Answer:
[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]
Step-by-step explanation:
To find - Find the average value fave of the function f on the given interval. f(x) = 5 sec²(x/6), [0, 3[tex]\pi[/tex]/2]
Proof -
We know that,
Average value of f in the interval [a, b] is -
[tex]f_{ave}[/tex] = [tex]\frac{1}{b - a}\int\limits^b_a {f(x)} \, dx[/tex]
Now,
Here a = 0, b = [tex]\frac{3\pi }{2}[/tex], f(x) = [tex]5sec^{2}(\frac{x}{6} )[/tex]
Now,
[tex]f_{ave}[/tex] = [tex]\frac{1}{\frac{3\pi }{2} - 0}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{2 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{10 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) }|^{\frac{3\pi }{2} }_0 \, ][/tex]
= [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) - tan({0) } \, ][/tex]
= [tex]{\frac{10 }{3\pi }}[ {1 - 0 } ][/tex]
= [tex]{\frac{10 }{3\pi }[/tex]
⇒[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]
Someone answered this question with a link that didn't work so i need help
Answer:
y=0.875x + 6
Step-by-step explanation:
Answer:
Y= 7/8X+6
Step-by-step explanation:
Good luck bro .
find the values of x and y.
Answer:
x= 60° , y = 60 °
Step-by-step explanation:
x = 60°
y = 60°
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Answer:
The answer is 5 beecause coefficients are the number when you multiply a number and a variable. For example 5a the coefficient in that term is 5 if you have 48e the coefficient is 48. So the coefficient is the number when you multiply a number times a variable.
in a raffle, one ticket will win a $530 prize, four tickets will win a $500 prize, ten tickets will win a $160 ze, and the other tickets will win nothing. There are 1,000 in the raffle. If you have a ticket, what is e expected payoff?
Does anyone know this answer???
Answer:
VX has the greatest length
Hans wanted to find the length of the hypotenuse of the triangle. Which statement correctly identifies his error?
A right triangle has side lengths 40 centimeters and 9 centimeters. The hypotenuse is labeled c.
9 squared + 40 squared = c squared. 81 + 80 = c squared. 161 = c squared. StartRoot 161 EndRoot centimeters = c.
He did not square 40, he just multiplied by 2.
He did not finish the problem. He should have divided 161 by 2 to find the square root.
He should have added 9 + 9 to find the value of 9 squared.
He should have subtracted the two squares to get 40 squared minus 9 squared = c squared because numbers get too large if both legs are squared and then added together.
Answer:
He did not square 40, he just multiplied by 2
Answer 41 centimeters.
Step-by-step explanation:
C²=40²+9²
C²=1600+81
C²=1681
√c²=√1681
C=41cm
Answer:
the answer is A
Step-by-step explanation:
edg
find the value of given expression
[tex] \sqrt{35 \times 35} [/tex]
Which expression shows the result of applying the distributive property to 12(5y+4)?
60y + 4
5y + 48
17y + 16
60y + 48
Answer:
60y+48
Step-by-step explanation:
Storage units are numbered 1 through 50. What is the probability that the operator will choose a unit that is not a multiple of 8?
Answer:
22/25
Step-by-step explanation:
Multiples of 8 betwen 1 - 50 =
8
16
24
32
40
48
there are 6 multiples of 8
Numbers that are not multiples of 8 = 50 - 6 = 44
Probability the operator will choose a unit that is not a multiple of 8 = 44/50
Expressing in simpler terms = 22/25
Find the measure of arc LM.
Answer:
arc LM = 119°
Step-by-step explanation:
KL = LM
arc KL = arc LM
2(arc LM) = 360° - 122° = 238°
arc LM = 119°
Help 10 pts!!!
A cedar chest is a shaped like a rectangular prism. The cedar chest is 2 feet tall, 4 feet wide, and 2 feet deep.
What is the surface area of the cedar chest?
Answer:
40 ft^2
Step-by-step explanation:
lateral surface area -Slat = 24 ft^2
top surface area-Stop = 8 ft^2
bottom surface area -Sbot = 8 ft^2
24+8+8= 40
total surface area -Stot = 40 ft^2
Answer:
40
Step-by-step explanation:
took the test
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:x=3
Step-by-step explanation:
the 3 angles of a triangle equal 180
you add 105 and 46, which equals 151
you subtract 151 from 180 to see what the missing angle is (29)
you would make 6x+11 equal to 29
-subtract 11 from 29= 18
6x/6, 18/6
the answer is 3
hope this helps! :)
Which one is the answer
Answer:
2667
Step-by-step explanation:
35 meters wide at the base
20.6 meters tall
h = 20.6 m
slant height s = 27.029798371427 m
side length a = 35 m
lateral edge length e = 32.200310557509 m
1/2 side length r = 17.5 m
volume V = 8411.6666666667 m3
lateral surface area L = 1892.0858859999 m2
base surface area B = 1225 m2
total surface area A = 3117.0858859999 m2
in all explanation, 2667 is the final answer.
hope this helped!
factor the trinomial 6y^2+19y+15?
Answer:
6y^2+43
Step-by-step explanation:
6y^2+(19+15)
Answer:
(2y+3)(3y+5)
Step-by-step explanation:
6y^2+19y+15
Factor the expression by grouping. First, the expression needs to be rewritten as 6y^2+ay+by+15. To find a and b, set up a system to be solved.
a+b=19
ab=6×15=90
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 90.
1,90
2,45
3,30
5,18
6,15
9,10
Calculate the sum for each pair.
1+90=91
2+45=47
3+30=33
5+18=23
6+15=21
9+10=19
The solution is the pair that gives sum 19.
a=9
b=10
Rewrite 6y^2+19y+15 as (6y^2+9y)+(10y+15).
(6y^2+9y)+(10y+15)
Factor out 3y in the first and 5 in the second group.
3y(2y+3)+5(2y+3)
Factor out common term 2y+3 by using distributive property.
(2y+3)(3y+5)
Drake produced 52 songs last year. If each new album has 15 songs on it, how many of his songs were not released on an album?
Answer:
7
Step-by-step explanation:
If each album has 15 songs, 15 * 3 = 45 so 52 - 45 = 7. Therefore, Drake produced 7 songs not in an album.
1 picture 2 questions please and thank you
Answer:
Step-by-step explanation:
Solve for k:
k over 6.12 = 8.7
1. k = 53.244
2. k = 1.42
3. k = 2.58
Answer:
1. k=53.244 or k=13311/250
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Answer:
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wasd is the moving mechanics in minecraft
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!
Answer:(-6.5,-5)
Step-by-step explanation:
P = (3A +1B)/(3+1)
P = (3(-7, -9) +(-5, 7))/4 = (-21-5, -27+7)/4 = (-6.5, -5)
You have to type up a 400 word paper. If you can type 25
words in 3 minutes, how long will it take you to type the
paper?
Answer:
48 minutes
Step-by-step explanation:
25=3 400/25=16x3=48
Answer:
48 minutes
Step-by-step explanation:
25 words - 3 minutes
400 words - x minutes
Cross multiply
25x = 400 x 3
25x = 1200
Divide both sides by 25
x = 1200/25
x = 48
need some help please
Answer:
A(t)+900=x
B(t)+500=x
for the sake of things X represents the answer and as both need to equal the same it works out so that plugging it into a calculator should give you the answer
Step-by-step explanation:
you could start by making a T chart on one Side A the other B starting with 900 at A and 500 at B go down by the appropriate increments 950, 600;1000, 700; 1050, 800; 1100, 900, 1150, 1000; 1200, 1100; 1250, 1200, and you guessed it, 1300, 1300. so there you go X=1300
Find the values of x and y so that GHJK is a dart. Be sure to show all work .
Answer:
Step-by-step explanation:
In dart, adjacent sides are equal
JK = GK
3x - 9 = x + 13 {Add 9 to both sides}
3x = x + 13 + 9
3x = x + 22 {Subtract 'x' from both sides}
3x -x = 22
2x = 22 {Divide both sides by 2}
x = 22/2
x = 11
JH = GH
9y = 5y + 8 {Subtract 5y from both sides}
9y - 5y = 8
4y = 8 {Divide both sides by 4}
y = 8/4
y = 2
If you are finding the range of a data set, are you finding a measure of center or a measure of variation?
center
variation
Answer:
i think variation
Step-by-step explanation:
» A group of 6 friends buy a video game that costs $60. They each
spend an equal amount of money. How much money does each
friend spend?
1» Let m stand for how much money each friend spends. Which equations
can be used to solve the problem? Choose ALL the correct answers.
m = 60 x 6
m= 60 = 6
m = 6 x 60
60 = 6 x m
Answer:
m = 60/6
60 = 6 x m
Step-by-step explanation:
Lucas is borrowing money to purchase a vehicle. A car dealership will loan Lucas $18,000 with a simple interest rate of 14.5% applied annually, and a 5-year payout plan. The bank will loan Lucas $18,000 with a compound interest rate of 8.9% applied annually and a 4-year payout plan. What is the difference in the total payback amounts?
Answer:
Difference in total payback = $5734.64
Step-by-step explanation:
Formula for the simple interest payout,
Interest = [tex]\frac{P\times r\times t}{100}[/tex]
P = Principal amount of loan
r = rate of interest (Annually)
t = Duration for the payment
Interest = [tex]\frac{18000\times 14.5\times 5}{100}[/tex]
= $13050
Total payable amount = 18000 + 13050
= $31050
Formula for the amount payable with compound interest,
Final amount = [tex]\text{Initial amount}(1+\frac{r}{n})^t[/tex]
Here, t = Duration of investment
r = rate of interest (Annual)
n = Number of compounding per year
Payable amount = [tex]18000(1+\frac{0.089}{1})^4[/tex]
= 18000(1.089)⁴
= $25315.36
Difference in total payback = $31050 - $25315.36
= $5734.64
If Lucas takes the 5-year payment plan he will end up paying $31,050. If Lucas takes the 4-year payment plan he will end up playing $24,408. Hope it helps.
What is an equation of the line that passes through the points (0,5) and (-5,7) Put your answer in fully reduced form
Answer:
y = 2/5x + 5
Step-by-step explanation:
I assume you want the equation in point slope form? So assuming that, (0, 5) is the y intercept which is b in the equation y=mx+b (b=5). Now you have to find the slope, paper is really handy (I like drawing a graph out to help me sometimes but an easy way to do it is another equation like this...
y2-y1/x2-x1=
7-5/-5-0=
2/5 --> So 2/5 is the slope, and that finishes the equation
Final equation in point slope form: y=2/5x+5
HOPE YOU UNDERSTAND NOW!!!! :)
The equation of the line that passes through the point (0, 5) and (-5, 7) is
y = - 2/5 x + 5
The equation can be represented in the slope intercept form below
y = mx + bwhere
m = slope
b = y- intercept
(0, 5)(-5, 7)
The slope can be found below
m = 7 - 5 / -5 - 0 = 2 / -5 = - 2/5
Therefore, using y = mx + b format
y = -2/5 x + b
let's find b using the coordinate (0, 5)
5 = - 2 /5 (0) + b
b = 5
Finally, the equation is
y = - 2/5 x + 5
read more: https://brainly.com/question/16569095?referrer=searchResults
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Please help me with this
Answer:
i cant see it...
Step-by-step explanation:
...
can somebody help me please
Answer:
Step-by-step explanation:
a - 7 = 3(b + 2)
a - 7 = 3b + 2*3
a - 7 = 3b + 6 {Subtract 6 from both sides}
a - 7 - 6 = 3b
a - 13 = 3b {Divide both sides by 3}
[tex]b =\frac{a-13}{3}[/tex]
Write an equation of the line in slope-intercept form. (0,2)(3,3)
Answer:
Slope = 1/3
Step-by-step explanation:
Hope this helps.