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]
Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They substitute their values shown below into the compound interest formula.
The question is incomplete. The complete question is :
Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They substitute their values shown below into the compound interest formula. Compound Interest Accounts Name Principal Interest Rate Number of Years Compounded Jaina $300 7% 3 Once a year Tomas $400 4% 3 Once a year. Which pair of equations would correctly calculate their compound interests?
Solution :
It is given that Jaina and Tomas wants to open an account by depositing a principal amount for a period of 3 years and wanted to calculate the amount they will have using the compound interest formula.
So for Jiana :
Principal, P = $300
Rate of interest, r = 7%
Time, t = 3
Compounded yearly
Therefore, using compound interest formula, we get
[tex]$A=P\left(1+\frac{r}{100}\right)^{t}$[/tex]
[tex]$=300\left(1+\frac{7}{100}\right)^{3}$[/tex]
[tex]$=300(1+0.07)^3$[/tex]
Now for Tomas :
Principal, P = $400
Rate of interest, r = 4%
Time, t = 3
Compounded yearly
Therefore, using compound interest formula, we get
[tex]$A=P\left(1+\frac{r}{100}\right)^{t}$[/tex]
[tex]$=400\left(1+\frac{4}{100}\right)^{3}$[/tex]
[tex]$=400(1+0.04)^3$[/tex]
Therefore, the pair of equations that would correctly calculate the compound interests for Jaina is [tex]$A=300(1+0.07)^3$[/tex] .
And the pair of equations that would correctly calculate the compound interests for Tomas is [tex]$A=400(1+0.04)^3$[/tex] .
Answer:
If anyone is having problems understanding the other persons answer it is (D)
Step-by-step explanation:
Solve for k, the constant of variation, in an inverse variation problem where y=17 x=6
Answer:
k=102
Step-by-step explanation:
hope this helps with your assignment
Odell Gleaves delivers Danberry Real Estate calendars to town residents after
school.
He is paid $0.06 for each calendar he delivers.
What is his total pay for a
week in which he delivered the following number of calendars?
Mon- 100
Tues- 130
Wed- 145
Thurs- 138
Fri- 210
Answer: $4.34
Step-by-step explanation:
Mon: 0.6x100= 60 cents
Tue: 0.6x130= 78 cents
Wed: 0.6x145= 87 cents
Thurs: 0.6x138= 82.8 cents
Fri: 0.6x210= 126 cents
60+78+87+82.8+126= 433.8 cents
There are 100 cents in a dollar
4.33.8 cents, so 4.34 if you round up (if the last number is five or greater round up)
Please help me please help ASAP this is really really important
Answer:
3rd. 1
Step-by-step explanation:
Which rules define the function graphed below?
Please help. I’ll give extra points and brainliest for a real answer
Answer:
y=x+2; y=5
Step-by-step explanation:
Answer:
y=x+2; y=5
Step-by-step explanation:
got it right on the quiz
A back account pays an interest rate of 6% every 1 year. You deposit $5000 into the account. How much money will you have in 5 years?
A. $7092
B. $3449
C. $3670
D. $6691
Answer:
C: $6691
Step-by-step explanation:
This problem is one in compound interest. The general formula is shown below. The principal, P, is $5000, the annual interest rate, r, is 0.06 (expressed as a decimal fraction), and the number of years, t, is 5 years: A represents the Amount after 5 years:
A = P(1 + r)^t becomes A = ($5000)(1 + 0.06)^5, or
A = (5000)(1.06)^5 = $6691.12 (Answer D)
From 99° to 70°f what is the percent decrease
Answer:
should be -29.29 %
Step-by-step explanation:
Answer:
29.(29)%
Step-by-step explanation:
can someone help me with the picture I put above please
Answer:
9
Step-by-step explanation:
3x+8=35
3x=27
x=9
please help me ! thank you
Answer:
57
Step-by-step explanation:
3 * 3 * 3 = 27 + 5*6 =30 27+30=57
Hope this helps!
Answer:
c.57
Step-by-step explanation:
.3^3= 27
.and 5 (6)=30
27+30=57
remember to use pemdas!! (parenthesis, exponents, multiplication/division, addition/subtraction)
ASSAP EASY MATH does a shape stay congruent when it has been rotated
Answer:
They are still congruent even after being rotated they still will remain the same shape.
Step-by-step explanation:
Answer:All the sides of each shape must be identical. so yes if it is
Step-by-step explanation:
Needed ASAP for tonight, 10 quick homework questions
30 points and a brainly (see attached picture)
5x – 9 > 8 + 5x Find the solution set:
Answer:
Here you go, it's In the attachment
find the value of given expression
[tex] \sqrt{300 \times 3} [/tex]
Answer:
√(300×3)=√900=√30²=±30 is your answer
the scale factor is 1 : 87. If the diameter of a wheel on a model train is 0.3 inch, what is the diameter of the actual wheel?
Answer:
26.1
Step-by-step explanation:
Consider 0.3 as 1. Now multiply 0.3 by 87.
Please help me with this
Answer:
Step-by-step explanation:
thank you lol i’m not smart sorry
Answer: 65
Step-by-step explanation: Sum of angles in triangles is always 180, we know one angle is 25 and another is 90, so 25 + 90 = 115, then 180 - 115 = 65.
pls help ill give brainliest. the red isnt part of it was just how it was screenshot.
Find the area of a circle with 7cm radius .
Use the value 3.14 for π, and do not round your answer.
Be sure to include the correct unit in your answer.
Answer:
153.9
Step-by-step explanation:
hope it helps
Yolonda withdrew 60 dollars from her checking account.Write a signed number to represent this change in her account.
Answer:
$ 60.00
Step-by-step explanation:
.
(xy^-6)^2
A. xy^-36
B. xy^36
C. x^2y^-12
Answer:
Step-by-step explanation: (9=4-38-838,256=2-60^7
Each side of a square sandbox is 36 inches long. What is the area of the sandbox
The area of the square sandbox is 1,296 square inches
What is area of square?The area of a square is the measure of the space or surface occupied by it. It is equal to the product of the length of its two sides. Since the area of a square is the product of its two sides, the unit of the area is given in square units.
Area of a square = Side × Side
= [tex]Side ^{2}[/tex]
According to the question
Side of a square sandbox = 36 inches
Therefore,
The area of the square sandbox = [tex]Side ^{2}[/tex]
= [tex](36)^{2}[/tex]
= 1,296 square inches
Hence, the area of the square sandbox is 1,296 square inches
To know more about area of square here:
https://brainly.com/question/1658516
#SPJ2
You are putting money into a bank account. You start with $100 and add $12 every month. The total amount of money in your account can be represented by the following equation. (where T is total amount and M is the number of months):
T = 100 + 12 M
If you have $208, how many months have passed?
Show the equation and how you got the answer.
100
Add 12 every month
Ex: 100 + 12
100 + 12 + 12+ 12+ 12+ 12+ 12+ 12+ 12+ 12
It wound not be 100 x 9 because 100 x 9 is 900
Therefore 9 months
9 x 12 = 108
so that would be 100+108= 208
Hope this helps~
What is the apparent solution to the system of equations graphed above?
Answer:
C
Step-by-step explanation:
Please helpppppp!!!!!!!!
Answer:
a, cube
Step-by-step explanation:
Help me fast I have 30 min to finish the testtt!!!!!!!!!
The weather forecast was calling for 8 inches of snow. It actually only snowed 2 1/4 inches. How far off was the forecast’s prediction?
Are the ratios 15:12 and 6:4 equivalent?
Answer:
No
Step-by-step explanation:
To get to 12 from 4 you'd have to multiply by 3 but, if you multiply 6 by 3 you get 18, not 15.
Suppose that P(n) is a propositional function. Determine for which nonnegative integers n the statement P(n) must be true if a) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) is true. b) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 3) is true. c) P(0) and P(1) are true; for all nonnegative integers n, if P(n) and P(n 1) are true, then P(n 2) is true. d) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) and P(n 3) are true
Solution :
a). [tex]$P(0)$[/tex] is true
Then ,[tex]$P(0+2)=P(2)$[/tex] is true.
[tex]$P(2+2)=P(4)$[/tex] is true
[tex]$P(4+2)=P(6)$[/tex] is true.
Therefore, we see that [tex]$P(n)$[/tex] is true for all the even integers : [tex]$\{0, 2,4,6,...\}$[/tex]
b). [tex]$P(0)$[/tex] is true
Then ,[tex]$P(0+3)=P(3)$[/tex] is true.
[tex]$P(3+3)=P(6)$[/tex] is true
[tex]$P(6+3)=P(9)$[/tex] is true.
Therefore, we see that [tex]$P(n)$[/tex] is true for all the multiples of 3 : [tex]$\{0, 3,6,9,12,...\}$[/tex]
c). [tex]$P(0)$[/tex] and [tex]$P(1)$[/tex] is true, then [tex]$P(0+2)=P(2)$[/tex] is true
[tex]$P(1)$[/tex] and [tex]$P(2)$[/tex] is true, then [tex]$P(1+2)=P(3)$[/tex] is true.
[tex]$P(2)$[/tex] and [tex]$P(3)$[/tex] is true, then [tex]$P(2+2)=P(4)$[/tex] is true.
So, we observe that [tex]$P(n)$[/tex] is true for all the non- negative integers : [tex]$\{0, 1,2,3,4,5,6,...\}$[/tex].
d). [tex]$P(0)$[/tex] is true,
So, [tex]$P(0+2)$[/tex] and [tex]$P(0+3)$[/tex] is true or [tex]$P(2)$[/tex] and [tex]$P(3)$[/tex] is true.
Now, [tex]$P(2)$[/tex] is true.
Again, [tex]$P(2+2)$[/tex] and [tex]$P(2+3)$[/tex] is true or [tex]$P(4)$[/tex] and [tex]$P(5)$[/tex] is true.
Now, [tex]$P(3)$[/tex] is true.
Again, [tex]$P(3+2)$[/tex] and [tex]$P(3+3)$[/tex] is true or [tex]$P(5)$[/tex] and [tex]$P(6)$[/tex] is true.
Thus,
[tex]$P(n)$[/tex] is true for all the non- negative integers except 1 : [tex]$\{0, 2,3,4,5,6,...\}$[/tex].
ryan has some donuts he takes 5 away
d - 5 = ?
Answer:
2
Step-by-step explanation:
To prepare for a party, Jada poured 0.45 liter of juice into each of several cups. Altogether she poured 9 liters of juice into the cups. How many cups did Jada fill? H e l p please :)
Answer:
20 cups
Step-by-step explanation:
Jada poured 0.45 liters of juice into several cups
9 liters was poured into each cup
Therefore the number of cups that Jada will fill up in the party can be calculated as follows
= 9/0.45
= 20
Hence Jada will fill up 20 cups
Solve for x.
6x – 4(3x – 5) = 2
A. x =113
B. x = 3
C. x = –3
D. x = –113