Evaluate [tex]\int\limits^e_0 {\frac{1}{x} } \, dx[/tex]

1

e^2-1/(1)

0

The integral diverges.

I think it is the last option, but I am not entirely sure.

Answers

Answer 1

Answer:

The integral diverges.

Step-by-step explanation:

∫₀ᵉ 1/x dx

(ln|x| + C) |₀ᵉ

ln|x| is undefined as x approaches 0, so the integral diverges.


Related Questions

3a/4+2a/3-a/12

a. a/3
b. 4/3
c. (4a)/3​

Answers

Answer: C

Step-by-step explanation:

[tex]\frac{3a}{4}+\frac{2a}{3}-\frac{a}{12}[/tex]

Find the least common denominator of 4, 3, and 12.

4-3-12 | 3

4-1-4   | 4

1-1-1    |-------- 12

The first fractions needs to be multiplied by 3, and the second fraction, by 4

[tex](\frac{(3a)*3}{(4)*3})+(\frac{(2a)*4}{(3)*4})-\frac{a}{12}[/tex]

Solve;

[tex]\frac{9a}{12}+\frac{8a}{12}-\frac{a}{12}[/tex]

Add the fractions with positive signs and subtract the one with negative sign.

[tex]\frac{(9a+8a)-a}{12}[/tex]

Solve;

[tex]\frac{17a-a}{12}=\frac{16a}{12}[/tex]

Simplify by 4;

16/4=4

12/4=3

[tex]\frac{4a}{3}[/tex]

Answer:

(4a)/3

Step-by-step explanation:

3a/4+2a/3-a/12

find L.C.M

9a+8a-1a/12=16a/12

16a/12=(4a)/3

An economy package of cups has 250 green cups if the green cups are 10% of the total package, how many cups are in the package?

Answers

Answer:

There are a total of 2500 cups

Step-by-step explanation:

10% of the cups are green

you can set up a equation for this

x = total cups

.10x = 250

multiply both sides by 10 to make x a whole number

x = 2500

how many solutions to x^2 =-16

Answers

Answer:

no real solutions

Step-by-step explanation:

Tan θ =
[tex] \sqrt{13} \div \sqrt{2} [/tex]

Answers

Answer:

Step-by-step explanation:

Tan θ = [tex]\sqrt{13} \div \sqrt{2}[/tex] = 2.5495

Therefore θ = [tex]Tan^{-1}[/tex] (2.5495) =68.5832°

Answer:

Tan θ =  2.5495097...

SA police department used a radar gun to measure the speed of a sample of cars on the highway.
Assume that the distribution of speeds is approximately Normal with a mean of 71 mph and a
standard deviation of 8 mph.
Using this distribution what is the z-score of a 65-mph speed limit? *​

Answers

Answer:

The z score of the 65-mph speed limit is -0.75

Step-by-step explanation:

The z score is given by the relation;

[tex]z = \frac{x- \mu}{\sigma}[/tex]

Where:

Z = Normal (Standard) or z score

x = Observed speed  score

μ = Mean, expected speed

σ = Standard deviation

Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;

[tex]z = \frac{65-71}{8}= \frac{-6}{8} = -\frac{3}{4}[/tex]

Hence the z score of the 65-mph speed limit =-3/4 or -0.75.

Sadie uses 9.8 pints of blue paint and white paint to paint her bedroom walls. 1 4 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?

Answers

Answer:

7.35 pints

Step-by-step explanation:

If we use 1/4 of the 9.8 pints for blue, then the remaining white paint takes up 3/4 of the 9.8 pints of paint. To find how many pints of paint is equal to 3/4 of it, you must multiply that fraction by the amount (9.8).

[tex]\frac{3}{4}[/tex] * 9.8 (or 0.75 * 9.8) = 7.35

Therefore, 7.35 pints of the total paint used is white.

Hope I helped! Please give me brainliest!

hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33

Answers

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

volume of cone with radius of 6 and heights of 8

Answers

Hey there! I'm happy to help!

To find the volume of a cone, you multiply the base by the height and then divide by three.

The base of a cone is a circle. To find the area of a circle, we square the radius and then multiply it by pi (we will use 3.14). Let's find the base below.

6²=36

36×3.14=113.04

Now, we multiply by the height.

113.04×8=904.32

Finally, we divide by three.

904.32÷3=301.44

Therefore, the volume of this cone is about 301.44 units cubed.

Now you can find the area of cones! I hope that this helps! Have a wonderful day!

Answer:

301.44

Step-by-step explanation:

In the past twenty years, scientists have seen the sea level rise at a rate of approximately 0.13 inches per year. If this rate continues, which best represents the change in sea level over the next 27 months (2.25 years)?

Answers

Answer:

The change in the sea level will be by 0.2925 inches

Step-by-step explanation:

First of all , we will need to write out the rate at which the sea level is rising. This is 0.13 inches, per year. This means that every year, the sea level increases by 0.13 inches.

Since the sea level increases by 0.13 inches every year, in 2.25 years, to get the sea level, we will have to multiply the current rate at which it is rising by that duration of time.

This will be 2.25 years X 0.13 inches/ year = 0.2925 inches

Therefore, the change in the sea level will be by 0.2925 inches

Answer:

0.2925 inches

Step-by-step explanation:

There is a unique positive real number x such that the three numbers
log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
The number x can be written as m/n, where m and n are relatively prime positive integers.
Find m+n.

Answers

Answer: 17  

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

What is geometric sequence?

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

I cant fail please help

Answers

He will have to leave at 5:37

Describe the process for calculating the volume of a cylinder.

Answers

Answer:

the formulae for the volume of a cylinder= πr²h

so we then put the figures at their respective positions. and for the pie we put either 22/7 or 3.143 or 3.14


There are 7 yellow, 6 blue, 9 red, and 3 green ribbons in a drawer. Once a ribbon is selected, it is not replaced. Find each probability.
P(a yellow ribbon and then a blue ribbon)


P(a yellow ribbon and then a blue ribbon)


a. 7/100
b. 42/635
c. 7/120
d. 7/125

Answers

Answer:

7/100

Step-by-step explanation:

7 yellow, 6 blue, 9 red, and 3 green ribbons in a drawer

Total ribbons = 25 ribbons

P( yellow) = yellow / total = 7/25

Then not replaced

6 yellow, 6 blue, 9 red, and 3 green ribbons in a drawer

Total ribbons = 24 ribbons

P( blue) = blue / total = 6/24 = 1/4

P(a yellow ribbon and then a blue ribbon) = 7/25 * 1/4 =7/100

Answer:

A: [tex]\frac{7}{100}[/tex]

Step-by-step explanation:

There are 25 ribbons total. The probability would be out of the 25 ribbons.

(1):

Yellow: [tex]\frac{7}{25}[/tex]

Blue:[tex]\frac{6}{25}[/tex]

Red:[tex]\frac{9}{25\\}[/tex]

Green:[tex]\frac{3}{25}[/tex]

When removing a ribbon that can't be replace, it'll leave you with a total of 24 ribbons.

(2):

Yellow: [tex]\frac{6}{24}=\frac{1}{4}[/tex]

Blue: [tex]\frac{5}{24}[/tex]

Red:[tex]\frac{8}{24}=\frac{1}{3}[/tex]

Green:[tex]\frac{2}{24}=\frac{1}{12}[/tex]

Multiply {(1) × (2)}:

Yellow:[tex]\frac{7}{25}[/tex] ×[tex]\frac{6}{24}[/tex] = [tex]\frac{7}{100}[/tex]

Blue:[tex]\frac{6}{25}[/tex] × [tex]\frac{5}{24}[/tex] = [tex]\frac{1}{20}[/tex]

The length of the line segment containing the points (1,7) and (5,5)
is 4.47 units
A, True
B. False

Answers

Answer:

True

Step-by-step explanation:

Let A denotes the point (1,7)

Let B denotes the point (5,5)

We are supposed to find The length of the line segment containing the points

Formula : [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(1,7)\\(x_2,y_2)=(5,5)\\ d = \sqrt{(5-1)^2+(5-7)^2}\\ d = \sqrt{4^2+(-2)^2}\\ d = \sqrt{4^2+(-2)^2}\\d=4.47[/tex]

So,The length of the line segment containing the points (1,7) and (5,5)  is 4.47 units is true.

Hence Option A is true

HELP!!!! calculate the difference and enter it below
-1 -7

Answers

Answer:

-8

Step-by-step explanation:

-8

Answer:

6.

Step-by-step explanation:

Difference between -1 and -7.

-1-(-7) = -1 + 7 = 6

two negative signs makes it a positive sign

13 POINTS!!!

In ΔABC, c = 4.2 inches, ∠C=24° and ∠A=115°. Find the area of ΔABC, to the nearest 10th of an square inch.

Answers

Answer:

12.9 [tex]in^{2}[/tex]

Step-by-step explanation:

So to find the area of this triangle, you will need to use the equation

Area = [tex]\frac{1}{2}[/tex]c*b*sin(A) = [tex]\frac{1}{2}[/tex]a*b*sin(C)

Here, we have ∠A, ∠C, and side c

We can use the fact that [tex]\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex] so solve for the other variables we do not have.

First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,

∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°

Now that we have all three angles, we can solve for the sides

Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.

Since [tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex], solving for b would give us [tex]b=\frac{csin(B)}{sin(C)}[/tex]. Then plugging in our values we get [tex]\frac{4.2sin(41)}{sin(24)}[/tex]= 6.77 = b

Now we can solve for the remaining side, a, using the same method.

Since [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex], solving for a would give us [tex]a=\frac{bsin(A)}{sin(B)}[/tex]. Then plugging on our values we get [tex]\frac{6.77sin(115)}{sin(41)}[/tex]= 9.36 = a

Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒

Area =[tex]\frac{1}{2}[/tex]c*b*sin(A)= [tex]\frac{1}{2}[/tex](4.2)(6.77)sin(115) = 12.9[tex]in^{2}[/tex] or [tex]\frac{1}{2}[/tex]a*b*sin(C) = [tex]\frac{1}{2}[/tex](9.36)(6.77)sin(24) = 12.9[tex]in^{2}[/tex]

The parallelogram does not have right angles. Its area is


less than ab.
equal to ab.
greater than ab.​

Answers

Answer:

equal to ab

Step-by-step explanation:

The area of a parallelogram is Area =  ab

therefore, the area is ab

Answer:

Less than ab

Step-by-step explanation:

Find the area of the shape shown below.

Answers

Answer:

The answer should be 4800

I Think There is ALLWAYZ a 50-50 CHANCE

What is the area of the parallelogram? A parallelogram with a base of 14 centimeters and a height of 5 centimeters.

Answers

Answer:

The answer is 70cm²

Step-by-step explanation:

Area of a parallelogram = base × height

From the question

base = 14 cm

height = 5 cm

Substituting the values into the above formula we have

Area = 14 cm × 5 cm

Area = 70cm²

Hope this helps you

Answer:

1,750

Step-by-step explanation:

7. How many Cones will it take to fill a Cylinder with the same height and radius?
O 6 cones
O 3 cones
O 1 cone
O 2 cones​

Answers

Answer:

3 cones

Step-by-step explanation:

This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.

Answer:

C) 3 Cones.

Explanation:

Hope this helps! :)


Given the fractions 8/15 and 18/35, find the largest number that these fractions can be divided by, so that the quotient will be a whole number.

Answers

Answer:

Therefore the largest number that these fractions can be divided by to give them a whole number is

a) 8/15 = The largest number is 8/15

b) 18/35 = The largest number is 18/35

Step-by-step explanation:

A quotient is the result obtained by dividing two numbers.

So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.

Let's assume the whole number is 1

a. 8/15

8/15 ÷ x = 1

8/15 × 1/x = 1

8/15x = 1

We would cross multiply

8 = 15x

We would divide both sides by 15

8/ 15 = x

Hence the largest number that would divide 8/15 and give it a whole number = 8/15

b) 18/35

18/35÷ x = 1

18/35 × 1/x = 1

18/35x = 1

We would cross multiply

18 = 35x

We would divide both sides by 35

18/ 315 = x

Hence the largest number that would divide 18/35 and give it a whole number = 18/35

Answer:

The answer is 2/105

Step-by-step explanation:

first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.

Now, put the GCF you found over the LCM.

ANSWER: 2/105

This fraction is the largest number you can divide both numbers by to get a whole number.

What is the most common number that will appear when you roll a 2 dice?

Answers

Answer:

7 is the most common roll with two six-s

( I hope this helped <3 )

Answer:

7/8

Step-by-step explanation:

I think the most common are 7/8.

What is the equation of the following line? Be sure to scroll down first to see all answer options.

A. y = 3x
B. y = x
C. y = 2x
D. y = -1/3x
E. y = -3x
F. y = 1/3x

Answers

choice D: y=-1/3x
explanation:




Polygon LMNO is similar to polygon QRST and LM and QR are corresponding sides. You know the perimeter of each polygon, and you know the measure of MN. What can you find

Answers

Answer:

I can find that the measure of RS

Step-by-step explanation:

The measure of RS can be discovered as both have corresponding sides. Therefore, both are the same

I'll give Brainliest!!!
What is 5 1/2 divided by 5 1/3 equal?

Answers

The answer is 33/32=1 1/32
Or
1.03125

Which best describes the transformation that occurs from
the graph of f(x) = x2 to g(x) = (x - 2)²+ 3?​

Answers

Answer:

The graph changes from the original position to right 3 units and down 1 unit.

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!

The areas of the squares adjacent to two sides of a right triangle are 32 units^2 and 32 units^2

Answers

Answer:

64 square units.

Step-by-step explanation:

In this problem, we have to find the area of an square adjacent to the third side of the right triangle.

To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.

[tex]h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u[/tex]

Therefore, the area of a square adjacent to the third side is 64 square units.

Answer:the answer is 8

Step-by-step explanation:

Solve the equation for x, and enter your answer below.

10x - 15x + 5= -45 + 40

Answers

Answer: x = 2

Step-by-step explanation:

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

plzzzzzzzzzzzzzaaaaaa

Answers

Answer:

C

Step-by-step explanation:

[tex]y^2+4y-32=0\\(y+8)(y-4)=0\\y=4,-8[/tex]

Therefore, the answer is C. Hope this helps!

A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games.
A) Design a simulation for this event,
B) what counts as a successful outcome?
C) Estimate the probability using your simulation.
Can anyone help me? I’m kind of confused on this problem

Answers

Answer:

C. Estimate the probability using your simulation.

Step-by-step explanation:

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