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:
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If 80 = y, then y = 80
Answeryes
Step-by-step explanation:
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
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
I NEED HELP PLEASE ASAP, It's due soon.
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer: The equation is y = 3x + 3
Step-by-step explanation:
How do I write the sum of 1 and q as an algebraic expression?
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.
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
The area of a square field is (49m^2 - 42m + 9) square units. find the dimensions of the field. ( STEP BY STEP EXPLANATION)
Answer:
(7m−3)(7m−3)
Step-by-step explanation:
Factor 49m2−42m+9
49m2−42m+9
=(7m−3)(7m−3)
1. What is the circumference of the circle
below
(18 m
C 113 m
A 36 m
B 56.5 m
D 324 m
Can someone help me please
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
I need help on this.. And I will give you a BRANILIST if you the first one with the right answer
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
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.
Answer:
I believe it has to be placed about 8 feet from the base
Step-by-step explanation:
sorry if wrong
FAST!!
Select ALL the correct answers.
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
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:
I’m stuck I need help please.
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
Someone help please
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.
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
what is 3 + 7 -90+180
Answer:
100
Step-by-step explanation:
3+7=10
-90+180=90
10+90=100
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?
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.
If h(x) = x3 + x and g(x) = 2x +3, then g(h(2))
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
Simplify the expression -2.2f+0.5f-13-3
Answer:
-1.7f - 16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-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 - 16A Lamborghini is worth $700,732 if the tax of this car is 5% what would be the full price?
Graph the following equation:
Graph f(x)= -2^x-2
Answer:
Step-by-step explanation:
PLEASE HELP!!
Find the 14th term of the sequence: 2,4,8,16...
Answer:
16384
Step-by-step explanation:
You have to find 2 to the 14th power (that's the rule)
Hope that helps!
cuál es el siguiente número de -10
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
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.
Answer:
25 or 50 points is that if 25 or 20 im not
Answer:
The hypotenuse equals 15cm
Please help, and plz don't be saying this is the right answer if u dont know for sure.
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
The side lengths of a triangle are 9, 12, and 18. Is this a right triangle? O A. Yes, because 92 + 122
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:
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
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
Solve using substitution. x − 6y = –8 x + 6y = 16 please help imma fail
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
Answer:
easy third one also plz give heart
Step-by-step explanation:
i just know
in an assignment and need help with this question