The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.
First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])
[tex]f(x) = g(x)[/tex] (1)
[tex]4\cdot x - 2 = x^{2}+1[/tex]
[tex]x^{2}-4\cdot x +3 = 0[/tex]
[tex](x-1)\cdot (x-3) = 0[/tex]
The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:
[tex]V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx[/tex] (2)
If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]
[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]
[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]
[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]
[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]
[tex]V = \frac{16\pi}{3}[/tex]
The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.
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What is the value of the expression? 75÷5−[(9−7)×3]×2
Answer:
3
Step-by-step explanation:
75÷5-[(9-7)×3]×2
do innermost inclusion symbols first, which would be 9-7
75÷5-[2×3]×2
now multiply 2 and 3
75÷5-(6)×2
now divide 75 by 5
15-6×2
now multiply
15-12
3
The required simplified value of the given expression is 13.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= 75÷5−[(9−7)×3]×2
Following the PEMDAS rule,
= 25 - [2×3]×2
= 25 -[6]×2
= 25 - 12
= 13
Thus, the required simplified value of the given expression is 13.
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A book club charges an initial joining fee of $30.00. The cost per book is $7.00. The graph shows the cost of belonging to the club as a function of books purchased. How will the graph change if the cost per book goes up by $1.50? (The new function is shown by the dotted line.)
Answer:
$82.50
Step-by-step explanation:
You add seven dollars to $1.50 and you would get the sum of 8.50 then you multiply the amount of books purchased. The Equation is 5($8.50) + $30.00= 82.50
Sorry if I get this wrong.
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )
Please help!!!
THE POPULATION OF NEW YORK STATE CAN BE MODELED BY:
==========================================================
Explanation:
We plug t = 220 into the given function. The 220 is from 2020-1800 = 220, i.e. we have a span of 220 years from 1800 to 2020.
[tex]P(t) = \frac{19.71}{1+61.22e^{-0.03513t}}\\\\P(220) = \frac{19.71}{1+61.22e^{-0.03513*220}}\\\\P(220) = \frac{19.71}{1+61.22e^{-7.7286}}\\\\P(220) \approx \frac{19.71}{1+61.22*0.00044005976972}\\\\P(220) \approx \frac{19.71}{1+0.02694045910226}\\\\P(220) \approx \frac{19.71}{1.02694045910226}\\\\P(220) \approx 19.192933558417\\\\P(220) \approx \boldsymbol{19.193}[/tex]
This indicates that the population of New York state in 2020 is roughly 19.193 million.
This converts to 19,193,000 which is 19 million, 193 thousand.
---------------
Extra info:
According to census data (census.gov), the more accurate population figure appears to be 20,201,249 which is a bit over 20.2 million. The given population function isn't too far off.
I NEED MORE HELP PLZZ
Answer:
1A: all real numbers
1B: x = {-3, 0, +18}
1C: (-3, 0) U [3, 18)
2A: h(x) = -1/160x^2 +1/2x
2B: focus: (40, -30); directrix: y = 50; axis of symmetry: x = 40
Step-by-step explanation:
1A:The graph is attached. The domain is all real numbers.
__
1B:The x-intercepts for x < 3 are the zeros of the quadratic:
x^3 -9x = 0
x(x^2 -9) = 0
x(x +3)(x -3) = 0 ⇒ x = 0, -3, +3 . . . . x=3 is not in the domain of this piece
The x-intercepts for x ≥ 3 are the zeros of the log function:
-log4(x -2) +2 = 0
log4(x -2) = 2 . . . . . . add log4(x -2)
x -2 = 4^2 . . . . . . . . . take the anti-log
x = 2 +16 = 18 . . . . . . add 2
The x-intercepts of g(x) are x = {-3, 0, +18}.
__
1C:The graph shows the function is positive on the intervals ...
(-3, 0) U [3, 18)
__
2A:The vertex of the curve is given as (40, 10). The vertical scale factor will make the function 0 at x=0.
h(x) = a(x -40)^2 +10
h(0) = 0 = a(-40)^2 +10 = 1600a +10
a = -10/1600 = -1/160 = -1/(4·40)
The equation of the parabola is ...
y = -1/(160)(x -40)^2 +10
In standard form, this is ...
y = -1/160x^2 +1/2x
__
2B:When we computed the leading coefficient (a) in Part A, we found it to be -1/(4·40). This corresponds to 1/(4p) where p=-40 is the focus to vertex distance. The negative sign means the focus is 40 units below the vertex, at (40, -30). The corresponding location of the directrix is 40 units above the vertex, at y=50.
Of course the axis of symmetry is the vertical line through the vertex: x = 40. These are shown in the second attachment.
PLEASE HELP ME WITH GEOMETRY <3
Answer:
answer is 25
Step-by-step explanation:
EKJ = 90, same as JHF, and EJK is 65 (because EJF =115 and 180-115=65
65+90=155
180-155=25
Luis wants to but a skateboard that usually sell for $79.64. All merchandise is discounted by 12%
Answer:
$79.64
Step-by-step explanation:
I think it's still 79.64
Answer:
it will be equal 70.08 $
WILL GIVE BRAINLIEST
Answer:
It has no solution because, 14x cancels out -14x when you move the variables to the left and leaves the equation as 0 = -12, however we know that 0 does not equal -12 which means this solution is false; therefore this equation has no solution since 0 does not equal -12.
Step-by-step explanation:
5 - 4x - 7 - 10x = -8x - 4 - 6x - 10 (Given)
-2 - 14x = -14x - 14 (Combine like terms)
0 = -12 (Move variables(x) to the left and the constants to the right)
12. After 80 years of 5.8% interest compounded monthly, an account has $102,393.44. What was the
original deposit amount?
Answer:
12195508,42
Step-by-step explanation:
A(1-R) NA is the depositR is the % presentN is the time period (exponent)A(1-5.8%)80=102,393.44An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
What is meant by deposit?A deposit is money held at a bank. A deposit is a monetary transaction in which money is transferred to another party for safekeeping.A deposit is money placed in a bank account. Deposits are classified into two types: demand deposits and time deposits. Checking, savings, and money market accounts are all examples of demand deposit accounts. Certificates of deposit (CD) and individual retirement accounts are examples of time deposit accounts.Therefore,
Assume that each year has 52 weeks: then compounding occurs.
n = 52 × 80n
times and the rate for each compounding is
[tex]$i=\frac{5.8 \%}{52}=\frac{0.058}{52}$[/tex]
If the original deposit amount is
PV
then the future value
FV
is equal to
[tex]$$F V=P V \cdot(1+i)^n=P V \cdot\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}$$[/tex]
We know the future value (which is given as $ 102,393.44), so calculating the present value is simple:
[tex]P V=F \frac{V}{(1+i)^n}=\frac{\$ 102,393.44}{\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}}[/tex]
The simplest way to compute this is to use a calculator:
[tex]$P V \approx \$ 991.45 .$$[/tex]
We can simplify this expression with great precision just for fun. It is well known that
[tex]$\left(1+\frac{1}{n}\right)^n \rightarrow e$[/tex]
which easily implies that
[tex]$\left(1+\frac{a}{n}\right)^n \rightarrow e^a$[/tex]
Here,
[tex]$$\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}=\left(\left(1+\frac{0.058}{52}\right)^{52}\right)^{80} \approx\left(e^{0.058}\right)^{80}=e^{0.058 .80}=e^{4.64}[/tex]
That is, [tex]P V \approx F V e^{-4.64}$.[/tex]
Hence, An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
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Integer Exponents
#1: Simplify the expression below using properties of exponents. Write your
answer using positive exponents. *
5-2
Answer:
Step-by-step explanation:
5 - 2 cannot be further simplified? No properties of exponents can be used due to already knowing the answer of the top of your head, it could be a mistype though, or I'm just very very d*mb.
Income You are starting your first job as an assistant manager at a
sporting goods store. You receive a base salary of $14.75 per hour with
time-and-a-half for hours in excess of 40 hours per week. You are paid
every two weeks. Social Security and Medicare are deducted from your
pay. Social Security tax is 6.2% of the gross pay. Medicare tax is 1.45% of
the gross pay. What is the bi-weekly (every two weeks) deduction for
Social Security and Medicare? *
O $118.00
O $76.50
$89.90
$90.27
The bi-weekly deduction for Social Security and Medicare is $90.27.
Since you receive a base salary of $ 14.75 per hour with time-and-a-half for hours in excess of 40 hours per week, and you are paid every two weeks, and Social Security and Medicare are deducted from your pay, and Social Security tax is 6.2% of the gross pay, and Medicare tax is 1.45% of the gross pay, to determine what is the bi-weekly (every two weeks) deduction for Social Security and Medicare, the following calculation must be performed:
(14.75 x 40 x 2) x ((1.45 + 6.2) / 100) = X 1180 x 0.0765 = X 90.27 = X
Therefore, the bi-weekly deduction for Social Security and Medicare is $90.27.
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Don't answer this question
Answer:
Ok
Step-by-step explanation:
Find the set of values of a for which the point P (2a + 3; 3a-2) is in the fourth quarter of the coordinate plane (with this
Not located on the coordinate axes).
Answer:
-3/2 < a < 2/3
Step-by-step explanation:
In the fourth quarter of the coordinate plane, x > 0 and y < 0. This means ...
2a +3 > 0
3a -2 < 0
__
The first inequality has the solution ...
2a > -3 . . . . subtract 3
a > -3/2 . . . . divide by 2
The second inequality has the solution ...
3a -2 < 0
3a < 2 . . . . add 2
a < 2/3 . . . divide by 3
The set of values of 'a' that put P in the fourth quarter is ...
-3/2 < a < 2/3
There are 52 grams of carbs in 1/4 cup of syrup for a particular brand. How many carbs are in 1 tablespoons?
Round your answer to the nearest integer.
There is a total of 52 grams of carbs in 1/4 cup, then 1 tablespoon will contain 208 grams of carbs.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
There are 52 grams of carbs in 1/4 cup of syrup
Let's assume that the amount of carbs in 1 tablespoon is x.
So,
x = (52 × 4)
x = 208 grams.
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I thought of a number. My friend thought of a number too. A third of my number is a half of his number. Who's number is bigger?
Answer:
yoours
Step-by-step explanation:
thanks again for your time and consideration and I am a kid I am a kid
Ernesto bought a 20-pound bag of dog food for his Great Dane, Tank. After 7 days, all the dog food was gone.
How much dog food did Tank eat each day?
Answer:
About 2.9 pounds per day.
Step-by-step explanation:
20÷7=2.85714...
rounded- 2.9
So Tank, the Great Dane, ate about 2.9 pounds per day.
Answer:
Step-by-step explanation:
2 6/7
I need help on math please
Answer:
if i correct pls comment I think it is 33
can someone help plz I need help ASAP!
Answer:
[tex]y= \frac{1}{3}x -9[/tex]
Step-by-step explanation:
First you must substract -5 to both sides
-5-4= -9
[tex]y= \frac{1}{3}x -9[/tex]
A container can hold 2400 litres of water. (a) A large tap alone can fill the container in x hours. Write down an expression, in terms of r, for the amount of water that the large tap can dispense per minute. {b) A small tap alone will take 1 hour longer than the large tap to fill the co tainer. Write down an expression, in terms of x, for the amount of water that the small tap can dispense per minute. (c) When both taps are turned on at the same time, they can fill the container in 3 hours. Form an equation in x and shows that it reduces tox? -5x-3=0. X 20.
Answer:
Determine the required value of the missing probability to make the distribution a discrete probability distribution. x p(x) 3 0.23 4 ? 5 0.51 6 0.08 p(4) = nothing (type an inte...
sixty students at gillette road middle school play a winter modified sport. if there are 500 students in the middle school, what percent of students play a sport
Answer:
60/500=0.12
so 12%
Hope This Helps!!!
The distances between the bull's-eye of a target and 100 darts thrown by an expert
2+6i/2-4i = a + bi What is the value of a? What is the value of b?
[tex]\dfrac{2+6i}{2-4i}\\\\\\=\dfrac{2(1+3i)}{2(1-2i)}\\\\\\=\dfrac{1+3i}{1-2i}\\\\\\=\dfrac{(1+3i)(1+2i)}{(1-2i)(1+2i)}\\\\\\=\dfrac{1+2i+3i+6i^2}{1-(2i)^2}\\\\\\=\dfrac{1+5i-6}{1+4}~~~~;[i^2=-1]\\\\\\=\dfrac{5i-5}{5}\\\\\\=\dfrac{5(i-1)}5\\\\=i-1\\\\=-1+i\\\\\text{It is in a form of a +bi so,}~ a = -1~ \text{and}~ b = 1[/tex]
Ten minus three tenths of n
Answer:
[tex]10 - \frac{3}{10} n[/tex]
Step-by-step explanation:
hope that is right and hope it helps
Which of the following is equal to 2,952 ÷ 24?
A.
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
B.
(2,400 + 24) ÷ (480 + 24) ÷ (72 + 24)
C.
(2,400 + 24) + (480 + 24) + (72 + 24)
D.
(2,400 ÷ 24) - (480 ÷ 24) - (72 ÷ 24)
Answer:
A
Step-by-step explanation:
After doing long division we then know that 2,952 ÷24 = 123
We 1st follow pemdas knowing this we solve the equations in parenthesis 1st
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
2,400 ÷ 24 = 100
480 ÷ 24 = 20
72 ÷ 24 = 3
We can then rewrite the equation as
100 + 20 + 3 We then solve left to right
100 + 20 = 120
120 + 3 = 123
5) Using the formula A=652
find the surface area of a
cube with sides measuring 8
inches.
Answer:
81.5
Step-by-step explanation:Cube has all sides of equal dimensions and like that it has 6 faces.
So total surface area of cube is equal to the combined area of all the six faces.
Now each face has equal dimensions so same area
Therefore,
area of a single face =side²
Therefore, area of entire cube = 6 times the area of a single face
= 6 * side²
.
Pauline wants to sell stainless steel water bottles as a school fundraiser.
She knows that she will maximize profits, and raise $1024, if she sells
the bottles for $28 each. She also knows that she will lose $4160 if she sells the bottles for only $10 each.
Write a quadratic relation to model her profit, P, in dollars, if she sells the bottles for x dollars each.
Answer:
P = -16(x -28)² +1024
Step-by-step explanation:
The equation can be written in vertex form as ...
P = -a(x -h)² +k
where (h, k) is the vertex, and 'a' is a scale factor. We are given the vertex (h, k) = (28, 1024) and another point (x, P) = (10, -4160). Using these points, we can find the value of 'a'.
-4160 = -a(10 -28)² +1024
-5184 = -324a . . . . simplilfy
a = 5184/324 = 16 . . . . divide by the coefficient of 'a'
A suitable quadratic relation is ...
P = -16(x -28)² +1024
Help needed rn i have a few minutes left
Answer:A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I need help with this please
Answer:
hello the answer you are looking for should be s3xy kong 243
Step-by-step explanation:
Determine the slope from the given graph below:
A ⇹ The slope is -7
B ⇹ The slope is−16
C ⇹ The slope is 6
D ⇹ The slope is -6
Step-by-step explanation:
the slope is the ratio of "y coordinate difference / x coordinate difference".
so, let's find 2 good points (I mean by that with integer coordinates). I see e.g.
(-1, -1) and (0, -7)
x changes by +1 (from -1 to 0).
y changes by -6 (from -1 to -7).
so, the slope is -6/1 = -6.
D is the right answer.
6. The California Tiger Salamander is an endangered species, which decreases at the rate of 4.6% per year in a habitat that currently has 60 of them. Write an exponential function and find how many California Tiger Salamanders will be left after 4 years.
7. Factor and solve the following equation 2x2 + x - 21 = 0.
8. Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.
9. Examine the graph of f(x) and the table that contains values of g(x). Which function has a greater rate of change over the interval [0,2]? Explain your answer.
[tex]\rule{2000pt}{1000000pt}[/tex]