Answer:
Average velocity of the function over the given interval
= [tex]log(\frac{7}{4} ) -2[/tex]
Step-by-step explanation:
Explanation:-
Given function y = 3/x -2 ...(i)
The average velocity of the function over the given interval
Average velocity = [tex]\frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx[/tex]
= [tex]\frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx[/tex]
now integrating
= [tex]\frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )[/tex]
= [tex]\frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}[/tex]
= [tex]\frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))[/tex]
by using formulas
log a-log b = log(a/b)
on simplification , we get
= [tex]\frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)[/tex]
= [tex]log(\frac{7}{4} ) -2[/tex]
Average velocity of the function over the given interval
= [tex]log(\frac{7}{4} ) -2[/tex]
find the measure of the indicated angle to the nearest degree. Show the work please.
Answer: 1) 65° 2) 17° 3) 53° or 37°
Step-by-step explanation:
[tex]1.\quad \cos \theta=\dfrac{adjacent}{hypotenuse}\\\\\\.\quad \quad \cos \theta=\dfrac{3}{7}\\\\\\.\qquad \qquad \theta=\cos ^{-1}\bigg(\dfrac{3}{7}\bigg)\\\\\\.\qquad \qquad \theta =65^o[/tex]
[tex]2.\quad \tan \theta =\dfrac{opposite}{adjacent}\\\\\\.\quad \quad \tan\theta =\dfrac{8}{26}\\\\\\.\qquad \qquad \theta =\tan ^{-1}\bigg(\dfrac{4}{13}\bigg)\\\\\\.\qquad \qquad \theta = 17^o[/tex]
3. Which angle do you need? I solved for both:
Bottom Right Top Left
[tex].\qquad \cos \theta=\dfrac{adjacent}{hypotenuse}\qquad \qquad \sin \theta = \dfrac{opposite}{hypotenuse}\\\\\\.\quad \quad \cos \theta=\dfrac{14}{23}\qquad \qquad \qquad \qquad \sin \theta=\dfrac{14}{23}\\\\\\.\qquad \qquad \theta=\cos ^{-1}\bigg(\dfrac{14}{23}\bigg)\qquad \qquad \quad \theta=\sin ^{-1}\bigg(\dfrac{14}{23}\bigg)\\\\\\.\qquad \qquad \theta =53^o\qquad \qquad \qquad \qquad \quad \theta =37^o[/tex]
Question 1:
cosθ = adj/hyp
cosθ = 3/7
θ = cos^-1(3/7)
θ = 65
Questions 2:
tanθ = opp/adj
tanθ = 8/26
θ = tan^-1(4/13)
θ = 17
Question 3:
Top left:
sinθ = opp/hyp
sinθ = 14/23
θ = tan^-1(14/23)
θ = 37
Bottom Right:
cosθ = adj/hyp
cosθ = 14/23
θ = cos^-1(14/23)
θ = 53
Best of Luck!
Why is√5 irrational?
A.)because it is less than one
B.)because it has no opposite
C.)because all square roots are irrational
D.)because it cannot be expressed as a ratio of integers
Answer: The expression x(x + 1) is even for any integer x (since either x or x + 1 is even). So this says that 5 × even + 1 = even, or odd = even. Since there is no integer that is both even and odd, we have reached a contradiction and √5 is irrational. So the answer would be D.) because it cannot be expressed as a ratio of integers
If five less than y is six more than x + 1, then by how
much is x less than y?
Answer:
12 more
Step-by-step explanation:
y-5= 6+ (x+1)
5+6+1=12
x is 12 less than y.
Five less than y is six more than x + 1,
y - 5= 6 + (x + 1)
5 + 6 + 1 = 12.
What are the steps in solving linear equations in one variable?Step 1: Simplify each side, if needed.Step 2: Use Addition/Subtraction Properties to move the variable term to one side and all other terms to the other side.Step 3: Use Multiplication/Division.Step 4: Check your answer.Learn more about linear equations here: https://brainly.com/question/14323743
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{12÷(9−6)}+4×6{12÷(9−6)}+4×6
Answer:
56
Step-by-step explanation:
9-6=3
12 divided by 3 is 4
4x6=24
24+4=28
Do the same to the other side and you get 28
28+28=56
Hope it’s right
On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0), and crosses the y-axis at (0, negative 3). What are the intercepts of the graphed function? x-intercept = (–1, 0) a y-intercept = (–3, 0) b x-intercept = (0, –1) c y-intercept = (0, –3) d x-intercept = (0, –1) e y-intercept = (–3, 0) f x-intercept = (–1, 0) g y-intercept = (0, –3)
Answer:
It’s d on edge
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Edge
If B is the midpoint of AC. AB = 4v and AC = 5v + 24. what is BC?
Answer:
v+24
Step-by-step explanation:
I first drew a line with A in one side and C in the other side. Then, I put B in the middle, as it is the midpoint. Under AB, I put 4v, and under AC, I put 5v+24. To get BC, you must subtract 5v+24 and 4v. I did 5v+24-4v. All I really had to do was subtract 4v from 5v which gave me v, since I can only subtract like-term numbers. Anyway, after that, I got v+24. Hope this helped!
Brianna has $75 saved. She works $12 per hour babysitting.
Part 1: Write an expression that represents how much money Brianna will
have total after workingh hours.
Part 2 How much money will she have after babysitting for 6.5 hours?
Answer:
$75 + $12x
$153 if you add the money she already had, $78 if you don't
Step-by-step explanation:
7a+1+3=18
Please answer quickly!
Answer:
2
Step-by-step explanation:
So we have the equation:
[tex]7a+1+3=18[/tex]
Add 1 and 3:
[tex]7a+4=18[/tex]
Subtract 4 from both sides:
[tex]7a=14[/tex]
Divide both sides by 7:
[tex]a=2[/tex]
And we're done!
which expression equals
[tex]9 \sqrt[3]{10} [/tex]
Answer:
B on edge
Step-by-step explanation:
5^3sqrt10+4^3sqrt10
The population of a colony of bacteria can be modeled by the function P(t) = 19,300(5)^t, where t is the elapsed time
in hours. What is the inverse function?
Answer:
C. P–1(t) = log5 (StartFraction t Over 19,300 EndFraction)
Step-by-step explanation:
The inverse function of P(t) is [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex]
What is an inverse function?The inverse function is a function obtained by reversing the given function. An inverse is a function that serves to “undo” another function. The domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.
For the given situation,
The function P(t) = 19,300(5)^t, where t is the elapsed time in hours.
Steps to find inverse function:
Step 1: Replace P(t) as y
[tex]P(t) = 19,300(5)^t[/tex]
⇒ [tex]y= 19,300(5)^{t}[/tex]
Step 2: interchange t and y
⇒ [tex]t = 19,300(5)^y[/tex]
Step 3: Now solve for y
⇒ [tex]\frac{t}{19300} =5^y[/tex]
By law of logarithm,
[tex]a^{x} = y[/tex]
⇒ [tex]log_{a} y=x[/tex]
Thus the equation becomes,
⇒ [tex]log_{5} \frac{t}{19300}=y[/tex]
Step 4: Now replace y as [tex]P^{-1}( t)[/tex]
⇒ [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex]
Hence we can conclude that the inverse function of P(t) is [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex].
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What is the value of 3 in the number 235,178???
Answer:
30,000
Step-by-step explanation:
Set the other digits to zero to obtain your answer:
030,000
The value of the 3 is 30,000.
___
It is in the "ten-thousands" place, so represents 3 ten-thousands, or thirty thousand.
Solve the equation for x.
x2 = 25
Answer:
x = 12.5
Step-by-step explanation:
x2 = 25 Divide both sides by 2
x = 12.5
Answer:
[tex]\huge\boxed{x = \± \ 5}[/tex]
Step-by-step explanation:
[tex]\sf x^2 = 25[/tex]
Taking sqrt on both sides
[tex]\sf \sqrt{x^2} = \sqrt{25}[/tex]
x = ± 5
Can you guys help me how to answer thus
Answer:
a, 32
b, -58
Step-by-step explanation:
a) g(0) = 6 - 0^2 = 6
--> f(g(0)) = 4 . 6 + 8 = 32
b) f(0) = 4 . 0 + 8 = 8
--> g(f(0)) = 6 - 8^2 = 6 - 64 = -58
Write the polynomial in standard form that represents the perimeter of the quadrilateral
3x - 2
2x
12x+1
5x - 2
The solution is
Answer:
Linear function
Step-by-step explanation:
4
The polynomial in a standard form that represents the perimeter of the quadrilateral is [tex]22x-3[/tex].
Important information:
The side lengths of a quadrilateral are [tex]3x-2,2x,12x+1,5x-2[/tex].We need to find the polynomial in a standard form that represents the perimeter of the quadrilateral.
Standard form of Polynomial:The perimeter of the quadrilateral is the sum of all of its sides.
[tex]\text{Perimeter}=3x-2+2x+12x+1+5x-2[/tex]
[tex]\text{Perimeter}=22x-3[/tex]
Therefore, the polynomial in a standard form that represents the perimeter of the quadrilateral is [tex]22x-3[/tex].
Find out more about 'Standard form of Polynomial' here:
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translate into words
5+x
Five added to the number, x.
Step-by-step explanation:
Five represents (5)
added to represents (+)
The number, x. represents (x)
On a family dinner table there are two plates for everybody, and only one plate for little Katelyn. 10 people and Katelyn came to the dinner. How many plates were on the table?
Answer:
21 plates
Step-by-step explanation:
10 people each got two plates, 10 x 2 = 20.
Plus Katelyn's plate, 20+ 1 = 21.
Hope this helps!
Answer:
its actually 21 plates
Step-by-step explanation:
10×2=20+1=21
The measure of an angle is 103°. What is the measure of its supplementary angle?
Answer:
77
Step-by-step explanation:
Let's let the unknown number be x.
Supplementary angles add up to a total of 180 degrees. Since we already know one angle is 103, this means that:
[tex]103+x=180[/tex]
Subtract 103 from both sides:
[tex]x=77\textdegree[/tex]
So, the measure of its supplementary angle is 77 degrees.
And we are done!
Answer:77
Step-by-step explanation:
Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as the probability of an arrival in any other one-minute period.
A. What is the probability of exactly three arrivals in a one-minute period?
B. What is the probability of at least three arrivals in a one-minute period?
Answer:
0.2240418 ; 0.57681
Step-by-step explanation:
Given the information above :
A) What is the probability of exactly three arrivals in a one-minute period?
Using poisson probability function :
p(x ; m) = [(m^x) * (e^-m)] / x!
Here, m = mean = 3, x = 3
P(3 ; 3) = [(3^3) * (e^-3)] / 3!
P(3;3) = [27 * 0.0497870] / 6
= 1.3442508 / 6
= 0.2240418
B) What is the probability of at least three arrivals in a one-minute period?
Atleast 3 arrivals
X >= 3 = 1 - [p(0) + p(1) + p(2)]
P(0 ; 3) = [(3^0) * (e^-3)] / 0! = (1 * 0.0497870) / 1 = 0.0497870
P(1 ; 3) = [(3^1) * (e^-3)] / 1! = (3 * 0.0497870) / 1 = 0.1493612
P(2 ; 3) = [(3^2) * (e^-3)] / 2! = (9 * 0.0497870) / 2 = 0.2240418
1 - [0.0497870 + 0.1493612 + 0.2240418]
1 - 0.42319 = 0.57681
a rectangular shape waiting room has an area 120ft and a perimeter of 44 ft.what are the dimensions?
Answer: W * L = 120
2W + 2L = 44
2W = 44 - 2L
W = 22 - L
(22-L) * L = 120
22L - L² = 120
L² - 22L = -120
L² - 22L + 121 = 121 - 120
(L - 11)² = 1
L - 11 = ±1
L = 11 ± 1
L = 10 or 12
Dimensions: 10 * 12
Step-by-step explanation: write it on paper
Find R U S, given the following sets:
P = {b, d, f, g}
Q = {a, b, c, d}
R = {c, e, f, g}
S = {a, d, g}
Answer:
(RUS)={ a,c,d,ef,g}
Step-by-step explanation:
All the number of alphabets present in R and S will be the union of set R and S
need help asap!!!! plsss i have 5min
Answer:
30
Step-by-step explanation:
x=10
x^2+3x-130=0
x=10 or -13
there is no negative angle so the answer is ten
Which angles are corresponding angles?
Check all that apply.
2
1
4
3
5 6
В
7
D A. 4 and 8
B. 2 and 6
C. 4 and 6
D. 2 and 7
E. 3 and 6
F. 3 and 7
Answer:
E
Step-by-step explanation:
Answer:
The answer is E
Step-by-step explanation:
Hope this answer is helpful...
Hope this answer is helpful...
Hope this answer is helpful... Make me as brainliest....
According to a November 2019 report by CNN, the startup company Heliogen has devised a high-heat solar oven that can be used to create concrete and steel without the use of fossil fuels. Currently, the creation of these materials produces 7% of the world's carbon emissions from fossil fuels. If the world's total carbon emissions in 2018 was 37.1 billion tons, how much of that carbon came from the creation of these building materials? Give your answer in billions of tons. Round to two decimal places.
Answer:
37,1bilion tons*0,07=2,60 bilion tons (2d.p.)
Step-by-step explanation:
On a coordinate plane, a line goes through points (0, 1) and (3, negative 1). Consider the graph of the line. Using the rise/run counting method, the slope of the line is .
Answer: The slope of the line is -2/3.
Step-by-step explanation:
How I think of it is that on the y plane on a graph, going from positive 1 to negative 1 you need to move down 2 places and thats the "rise" part of rise over run eventhough you moved down. Then on the x plane, going from 0 to 3 you need to move 3 spaces to the right on the graph and thats the "run" part of rise over run because you can either move left or right. Rise over run can also be thought of as change in y over change in x which means that since i went down 2 places on the y, the change in y was 2 and since we moved 3 places over on the x plane the change in x whould be 3. Since we move down and then to the right on the graph, the line being created would be negative, so you final answer for the slope is -2/3!
I hope this helps :)
Answer:
-2/3
Step-by-step explanation:
Hope this helps!
Is 7.787887888… a rational number? PLEASE ANSWER ASAP!! WILL GIVE BRAINLIEST!!!!!
Answer:
yes it is a rational number because the number has a repeating pattern
Step-by-step explanation:
The number 7.787887888... is rational, Yes; it has a pattern that is repeating.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
It is given that:
The number is 7.787887888
As we know,
The rational number can be represented in the form of p/q where q cannot be equal to zero.
If the number is terminated after some decimal places then it is said to be a rational number.
If the number is repeating its digit after decimal then it is said to be an irrational number.
Thus, the number 7.787887888... is rational, Yes; it has a pattern that is repeating.
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what is the product?
x^2 -16 • x^3 - 2x^2 + x———— ——————–—
2x +8 x^2 +3x -4
Answer:
A) x(x-4)(x-1)/2(x+4)
Step-by-step explanation:
(x²-16)/(2x+8) * (x³-2x²+x)/(x²+3x-4)
factor
(x+4)(x-4)/2(x+4) * x(x-1)(x-1)/(x+4)(x-1)
You can take out both (x+4) from the first side, and both (x-1) on the second side. Then you’re left with:
(x-4)/2 * x(x-1)/(x+4)
which equal
x(x-4)(x-1)/2(x+4)
which is A.
A medical secretary maintains the accounts and writes the paychecks
for a medical office complex. There are 36 people on the payroll. Eight people earn $10 per hour, eleven people earn $15 per hour, four people earn $18 per hour, six people earn $21 per hour, and seven people earn $26 per hour. If everyone works 40 hours per week, what is the total amount of money needed for the payroll each week?
Answer:
$25,000
Step-by-step explanation:
8 x $10 = 80 x 40 = $3,200
11 x $15 = 165 x 40 = $6,600
4 x $18 = 72 x 40 = $2,880
6 x $21 = 126 x 40 = $5,040
7 x $26 = 182 x 40 = $7,280
3200 + 6600 + 2880 + 5040 + 7280 = $25,000
I hope this helps!
-TheBusinessMan
How many models of 100 do you need to model 7,600? Enter the number. Then complete the explanation.
Answer:
76
Step-by-step explanation:
Well if you simply multiply 100x76 you would get 7,600. Or if you still have not learned to multiply just add 76+76 on a calculator until you get 7,600.
identify the degree of the polynomial x^2y+5xy^3-7y^2+2
We have three parts of the equation with a power:
x^2y, 5xy^3, and 7y^2
We can find the degree of each by the following:
x^2y; 2 + 1 = 3
5xy^3; 1 + 3 = 4
7y^2; 2
Therefore, the highest degree is 4.
Best of Luck!
what is 48 divide by -6 =
Answer:
-8
Step-by-step explanation:
any number divided by a nega is going to be neg if it is multiplied by two nega's its positive.