The volume of the solid generated by revolving the region R bounded by
y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units
Given the region R bounded by y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9.
We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.
The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.
Then, volume, V = [tex]\int\limits^0_{ln9} {y^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {(e^{-2x})^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {e^{-4x}} \, dx[/tex]
= [tex]\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}[/tex]
= [tex]\frac{e^{-4 ln9}}{-4} +\frac{1}{4}[/tex]
= [tex]\frac{9^{-4}+1}{4}[/tex] ≈ 0.25 cubic units
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Simplify the following expression.
(13x + 9y) + (38x + 33y)
-----------------------------------
22x + 42y (A)
22x + 46y (B)
51x + 42y (C)
51x + 46y (D.)
Answer:
C: 51X+42Y
13x + 38x + 9y + 33y
adding,
51x + 42y so option C
Please help me!!! I need help asap on this question Whoever is correct will get brainly!
Answer:
I am not 100% sure more like 12% sure that it is c
Step-by-step explanation:
Peter is 10 years old and is 5 years younger than half his dad's age. If his dad is Z years old, what is Z?
Answer:
Z = 30
Step-by-step explanation:
trust me bro
fhfhfhfhhffh
Answer:
Please give brainliest if you think it applies
30
Step-by-step explanation:
Z/2 -5 = 10
Add 5 to both sides
Z/2 = 15
Multiply both sides by 2
Z = 30
The function f is defined by the following rule
f(x)=2x-1
Complete the function table
The value of the function at x = -3, -2, 0, 1, and 5 will be -7, -5, -1, 1, and 9, respectively.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The function is given below.
f(x) = 2x - 1
The value of the function at x = - 3 will be
f(-3) = 2(-3) - 1
f(-3) = - 6 - 1
f(-3) = - 7
The value of the function at x = - 2 will be
f(-2) = 2(-2) - 1
f(-2) = - 4 - 1
f(-2) = - 5
The value of the function at x = 0 will be
f(0) = 2(0) - 1
f(0) = 0 - 1
f(0) = - 1
The value of the function at x = 1 will be
f(1) = 2(1) - 1
f(1) = 2 - 1
f(1) = 1
The value of the function at x = 5 will be
f(5) = 2(5) - 1
f(5) = 10 - 1
f(5) = 9
The value of the function at x = -3, -2, 0, 1, and 5 will be -7, -5, -1, 1, and 9, respectively.
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what is the value of a?
A.-16
B.-3
C.3
D.16
Answer:
Which equation do I refer to?
Step-by-step explanation:
(c) Solve the equation 7x³ +28x² = 0
Answer:
x = - 4 , x = 0
Step-by-step explanation:
7x³ + 28x² = 0 ← factor out 7x² from each term on the left side
7x²(x + 4) = 0
equate each factor to zero and solve for x
7x² = 0 ⇒ x² = 0 ⇒ x = 0
x + 4 = 0 ⇒ x = - 4
2) How many distinguishable letter arrangements can be made from the letters in:
a) FLUKE?
b) PROPOSE?
Answer:
for "FLUKE" its 5! = 120
and "PROPOSE" its 7! /2!×2! = 1260
Step-by-step explanation:
"FLUKE" has no repeating letters.
"PROPOSE" has two repeating letters.
we divide by the repeating letters like I did on "PROPOSE" .
THANK YOU.
how do put this 7+2x=11+5x
Help? Anyone pls. I'd give brainliest
Answer:
3/2
Step-by-step explanation:
xy= -2 X -3
= 6
z = 4
so xy/z is 6/4 which is 3/2.
A hardware store sells planks of wood. the lengths, in centimetres, of the planks are normally distributed with mean 210 and standard deviation 7. two planks are selected at random. find the probability that they differ in length by more than 10 cm.
The required probability that they differ in length by more than 10 cm is 1.
Given that,
A hardware store sells planks of wood. the lengths, in centimeters, of the planks are normally distributed with a mean of 210 and a standard deviation of 7. two planks are selected at random. find the probability that they differ in length by more than 10 cm is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
The
P(x > 10) = p(z = (x - μ)/σ)
P(x > 10) = p(z = (10 - 210)/7)
P(x > 10) = p(z = -28.57143)
P(x > 10) = 1
Thus, the required probability that they differ in length by more than 10 cm is 1.
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What is the value of cosine (startfraction 4 pi over 3 endfraction)? negative startfraction startroot 3 endroot over 2 endfraction negative one-half one-half startfraction startroot 3 endroot over 2 endfraction
The value of Cos(4π/3) is (-1/2) i.e., negative one half.
The given function is Cosine (Start fraction 4 pi over 3 end fraction) and this can be written simply as,
Cos(4π/3)
On splitting 4π/3 in two parts, this can also be written as
= Cos(π + (π/3))
(π + (π/3)) lies in the third quadrant and in the third quadrant the value of cosine function is negative. So, using quadrant sign for cosine function, this can be written as
= -Cos(π/3)
Now, Substitute the value of Cos(π/3) = 1/2.
= (-1/2)
Cos(4π/3) = (-1/2)
The value of Cos(4π/3) is (-1/2) i.e., negative one half.
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Answer:
It's B
Step-by-step explanation:
i need help because i dont gettt itttt
Answer:
[tex]\boxed{3} \;v^2 + \boxed{4}\;v + \boxed{5}[/tex]
Step-by-step explanation:
Original expression: 3 + v + 4v² + 2 - v² +3v
Combining like terms in a equation means grouping them together to get a single instance of that term instead of multiple
For example in this expression we can see there is a +4v² and a -v². Group these together and simplify algebraically to get a single v² expression. Do the same with the others.
3 + v + 4v² + 2 - v² +3v
Group the v² terms together to get 4v² - v² = 4v² - 1v² = 3v² (v² == 1v²)
(since the variables are same we can simply add the coefficients
Now group the v terms and simplify
3 + v + 4v² + 2 - v² + 3v
v + 3v = 4v
Finally group the constants
3 + v + 4v² + 2 - v² +3v
3 + 2 = 5
So the final expression is
3v² + 4v + 5
The numbers are what you put in the boxes for each
Usually this process is done in a few steps
3 + v + 4v² + 2 - v² +3v
= (4v² - v²) + (v + 3v) + (3 +2)
= 3v² + 4v + 5
A sample of hamburger had a total mass of 200. g, of which 30.0 g was found to be fat. what is the percent of fat in this hamburger sample?
The percentage of fat in this hamburger sample is 15 %.
What is percentage ?Percentage is the value per hundredth.
According to the given question a sample of hamburger had a total mass of 200. g, of which 30.0 g was found to be fat.
To find what percentage of the hamburger contains fat we put amount of fat in the numerator and total amount on the denominator and multiply this fraction by 100 to obtain the result in terms of percentage.
∴ (30/200) × 100
= 3000/200
= 30/2
= 15 %.
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i need this done help i need all the work shown
30 POINTS
Write and solve an absolute value equation for the minimum and maximum times for an object moving at the given speed to travel the given distance. Absolute value 3 ft. 10 ft/s for 30 ft
Answer:
Step-by-step explanation:
12
what is the difference between 25 and 21.2?
Answer: 3.8
Step-by-step explanation:
25.0
-
21.2
--------------
3.8
How long will it take you to bike 225 miles at
a
speed of 15 miles per hour?
Am I supposed to divide
Answer:
15
Step-by-step explanation:
225/15
√a² + b² = a + b
is this true or false? i think its true but i cant explain it right
Answer:
False
Step-by-step explanation:
Consider a=3 and b=4. The left hand side is 5 but the right hand side is 7.
-8(1-a)=-8(a-7) solve the equation
Answer:
a=4
Step-by-step explanation:
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answer:
1/3
Step-by-step explanation:
5/6 - 1/9 = ?/? - ?/? = ?/?
please help 20 points
i need to know what each ( ?/? ) is
5/6 - 1/9=?/? - ?/? = ?/? , value of each (?/?) is
5/6 -1/9 =15 /18 -2/18 =13 /18.
As given,
5/ 6 - 1/9 =?/? -?/? =?/?
Convert the given terms into like terms
Least common multiple of (6,9)=18
Value of each ( ?/?)
(5/6 ) × ( 3/3) -(1/9) × (2/2)
= 15 /18 - 2/18
= 13 /18
Therefore,5/6 - 1/9 = ?/? - ?/? = ?/? , value of each (?/?) is equal to
5/6 -1/9 = 15 /18 -2/18 = 13/18.
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To pay for a home improvement project that totals $9,000, Genesis is choosing between taking out a simple interest bank loan at 9% for 3 years or paying with a credit card that compounds monthly at an annual rate of 18% for 7 years. Which plan would give Genesis the lowest monthly payment?
The monthly credit card payment would be $295, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $272.50, which is lower than the monthly credit card payment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
The monthly credit card payment would be $374.21, which is lower than the monthly payment on the bank loan.
well, first off, let's see how much each one costs per month.
so, hmmm if she goes with the Bank loan at 9% for 3 years
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ A=9000[1+(0.09)(3)] \implies \boxed{A = 11430}[/tex]
now, that's for 36 months, so she'd be owing the Bank per month [tex]\cfrac{\stackrel{total}{11430}}{\underset{months}{36}}~~ = ~~\text{\LARGE 317.5}[/tex]
now let's take a look at the Credit Card's loan at 18% for 7 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9000\\ r=rate\to 18\%\to \frac{18}{100}\dotfill &0.18\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases} \\\\\\ A=9000\left(1+\frac{0.18}{12}\right)^{12\cdot 7} \implies A \approx \boxed{31433.31}[/tex]
now, in 7 years there are 84 months, thus [tex]\cfrac{\stackrel{total}{31433.31}}{\underset{months}{84}}\approx \text{\LARGE 374.21}[/tex]
so, the Bank will give her a better deal per month, and to be honest altogether.
The plan with simple interest will give the lowest monthly repayment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
Option C is the correct answer.
What are simple interest and compound interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Compound interest is the interest that is made from the principal and the interest as well in consecutive years.
We have,
Simple interest:
Principal = $9000
Rate = 9%
Time = 3 years
Simple interest:
= P x R x T / 100
= 9000 x 9 x 3 / 100
= 2430
Amount = simles interest + principal
A = 9000 + 2430 = $11430
3 years = 36 months
Monthly payment = 11430 / 36 = $317.5
Compound interest:
Principal = $9000
Rate = 18%
Time = 7 years
A = P [tex](1 + \frac{18}{100}) ^{7}[/tex]
A = 9000 [tex](1 + 0.18) ^{7}[/tex]
A = 9000 x3.19
Amount = $28,710
7 years = 84 months
Monthly payment = 28710 / 84 = $341.78
Thus,
The plan with simple interest will give the lowest monthly repayment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
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Adding -6 is the same as:
Answer:
It is the same as subtracting 6.
Step-by-step explanation:
1 + (-6) = 5
1 - 6 = 5
1 of 6
01:52 / 08:00
When this expression is simplified, what is my final answers
-5(2x - 5)
O 10x + 25
O 52x - 25
O-7x + 25
O-10x + 25
Answer:
-10x + 25
Step-by-step explanation:
We will distribute the - 5 in to 2x which is - 10x
Then distribute - 5 to - 5 which is 25
What is an equation of the line that passes through the
points (2, -3) and (2, 6)?
Answer: It is the point where the line crosses the x axis of the cartesian coordinates. We can write an equation of the line that passes through the points y=0 as follows: Using the equation: y = 3x – 6, put y=0. To find the x-intercept. 0 = 3x – 6. 3x = 6. The x-intercept is 2 of the slope-intercept form of line
True/False: Negative numbers closed under subtraction.
Provide an example if false.
The statement is false .
let ; n=-5
m=-6
n - m= -5 -( -6 )
= -5 + 6
= 1
which is not a negative real number .
therefore it shows that negative real number are not closed under substrsction.
the process or skill of taking one number or amount away from another.
Example: 7-5=2
7 is a minuend
5 is a subtrahend
and 2 is a differenceSubtraction is an arithmetic operation that represents the operation of removing objects from a collection.
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What is 1+1 answer please despite
Answer:
2...?
Step-by-step explanation:
Find the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame.
Answer:
The length is 5.
Step-by-step explanation:
Since the proportions are the same, 3 is 3 times less than 9. The same applies to 15, which 3 times less would be 5. It has a ratio of 3:5.
A tank truck fills the gas stations reservoir at the rate of 10 1/4 gallons per minute.if the reservoir was empty and it is now 41 gallons full how long has the tanker been filling the reservoir
The tanker has been filling the reservoir for 4 minutes given that it fills at a rate of 10 1/4 gallons per minute.
Rate refers to the relationship of two quantities of different units. Usually, it is a measure or quantity of something per unit time.
rate = amount / time
If a tank truck fills the gas station's reservoir at the rate of 10 1/4 gallons per minute, and if the reservoir is empty at the start and become 41 gallons full, we can determine how long the tanker has been filling the reservoir by dividing the final amount by the rate.
time = amount / rate
where amount = 41 gallons
rate = 10 1/4 gallons per minute
time = 41 gallons / 10 1/4 gallons per minute
time = 4 minutes
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10.) The height of a tree trunk is 20 meters, and the base has a diameter of 1 meter. If the tree has the mass
420, what is the density of the tree?
26.27 kgm⁻³
Density is the ratio of mass to volume
Density = Mass / Volume
Let us assume tree is a cylinder,
d= 1
r = d/2 = 0.5 m
h= 20 m
m= 420kg
Volume = π r²h
= 22/7 x o.25 x 20
Density = mass / volume
= 420 / 22/7 x o.25 x 20
= 26.27 kgm⁻³
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