for what x is the area under the graph of f(t) = 1/t between t = 1 and t = x equal to 1?

Answers

Answer 1

The area under the graph of f(t) = 1/t between t = 1 and t = x is equal to 1 when x = e.

To find the value of x for which the area under the graph is equal to 1, we need to evaluate the definite integral of f(t) from t = 1 to t = x and set it equal to 1:

∫[1,x] 1/t dt = 1

Integrating the function 1/t with respect to t, we get:

ln|t| | [1,x] = 1

Using the properties of logarithms, we can rewrite this equation as:

ln|x| - ln|1| = 1

Since ln|1| equals 0, the equation simplifies to:

ln|x| = 1

Taking the exponential of both sides, we have:

e^(ln|x|) = e^1

|x| = e

Therefore, the absolute value of x is equal to e. Since the natural logarithm function is defined for positive and negative values, the solution can be x = e or x = -e. However, since we are considering the area under the graph, which requires positive values, the solution is x = e.

In summary, the area under the graph of f(t) = 1/t between t = 1 and t = x is equal to 1 when x = e.

Learn more about absolute value here:

https://brainly.com/question/17360689

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Related Questions

Find the equation of the linear function represented by the table below in slope-intercept form.

Answers

Answer: The equation is y = 3x + 3

Step-by-step explanation:

1. What is the circumference of the circle
below
(18 m
C 113 m
A 36 m
B 56.5 m
D 324 m

Answers

Answer : 56.5

The formula for circumference is C = pi(d)
If the diameter was 18 all you would do is multiply 18x3.14 is would give you 56.5.

Hope it helped :)!

Please help
(10 points)
A bill for dinner at a restaurant is $98.87. A 15% tip for the server is added
to the bill. What is the total amount of the bill?
A $100.37
B $109.26
$113.70
D $113.87

Answers

$ 113.70 : 98.87 x .15 = 14.83. ; add that to 98.87

If h(x) = x3 + x and g(x) = 2x +3, then g(h(2))

Answers

Answer:

They both equal 23 so it’s a true statement

Step-by-step explanation:

h(x) = x3 + x and g(x)

=

h(2) = 2^3 + 2

= 8 + 2

= 10

g(h(2))

= g(10)

= 2*10 + 3

= 20 + 3

= 23

2x +3, then g(h(2))

=

h(2) = 2^3 + 2 = 8+2 = 10

Now we will substitute into g(h(2)

g(h(2)) = g(10)

Now we will substitute into g(x).

g(10) = 2*10 + 3 = 23

g(h(2)) = 23

They are both equal 22 so it’s equal

in an assignment and need help with this question

Answers

8 8/3 is 29.3
hope this is correct

The side lengths of a triangle are 9, 12, and 18. Is this a right triangle? O A. Yes, because 92 + 122 ​

Answers

Answer:

O A. Yes, because 92 + 122 = 152

B. No, because 9 + 12 15.

C. Yes, because 92 + 122> 152.

D. No, because 92 + 122 + 15 ^2

1

SEE ANSWER

Step-by-step explanation:

Someone help please

Answers

what do you need help with?

BRAINLIEST TO WHOEVER ANSWERS FIRST!
A painter is placing a ladder to reach the third story window, which is 39 feet above the ground and
makes an angle with the ground of 80°.
How far out from the building does the base of the ladder need to be positioned? Round your answer to
the nearest tenth.
The base of the ladder needs to be positioned
feet out from the building.

Answers

Answer:

I believe it has to be placed about 8 feet from the base

Step-by-step explanation:

sorry if wrong

what is 3 + 7 -90+180

Answers

Answer:

100

Step-by-step explanation:

3+7=10

-90+180=90

10+90=100

Please help, and plz don't be saying this is the right answer if u dont know for sure.

Answers

Answer:

135 degrees

Step-by-step explanation:

(8x-7)+(12x+57)=180

combine like terms

20x+50 = 180

subtract 50 on both sides

20x = 130

divide by 20

x = 130/20

x = 13/2

x = 6.5

cpq = 12x+57

cpq = 78 + 57

cpq = 135

If 80 = y, then y = 80

Answers

Answeryes

Step-by-step explanation:

I need help on this.. And I will give you a BRANILIST if you the first one with the right answer ​

Answers

Answer:

0.1

Step-by-step explanation:

(9,4) (5,1)    [tex]\frac{y_{2} y_{1} }{x_{2} x_{1} }[/tex], plug in the numbers, [tex]\frac{(1)(4)}{(5)(9)}[/tex]= [tex]\frac{4}{40} or \frac{1}{10}[/tex], to write it as a decimal, you divide the numerator by the denominator, 0.1

Solve using substitution. x − 6y = –8 x + 6y = 16 please help imma fail

Answers

Answer:

x=−16/7

Step-by-step explanation:

happy to help ya :)

Answer:

x = 4, y = 2

Step-by-step explanation:

x - 6y = - 8 is the same as x = 6y - 8

sub that into x + 6y = 16 :

6y - 8 + 6y = 16

12y = 16 + 8

y = 2

sub that into x = 6y - 8:

x = 12 - 8 = 4

                     

TIMED!!

PLEASE HELP!!

WILL give brainliest

Answers

Answer:

easy third one also plz give heart

Step-by-step explanation:

i just know

I’m stuck I need help please.

Answers

Answer:

6

Step-by-step explanation:

30+25n=90+15n

10n=60

n=6

Answer:

She would have to buy 4 personal training sessions

Step-by-step explanation:

30 + 25 + 25 + 25 (3 training sessions)

= 105

90 + 15 (1 training session)

= 105

I NEED HELP PLEASE ASAP, It's due soon.

Answers

Answer: y=3/4x+30
(I cannot see the x amounts to see if the units match, if the units are not moving up by 1 on the c axis the slope will be considered wrong)

Why?
Y=mx+b
M=slope
B= y intercept
Slope= rise/run
I moved up from point that directly intersects a point on the graph and moved up 3 and to the right 4 to another point that directly intersects a point.
To find the y intercept I can see that it will directly pass through 30 on the y axis so that is the y intercept

Hope this helps (if I need to explain better or if the x axis doesn’t move by 1s and I need to redo the slope just say something in the comments)

cuál es el siguiente número de -10​

Answers

Answer:

en los números negativos es opuesto a los positivos es decir en los positivos después del 302 ira el 303 encambio en los negativos del

-10 irá el -9

Simplify the expression -2.2f+0.5f-13-3

Answers

Answer:

-1.7f - 16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

-2.2f + 0.5f - 13 - 3

Step 2: Simplify

Combine like terms (f):                                                                                    -1.7f - 13 - 3Combine like terms (Z):                                                                                  -1.7f - 16

How do I write the sum of 1 and q as an algebraic expression?

Answers

Answer:

1+Q

Step-by-step explanation:

Answer:

1 + q

Step-by-step explanation:

since sum means to add, and they give the values of 1 and q, we just need to plug it in.

the pythagorean theorem states that a^2 + b^2 = c^2 If A and B represent the length of the legs of a right triangle and C represents the length of the hypotenuse. Find the length of the hypotenuse Is the length of the legs are 9cm and 12cm.​

Answers

Answer:

25 or 50 points is that if 25 or 20 im not

Answer:

The hypotenuse equals 15cm

PLEASE HELP!!

Find the 14th term of the sequence: 2,4,8,16...

Answers

Answer:

16384

Step-by-step explanation:

You have to find 2 to the 14th power (that's the rule)

Hope that helps!

Jana has $10. She wants to buy a bottle of nail polish for $9.50. The sales tax is 7%. Does she have enough money?

Answers

Answer:no, she would be 17 cents short

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

Compute the tax =

9.50 * 7% = 9.5 * .07 or 66.5 cents.

Since she only has $10, she does not have enough money.

During the summer, Mr. Brust does a lot of napping (and snoring)! In a typical nap, Mr. Brust will snore on average 320 times (or the ratio of naps to snores is 1 nap : 320 snores). Find the total number of times Mr. Brust snored last summer during naps in July and August if he took one nap everyday.

Answers

Answer: Mr Brust snored a total of 19,840 times last summer

Step-by-step explanation:

Mr Brust snores in the ratio of 1 nap : 320 snores or 1 nap = 320 snores

Given that he took a  nap everyday,  last summer We have that  .

For the month of July,

he had 31 naps( 31 days are in July)

Number of snores he made =31 x 320=9,920 snores

For the month of August

he also took 31 naps ( 31 days are in AugusT)

Number of snores he made = 31 x 320=9,920 snores

Therefore  Mr Brust snored a total of 9,920+ 9,920 =19,840 times

Samuel Morse determined that the percentage of t's being used in the English language in the 1800's was 9%. A random sample of 600 letters from a current newspaper contained 48 t's. Test the claim that the proportion of t's has changed in modern times, using the current newspaper data and a significance level of 0.05

Answers

Answer:

There is insufficient evidence to indicate that the population proportion of t’s in modern newspaper is different from 0.09. The result is not statistically significant

Step-by-step explanation:

H0 : p0 = 0.09

H1 : p0 ≠ 0.09

Sample size, n = 600 ; α = 0.05

Decision region

Zstatistic < Zcritical ; reject H0

P = 48 / 600 = 0.08

Zstatistic = (p - p0) ÷ sqrt((p0(1 - p0)) /n)

Zstatistic = (0.08 - 0.09) ÷ sqrt(0.09(0.91))/600)

Zstatistic = - 0.01 /0.0116833

Zstatistic = - 0.856

Zcritical at 0.05, = - 1.96

Zstatistic > Zcritical

-0.856 > - 1.96

Hence, we fail to reject the Null

Graph the following equation:
Graph f(x)= -2^x-2

Answers

Answer:

Step-by-step explanation:

The area of a square field is (49m^2 - 42m + 9) square units. find the dimensions of the field. ( STEP BY STEP EXPLANATION)

Answers

Answer:

(7m−3)(7m−3)

Step-by-step explanation:

Factor 49m2−42m+9

49m2−42m+9

=(7m−3)(7m−3)

A six-sided Fair number cubis rolled 100 times as part of an experiment. The frequency of the role of the number 3 is 20. W hich statement about rolling a 3 is correct

Answers

Answer:

The Theoretical probability is 1/6.

The experimental probability is 1/5

Step-by-step explanation:

Given

Rolls: 100

Outcome of 3 : 20

Required

Which of the options is true (See attachment for options)

From the attachment, we understand that the question requires that we calculate the experimental and theoretical probability.

The experimental probability (E) is calculated as thus:

[tex]E = \frac{Outcomes}{Total\ Rolls}[/tex]

[tex]E = \frac{20}{100}[/tex]

[tex]E = \frac{1}{5}[/tex]

The theoretical probability (T) is calculated as thus:

A cube has 6 faces, one of which is the face 3.

So, T is:

[tex]T = \frac{n(face\ 3)}{n(Total)}[/tex]

[tex]T = \frac{1}{6}[/tex]

Hence, C is true

A Lamborghini is worth $700,732 if the tax of this car is 5% what would be the full price?

Answers

It would be 735,768.6
Because you want to multiply 700,732 by 5% or .05 which would give you 35,036.6 which you then add with 700,732 to get 735,768.6

Can someone help me please

Answers

Answer:

X=3-(y/2)=8

Step-by-step explanation:

suppose the numbers is X

3 less than half the product of a number is 8

X= 3- (y/2)=8

1/2(8n)-3

Hope that helps

FAST!!
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With which information can you construct more than one triangle?

the measurements of two angles

the measurements of two angles and the length of the included side

the measurements of all the angles

the lengths of two sides and the measurement of the included angle

Answers

Answer:

a b and d

Step-by-step explanation:

Answer:

the measurements of two angles

the measurements of two angles and the length of the included side

the lengths of two sides and the measurement of the included angle

Step-by-step explanation:

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