Answer:
Step-by-step explanation:
If you were to graph this on a coordinate plane, it looks like a log function. It starts at (0, 0) and ends, according to the boundaries given, at x = 8. Because we are to solve for the volume using the shell method, we need x = y equations (which we have, thankfully!) and y intervals. The y-interval is given to us within the problem as 0≤y≤2. If we are to revolve this solid about the line y = 2, the line of rotation is above the solid, so we have to go backwards to get there. That's very important. The formula we need for shells is
[tex]2\pi\int\limits^2_0 {p(y)h(y)} \, dy[/tex]
where p(y) is the distance between the axis of rotation and the solid, and h(y) is the height of the representative rectangle. Since we are using the shell method, the representative rectangle is parallel to the axis of rotation, so it is 8 units long (or high).
p(y) is the distance from y = 2 to the solid, so p(y) = 2 - y
h(y) is the length of the representative rectangle, so h(y) = 8
and filling in the formula:
[tex]2\pi\int\limits^2_0 {(2-y)(8)} \, dy[/tex] and simplifying a bit:
[tex]2\pi\int\limits^2_0 {16-8y} \, dy[/tex]
Integrating we get
[tex]2\pi[16y-4y^2][/tex] from 2 to 0. Using the First Fundamental Theorem of Calculus:
[tex]2\pi[(32-16)-(0)][/tex] simplifies to
[tex]2\pi(16)[/tex] which is, finally,
[tex]V=32 \pi[/tex]
In this exercise we have to use the fundamental calculus theorem to calculate the volume of a rotating cylinder, thus we find that:
[tex]V=32\pi[/tex]
If you were to graph this on a coordinate plane, it looks like a log function. It starts at (0, 0) and ends, according to the boundaries given, at x = 8. Because we are to solve for the volume using the shell method, we need x = y equations and y intervals. The y-interval is given to us within the problem as 0≤y≤2. If we are to revolve this solid about the line y = 2, the line of rotation is above the solid, so we have to go backwards to get there. That's very important. The formula we need for shells is
[tex]2\pi \int\limits^2_0 {p(y)h(y)} \, dy[/tex]
Where p(y) is the distance between the axis of rotation and the solid, and h(y) is the height of the representative rectangle. Since we are using the shell method, the representative rectangle is parallel to the axis of rotation, so it is 8 units long (or high).
p(y) is the distance from the solid, so: [tex]p(y) = 2 - y[/tex] h(y) is the length of the representative rectangle, so: [tex]h(y) = 8[/tex]
and filling in the formula:
[tex]2\pi \int\limits^2_0 {16-8y} \, dy[/tex]
Integrating we get;
[tex]2\pi [ 16y-4y^2][/tex]
Using the First Fundamental Theorem of Calculus:
[tex]2\pi [ (32-16)-(0)][/tex]
[tex]2\pi (16) \\V=32\pi[/tex]
See more about volume at brainly.com/question/1578538
Anyone pls I need help at this
Answer:
$62.7solution,
She starts to work at 7:45 am
She stops the work at 12:30 for lunch.
Before launch, she works 4:15 hours.
And after lunch ,she works 4 hours
Now,
total she works 8 hours 15 minutes.
For each hour,she earn 7.60
[tex]8 \times 7.60[/tex]
=$ 60.8
For another 15 min,she earns $ 1.9
So,
Total earning=60.8+1.9
=$ 62.7
Hope this helps...
Good luck on your assignment...
precalculus help! i'm having some trouble with my summer assignment. help would be very appreciated :)))
6.
[tex]y^2\sqrt[8]{8}[/tex]
Step-by-step explanation:
[tex]\sqrt[8]{8*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y}[/tex]
Since there are eight y's in two groups we can take them out which turns into
[tex]y^2\sqrt[8]{8}[/tex]
:)
3.
Problem 3:
We are given the following complex number and I'm assuming we want to simplify it:
[tex]\dfrac{5+i}{6+i}[/tex]
Using the complex arithmetic rule (research about this if you're not familiar with it, it's very helpful):
[tex]=\dfrac{(5\times6+1)+(6-5)i}{6^2+1^2}[/tex]
[tex]=\dfrac{31+i}{37}[/tex]
Simplifying gives us:
[tex]=\dfrac{31}{37}+\dfrac{1}{37}i[/tex]
Problem 6:
You seem to have done this problem correctly
[tex]\sqrt[8]{8y^{16}}[/tex]
Expanding gives us:
[tex]=\sqrt[8]{y^{16}}\times\sqrt[8]{8}[/tex]
[tex]=y^2\sqrt[8]{8}[/tex]
This can't be simplified further as the 8th root of 8 gives us an irrational number
Let me know if you need any clarifications or extra help, thanks!
Find the value of x.
14
3x-12
A
A
21
x = [?]
Answer:
Step-by-step explanation:
Set up a ratio.
An angle bisector divides the side opposite it in the same ratio as the two sides defining the angle where the vertex and angle bisector meet.
14/6 = 21 / 3x - 12
Cross multiply
14(3x - 12) = 6*21
Remove the brackets
42x - 168 = 126
Add 168 to both sides
42x = 168 + 126
Combine
42x = 294
Divide by 42
x = 294/42
x = 7
express x^2-8x+20 in the form (x-a)^2+a where a is an integer
Answer:
(x-4)²+4
Step-by-step explanation:
Answer:
[tex](x-4)^2+4[/tex]
Step-by-step explanation:
[tex]x^2 - 8x + 20\\**********************************\\\frac{8}{2} =( 4 )^2 = 16 \\\\20 - 16 = 4\\**********************************\\x^2 - 8x + 16 + 4\\(x-4)^2+4[/tex]
Which expression is equivalent to 3\dfrac78 - 6\dfrac143 8 7 −6 4 1 3, start fraction, 7, divided by, 8, end fraction, minus, 6, start fraction, 1, divided by, 4, end fraction? Choose 1 answer: Choose 1 answer: (Choice A) A 3\dfrac78+\left(-6\dfrac14\right)3 8 7 +(−6 4 1 )3, start fraction, 7, divided by, 8, end fraction, plus, left parenthesis, minus, 6, start fraction, 1, divided by, 4, end fraction, right parenthesis (Choice B) B -6\dfrac14+\left(-3\dfrac78\right)−6 4 1 +(−3 8 7 )minus, 6, start fraction, 1, divided by, 4, end fraction, plus, left parenthesis, minus, 3, start fraction, 7, divided by, 8, end fraction, right parenthesis (Choice C) C 6\dfrac14-\left(3\dfrac78\right)6 4 1 −(3 8 7 )6, start fraction, 1, divided by, 4, end fraction, minus, left parenthesis, 3, start fraction, 7, divided by, 8, end fraction, right parenthesis (Choice D) D 3\dfrac78+\left(6\dfrac14\right)3 8 7 +(6 4 1 )
Answer:
[tex](A) 3\dfrac78+\left(-6\dfrac14\right)[/tex]
Step-by-step explanation:
Given the expression:[tex]3\dfrac78 - 6\dfrac14[/tex]
The given options are:
[tex](A)3\dfrac78+\left(-6\dfrac14\right)=3\dfrac78-6\dfrac14\\\\(B)-6\dfrac14+\left(-3\dfrac78\right)=-6\dfrac14-3\dfrac78\\\\(C)6\dfrac14-\left(3\dfrac78\right)=6\dfrac14-3\dfrac78\\\\(D)3\dfrac78+\left(6\dfrac14\right)=3\dfrac78+6\dfrac14[/tex]
We can see therefore that Option A is equivalent to the given expression.
Answer:
-25/-33
Step-by-step explanation:
-5/3x5/-11=
Which point is an x-intercept of the quadratic function f(x)=(x-8)(x+9)? 1. (0,8) 2.(0,-8) 3.(9,0) 4.(-9,0) If yk how to do these, pls help with my other questions :( <3
Answer:
x intercept is when y = 0, so when y is 0, x should be -9 or 8, so 4. is the only that satisfies it, therefore (-9,0)
Step-by-step explanation:
Follow me at "btracta" on insta and we can talk
What's your instagram then?
Yes 80 followers following 10 is me
which number produces an irrational number when added to 1/2?
A. 0.373737...
B. 3.14159265...
C. √16
D. -4/7
The number 3.14159265 produces an irrational number when added to 1/2.
What is the sum of an irrational number and a rational number?
The sum of any rational number and any irrational number will be always an irrational number.
What is irrational number?An irrational number is a type of real number which cannot be represented as a simple fraction.
What is rational number?A number that can be represented as the quotient p/q of two integers such that q ≠ 0 is called a rational number.
According to the given question
We have a rational number 1/2.
Since, 0.373737373.... is a rational number because it is recurring and its behavior it known that 37 is repeating.
And we know that when any rational number is added with a rational number it with number we will get always a rational number.
⇒ 0.3737373737... + [tex]\frac{1}{2}[/tex] = rational number.
3.14159265... is an irrational number because its behavior is not known and it is not terminating.
So, when we add 1/2 to 3.14159265.. we get a irrational number.
√16 = 4 is a rational number. And it can be written as [tex]\frac{4}{1}[/tex].
So, [tex]\frac{4}{1} + \frac{1}{2} = \frac{9}{2}[/tex] which is a rational number.
-4/7 is a rational number. And when we add 1/2 to -4/7 we get a rational number.
i.e. [tex]\frac{-4}{7} + \frac{1}{2} = \frac{-1}{14}[/tex] which is rational number.
Hence, the number 3.14159265 produces an irrational number when added to 1/2.
Learn more about rational and irrational number here:
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which of the following are binomials? check all that apply
Answer: A, D, F
Step-by-step explanation: Binomials are the sums of two terms (the sum two monomials). Therefore those with two terms being added are considered binomials.
92.6 % of 103.93 km Give your answer rounded to 2 DP.
Answer:
[tex]Result = 96.24\ km[/tex]
Step-by-step explanation:
Given
92.6 % of 103.93 km
Required
Solve (to 2 decimal places)
To solve this, we simply multiply both 92.6% and 103.93 km together;
[tex]Result = 92.6\% * 103.93\ km[/tex]
Convert percentage to fraction
[tex]Result = \frac{92.6}{100} * 103.93\ km[/tex]
Combine to form a single fraction
[tex]Result = \frac{92.6 * 103.93\ km}{100}[/tex]
[tex]Result = \frac{9623.918\ km}{100}[/tex]
[tex]Result = 96.23918\ km[/tex]
[tex]Result = 96.24\ km[/tex] (Approximated to 2 decimal places)
Help please!!
Solve the equation -5m = -20.
m = 1/4
m = -1/4
m = -4
m = 4
Answer:
m=4
Step-by-step explanation:
-5m=-20
m= - 20/-5
m=4
Answer:
M=4
Step-by-step explanation:
This question was on my online school assignment. I can go back on my assignments and review and I had got it right.
What is the area of the composite figure? ___ units^2
Answer:
34 square units
Step-by-step explanation:
The figure can be considered to be a trapezoid with a rectangle removed.
The area of the trapezoid is ...
A = (1/2)(b1 +b2)h
A = (1/2)(10 +6)(5) = 40
The area of the rectangle is ...
A = LW
A = (3)(2) = 6
Then the area of the shaded portion of the figure is ...
shaded area = trapezoid area - rectangle area
= 40 - 6 = 34 . . . square units
The law f(t) = -t2 + 6t + 15 represents the number of kilometers of congestion, as a function of time, registered in a city. With that, determine the maximum number of congestion in that city and the maximum time to reach this value.
Answer:
Maximum Congestion: 24
Maximum Time to reach Congestion: 3
Step-by-step explanation:
Easiest and fastest way is to graph the equation and analyze the graph for it's maximum vertex.
Which ordered pairs are solutions to the inequality y−4x≤−6? Select each correct answer. (−1, −9) (0, −5) (3, 5) (−2, −14) (1, 3)
Answer:
(3,5) (-2,-14)
Step-by-step explanation:
Just plug in values (x,y) in inequality
.Nisha bought a backpack that was on sale at 35% off for $63. How much was the original price of the backpack?
Answer:
$180
Step-by-step explanation:
100%=x
35%=$63
63 x 100=6300/35=$180
Answer:
96.92
Step-by-step explanation:
If the backpack was 35% off you will still pay 100 -35 or 65%
Let x be the original price
x * 65% = 63
Change to decimal form
x * .65 = 63
Divide each side by .64
x*.65/.65 = 63/.65
x =96.92
Which of the following are true statements about 30 6090 triangle
Answer:
30-60-90 triangles have one short side, one long side, and a hypotenuse.
The ratio between the sides (from short to hypotenuse to long) is 1 : 2 : sqrt(3).
Hope this helps!
A "necklace" is a circular string with several beads on it. It is allowed to rotate a necklace but not to turn it over. How many different necklaces can be made using 13 different beads? help plz i will give brainlyist to right awnser :3
Answer:
We have 13 different beads to use in our necklace, and the thing that will make a necklace different to others, is the position of the beads.
And because we can not turn the necklaces over, the mirrored necklaces are different (the positions of the beads are mirrored)
For the first bead, we have 13 options, for the second, 12 options, and so on
the total number of combinations is equal to the product of the options for each selection, then we have:
C = 13*12*11*10*9*8*7*6*5*4*3*2*1 combinations:
C = 6,227,020,800.
Now, we are allowed to rotate the necklace, this means that a combination.
a b c d e f g h i j k l m (each letter is equivalent to one of the different beads)
is the same as other ordered as
m a b c d e f g h i j k l
And for each combination, we have 13 rotations, then the actual number of combinations is:
C/13 = 6,227,020,800/13 = 479,001,600
Using arrangements, it is found that 6,227,020,800 different necklaces can be made using 13 different beads.
The beads can be exchanged among the positions to form the necklace, hence, the arrangements formula is used.
This formula gives the number of possible arrangements of n elements, and is defined by:
[tex]A_n = n![/tex]
In this problem, the necklaces are formed by 13 beads, hence [tex]n = 13[/tex] and:
[tex]A_{13} = 13! = 6227020800[/tex]
6,227,020,800 different necklaces can be made using 13 different beads.
A similar problem is given at https://brainly.com/question/24648661
Which table represents a linear function
Answer:
What are the other tables/answer choices?
Step-by-step explanation:
NEED HELP WITH PART B
gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to
download, y, for a certain number of weeks, X: .picture above
Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and
initial value. (6 points)
Part B: Write an equation in slope-intercept form to model the relations
Answer:
y = -20x + 100
Step-by-step explanation:
As per your requirement For Part B, the solution is
The equation in slope-intercept form to model the relations is below:-
To reach 2 points on the graph the line passes through
lets use p1(0, 100), p2(1, 80)
now we will compute the slope:
[tex]m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]
[tex]m = \frac{(80 - 100)}{(1 - 0)}[/tex]
= -20
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 100 = -20(x - 0)
y = -20x + 100
Answer:
Part A:
initial value = 100 (total amount of songs to download)
rate of change = -20 songs/week (100-80 and so on)
Part B:
ANSWER: y = -20x + 100
y = mx + b, where m is the slope and b is the y-intercept (or initial value).
Help me pweasee
Find the value of the function f(x) = x2 + 9x + 14, when x = -2.
Answer:
-8
Step-by-step explanation:
(-2)2+9(-2)+14
-4+-18+14
-22+14
=-8
Hope this helps
Answer:
0
Step-by-step explanation:
f(x) = x^2 + 9x + 14, when x = -2.
f(x)=(x+7)(x+2)
f(x)=(-2+7)(-2+2)=0
You deposit $20,000 in an account that pays 7.77% annual interest. Find the balance after 2 years when the interest is compounded monthly.
Answer:
The account balance after 24 months will be $23,092.70
Step-by-step explanation:
Given data
P= $20,000
r= 7.77%= 0.077
t= 2 years
A= ?
n= 24
The compound interest formula is
[tex]A= P(1+t)^t[/tex]
Inserting our values to solve for A we have
[tex]A= 20000(1+\frac{0.077}{24} )^2^*^2^4\\\\A= 20000(1+0.003 )^2^*^2^4\\\\A= 20000(1.003 )^2^*^2^4\\\A= 20000(1.003 )^4^8\\\A= 20000*1.15463517818\\\A= 23092.7035636\\\A= 23,092.70[/tex]
Pls help!!!!!!! I need help on this
Answer:
x = 3 ft
y = 83
Step-by-step explanation:
DEFG ≅ SPQR
So, corresponding part will be congruent
∠D ≅ ∠S ; ∠E ≅ ∠P ; ∠F≅ ∠Q ; ∠G ≅ ∠R
DE = SP
x = 3 ft
Sum of interior angles = 360
∠D + ∠E + ∠F + ∠G = 360
∠S + (y+3) + ∠Q + (y +1) = 360
107 + y + 3 + 83 + y+1 = 360
194 + 2y = 360
2y = 360 - 194
2y = 166
y = 166/2
y = 83
HELPPP HELPPPP. iS this function or relation and why?
Answer:
a function, it passes the vertical line test
Step-by-step explanation:
Answer:
Function
Step-by-step explanation:
This is a function because when you do the line test there are no 2 points on the same line. The line test is when you have a bunch of lines going up and down to see if more then one point is on the same line if so it is not a function. When only one point lays on each line then it is a function.
Four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containing 55% spinach. The resulting salad contains 50% spinach. How many cups of salad are in the resulting mixture? 8 9 12 13
Answer:
12 cups of salad
Step-by-step explanation:
Let the unknown cups of salad in the mixture be x( unknown cup in 55% mixture)
Thus, we have the following expression that shows the number of salad in the resulting mixture;
4(40%) + x(55%) = (4+x)(50%)
= 0.4(4) + x(0.55) = 0.5(4 + x)
= 1.6 + 0.55x = 0.2 + 0.5x
0.2 -1.6 = 0.55x-0.5x
0.4 = 0.05x
x = 0.4/0.05
x = 8 cups of salad
So the number of salad cups in the resulting mixture = x + 4 = 8 + 4 = 12 cups of salad
Answer:
12
Step-by-step explanation:
yes
the picture is the qestion
Answer:
12/18 bcz simplyfing 12/18 will give us 2/3
6/9 (divided by 2)
2/3 (divided by 3)
Step-by-step explanation:
The following function represents an arithmetic sequence.
f(1)=2
f(n+1)=f(n)+4
What is f(10)?
Enter your answer as a number, like this: 42
Answer:
f(10)=34
Step-by-step explanation:
This is an arithmetic sequence of common difference "d = 4" (the number added to a term in order to get the next term), and first term 2,
Then we use the formula to find the nth term of an arithmetic sequence with is:
[tex]f(n)=f(1) +\,(n-1)\,d[/tex]
In our case this formula for the term number 10 becomes:
[tex]f(n)=f(1) +\,(n-1)\,d\\f(10)=f(1)+(10-1)\,4\\f(10=2+9*4\\f(10)=2+32\\f(10)=34[/tex]
Answer: Just took it!!!
f(10)=38
Step-by-step explanation:
f(1)=2
f(n+1)=f(n)+4
f(2)=6
f(3)=10
f(4)=14
f(5)=18
f(6)=22
f(7)=26
f(8)=30
f(9)=34
f(10)=38
Martin is an after-school math tutor. He noticed that 6 people still needed help and only 2/5 of the tutoring session time was left. Since each person is to be given an equal amount of time, Martin wrote the expression below to find the fraction of the tutoring session each person who still needed help would be allotted. 2/5÷6 Which expression is equivalent to Martin’s expression? A.6/15÷6 B.6/5÷2 C.5/2÷6 4.2/5÷6 Help!! A:18 ÷2/9 B:18×2/9 C:2/9
Answer:
A
Step-by-step explanation:
Trust me on this and I also have a reason.
Divide 2/5 by 6 to get 1/15, then divide 6/15 by 6 to get 1/15, and both of these are simpflied.
Can I also get brainlest, I hope you do well!
The expression equivalent to Martin's expression is A. 6/15 ÷ 6.
What is Division?Division is simply the opposite operation of multiplication. It is one of the basic mathematical operations where a number is divided into equal parts as that of another number.
The number being divided is called dividend and the number which divides dividend is called divisor. The resulting number after the operation is called quotient.
We have to divide the expression 2/5 ÷ 6.
When a fraction is divided by another number the divisor is change into it's reciprocal and the multiplied to the dividend.
Here dividend = 2/5 and divisor = 6
Reciprocal of 6 = 1/6
So 2/5 ÷ 6 = (2/5) × (1/6) = 2/30 = 1/15
Simplify the numbers in the options.
A. 6/15 ÷ 6 = (6/15) × (1/6) = 1/15
Hence the equivalent expression of 2/5 ÷ 6 is 6/15 ÷ 6.
Learn more about Division here :
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Two friends decide to run everyday for exercise Steve runs 2.5 miles per day. Sam runs 6.5 miles per day gho many days will it take for the to reach 450 miles combined?
Hey there! I'm happy to help!
We see that Steve runs 2.5 miles per day and Sam runs 6.5 miles per day. If you add these together, we see that they run 9 miles every day.
We now need to see how many of these 9 mile days fit into this 450 miles. Let's divide 450 by 9 and we will see how many days it will take for them to reach 450 miles combined.
450÷9=50
Therefore, it will take Steve and Sam 50 days to reach 450 miles combined!
Have a wonderful day! :D
write down the value of 5 in 19.54
Answer:
10ths Place (Decimal)
Step-by-step explanation:
Whole numbers:
The 1 in 19.54 is in the tens place.
The 9 is in the ones place.
Decimals:
The 5 is in the tenths place.
The 4 is in the hundredths place.
Answer:
look below for your answer
Step-by-step explanation:
5 is in the tenth column
i hope i helped you
please mark my answer as brainliest
A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width from the pool on all sides. If the patio area equals the area of the pool, how wide is the distance from the pool edge to the patio edge? If x represents the width of the patio, then which of the following equations could be used to solve the word problem?
Answer:
Let
x-------> the width of the patio
we understand that
region of the pool=40*60-----> 2400 ft²
vicinity of the patio=[(40+2x)*(60+2x)]-2400
place of the patio=2400 ft²
so
[(40+2x)*(60+2x)]-2400=2400
2400+80x+120x+4x²-4800=0
4x²+200x-2400=0------> divide by 4 both sides----> x²+50x-600=0
therefore
the answer is
x²+50x-600=0
Which expression is equivalent to (–3y – x) – (5y – 8x)?
Answer:
-8y +7x
Step-by-step explanation:
(–3y – x) – (5y – 8x)Distribute
-3y -x -5y +8x
Combine like terms
-3y-5y -x+8x
-8y +7x