0

Answers

In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

For such more question on proportional

https://brainly.com/question/1496357

#SPJ8

0.4 r =1.5 r=? please and ty

Answers

Answer:

Step-by-step explanation:

Ok so this is an inequality problem:

0.4*r=1.5

Divide both sides:

1.5/0.4=r

r= 3.75

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in

20.4 days
22.5 days
25.6 days
30.1 days

Answers

**22.5 days is the answer*

Let's assume that B can do the job alone in x days.

Then, according to the question, A can do the same job alone in (1/3)x days.

Also, we know that A takes 60 days less than B to finish the job, so:

(1/3)x = x - 60

Solving for x, we get:

x = 90

Therefore, B can do the job alone in 90 days and A can do the same job alone in (1/3) * 90 = 30 days.

To find out how long they take to finish the job together, we use the formula:

(AB)/ (A+B)

where AB is the product of their individual times and A+B is their combined time.

Plugging in the values, we get:

(30 * 90)/(30+90) = 22.5

Therefore, working together, they can finish the job in 22.5 days.

Answer: Option B - 22.5 days

The radius of a circular rug is 4 feet. How much ribbing will you need to buy to go around the rug? Use 3 for i.
A)
12 feet
B)
24 feet
C)
36 feet
D)
48 feet

Answers

D because that’s the more correct answer trust

Line Segment AC is 10 centimeters (cm) long, Point M is the midpoint of AC.What will happen to the length of AC if Point A is moved so that the length of AM is squared and the length of MC remains the same?The length of AC will triple.The length of AC will double.The length of AC will be squared.The length of AC will be five times as large.

Answers

We know that AC is 10 centimeters long, and M is the midpoint of AC.

If we move point A as the problem says, we have.

As you can observe, the length of AC is triple.

Hence, the right answer is the first option: The length of AC will triple.

Line Segment AC is 10 centimeters (cm) long, Point M is the midpoint of AC.What will happen to the length

Line s passes through points (3, 1) and (10, 6). Line t is perpendicular to s. What is the slope
of line t?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Step-by-step explanation:

$ \frac{y {}^{2} - y {}^{1} } {x {}^{2} - x {}^{1} } $

$ \frac{6 - 1} {10 - 3} $

answer:

$ \frac{5}{7} $

These four numbers are plotted on a number line:

-23,58,-35,-12

Which is the correct ordering on the number line, from left to right? A . -12,-35,-23,58 B. -12,-35,58,-23 C. -23,-35,-12,58 D. -35,-23,-12,58

Answers

Answer:

Step-by-step explanation:

1. A. What is the formula for the Pythagorean Theorem? (1 point)

B. Find the missing leg of the triangle using the Pythagorean Theorem. Remember that drawings may not be to scale (Round to the nearest tenth).
Show your work. (4 points)
20 ft
18 ft
x

Answers

Answer:

side 1^2 + side 2 ^2 = hypotenuse ^ 2

18^2 + 20^2 = hypotenuse^2

324 + 400 = 724

hypotenuse^2 = 724

hypotenuse = 26.9072480941474

hypotenuse = 26.9

Step-by-step explanation:

an airlane is on heading of 075 degree at 250 km/h wind is blowing from 300 Determine the resultan velocity of the airplane using cartesian vectors and state the ground speed and bearing of the resultant

Answers

The airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

How to solve for the airplane's groundspeed

To determine the resultant velocity of the airplane, we need to break down the airplane's velocity and the wind's velocity into their respective components and add them. Let's assume that the angles are measured clockwise from true north.

Let's denote:

Vp = airplane's speed = 250 km/h

θp = airplane's heading = 075 degrees

Vw = wind's speed = 85 km/h

θw = wind's heading = 300 degrees

We can then find the eastward (x) and northward (y) components of the velocities:

For the airplane:

Vpx = Vp * cos(θp) = 250 * cos(75 degrees) = 64.95 km/h

Vpy = Vp * sin(θp) = 250 * sin(75 degrees) = 241.92 km/h

For the wind:

Vwx = Vw * cos(θw) = 85 * cos(300 degrees) = 73.60 km/h

Vwy = Vw * sin(θw) = 85 * sin(300 degrees) = -42.50 km/h

We then sum the x and y components of the two velocities to find the resultant velocity components:

Vrx = Vpx + Vwx = 64.95 km/h + 73.60 km/h = 138.55 km/h

Vry = Vpy + Vwy = 241.92 km/h - 42.50 km/h = 199.42 km/h

The magnitude of the resultant velocity, which represents the groundspeed (Vr), is found using the Pythagorean theorem:

Vr = sqrt((Vrx)^2 + (Vry)^2) = sqrt((138.55)^2 + (199.42)^2) = 242.25 km/h

The bearing (θr) of the resultant velocity (relative to north) can be found using inverse tangent:

θr = atan2(Vry, Vrx) = atan2(199.42, 138.55) = 55.04 degrees

Therefore, the airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

Read more on resultant velocity here https://brainly.com/question/4945130

#SPJ1

Other Questions