S(r) = 2pi*r*h + 2pi*r^2
S ' (r) = 2pi*h + 2*2*pi*r .... differentiate with respect to r
S ' (r) = 2pi*h + 4pi*r
S ' (3) = 2pi*h + 4pi*3 ... plug in r = 3
S ' (3) = 2pi*h + 12pi
S ' (3) = 2pi*2 + 12pi .... plug in h = 2
S ' (3) = 4pi + 12pi
S ' (3) = 16pi
---------------
Answer: D) 16pi
The instantaneous rate of change of the surface area with respect to the radius, r, when r = 3, is 16π
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
Given that, the surface area of a right circular cylinder of height 2 feet and radius r feet is given by S(r) = 2πrh+2πr².
We need to find, the instantaneous rate of change of the surface area with respect to the radius, r, when r = 3.
Taking the differentiation, of the formula given, S(r) = 2πrh+2πr². w.r.t radius r,
d [S(r)] / dr = 2πh + 4πr
= 2π [h + 2r]
Put h = 2, r = 3
= 16π
Hence, the instantaneous rate of change of the surface area with respect to the radius, r, when r = 3, is 16π
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Enter the equations of the asymptotes for the function
Answer:
x = 7 and y = 2
Step-by-step explanation:
the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote
solve x - 7 = 0 ⇒ x = 7 is the asymptote
horizontal asymptotes occur as
[tex]lim( x → ± ∞), f(x) → c ( where c is a constant )
divide terms on numerator/ denominator by x
f(x) = (3/x/x/x -7/x ) + 2
as x → ± ∞, f(x) → 0 / 1 - 0 + 2 = 2
y = 2 is the asymptote
Answer: Vertical asymptote is x = 7
Horizontal asymptote is y = 2
Step-by-step explanation:
The vertical asymptote is the restriction on the domain (x-value). Since the denominator cannot be zero ⇒ x - 7 ≠ 0 ⇒ x ≠ 7 so the vertical asymptote is at x = 7.
The horizontal asymptote (H.A.) is the restriction on the range (y-value). There are three rules that determine the horizontal value which compare the degree of the numerator (n) with the degree of the denominator (m):
If n > m , then there is no H.A. (use long division to find the slant asymptote) If n = m , then the H.A. is the coefficient of n ÷ coefficient of mIf n < m, then the H.A. is y = 0In the given problem, n = 0 and m = 1 ⇒ n < m ⇒ H.A. is y = 0
Since there is a vertical shift of +2 units, the H.A. is y = 0 + 2 ⇒ y = 2
You are in charge of buying the hamburgers and chicken for a party. The hamburgers cost $2 per pound and the chicken is $3 per pound, You have $60 to spend.
Which expression are a factor of 36abc-9bcd+24abc
PLEASE HELP A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled by this equation:an=500+(k-1)10 Use summation notation to model and evaluate the sales for the first ten years. Explain your steps.
Answer: 131,400$
Step-by-step explanation:
The sale for first month is $500.
The sale increases by $10 each month, as modelled by the equation:
a_k=500+(k-1)10
where, k = 1 (first month)
k = 2 (second month)
.... and so on.
we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)
Total sales = ∑ a_k
∑ a_k = ∑ (500+(k-1)10)
= 500k + ∑ (10k - 10)
= 500k + 10∑k - 10k
= 490k + 10∑k
= 490k + 10 {k*(k+1)/2}
= 490k + 5{k*(k+1)}
= 490k + 5k^2 + 5k
= 5k^2 + 495k
∴∑ a_k = 5k^2 + 495k
For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)
= 5*(120*120) + 495*120
= 72,000 + 59, 400
= 131,400$
Answer:
Distribute 10 to (k – 1) and simplify.
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used. The upper index is 10*12=120.
The values of the summations are 58,800 + 72,600. So, the total sales is $131,400.
Step-by-step explanation:
Algebra 1 A Semester Exam
30. Write y=-3/4x-6 in standard form using integers. (1 point)
Final answer:
To convert y = -3/4x - 6 to standard form with integers, multiply by 4 to remove the fraction and then arrange the equation as 3x + 4y = -24.
Explanation:
To write the equation y = -3/4x - 6 in standard form using integers, we need to rearrange the terms so that the x and y terms are on the left side of the equation and the constant is on the right side. Moreover, in standard form, the coefficients should be integers. The standard form is typically expressed as Ax + By = C.
Starting with the given equation:
y = -3/4x - 6
Multiply each term by 4 to remove the fraction:
4y = -3x - 24
Now, we need to move the x term to the left side of the equation:
3x + 4y = -24
This is the standard form of the equation, and all the coefficients are integers.
Which of the following is a trinomial with a constant term?
A. x3 + 12x2 + x
B. y - 426
C. -x + 42
D. x + 7y + 6
E. x7 - 6
F. y13
Choice A is a trinomial, but it doesn't have a constant term
Choice D is the only other trinomial. This has a constant term, which is 6. The constant is the term without any variables attached to it.
Answer: Choice D
Answer: D. [tex]x+7y+6[/tex]
Step-by-step explanation:
We know that a trinomial is a polynomial with three terms.
From all the given options, only option A. [tex]x^3+12x^2+x[/tex] and option D. [tex]x+7y+6[/tex] are trinomials having three terms .
But option A [tex]x^3+12x^2+x[/tex] does not have any constant term .
On the other hand option D. [tex]x+7y+6[/tex] has a constant term of 6.
Therefore, the option D. [tex]x+7y+6[/tex] represents a trinomial with a constant term.
People need to develop a financial plan to accomplish their retirement goals. True False
Answer:
True
Step-by-step explanation:
The reason I say this is because of the fact you can't go into retirement without knowing how much your going to get. You need to create a financial plan stating how much you will get and how much you have saved prior to this occurence.
Hope This Helps :)
Answer: True
Step-by-step explanation: People need to develop a plan to overcome the effects of taxation, inflation, and purchasing power risk. In addition, people need to coordinate their company benefits with a personalized financial plan. Because there are many complexities in dealing with the stock market and real estate, you need to have a properly constructed financial plan.
A survey of households revealed that 38% have a dog, 47% have a cat, and 15% have both a cat and a dog.
Given that a household owns a dog, what is the probability that it also owns a cat?
P(cat│dog)=
Since P(cat│dog)=39.47% and P(cat)=47%, are the events independent or not independent?
What is the probability of a household owning a cat or a dog?
P(cat or dog)=
Answer:
I) P(cat│dog) = [tex]\frac{0.15}{0.38}[/tex]
II) These events are not independent
III) P(cat or dog)= 0.7
Step-by-step explanation:
Given : Households have dogs = 38%
So, P(dog) = 0.38
Households have cats = 47%
So, P(cats) = 0.47
Households have both dogs and cats = 15%
So, P(both dog and cat ) = [tex]P(cat\cap dog)[/tex] = 0.15
solution :
i) By formula P(A│B) =[tex]\frac{P(A\cap B)}{P(B)}[/tex]
P(cat│dog)= [tex]\frac{P(cat\cap dog)}{P(dog)}[/tex]
P(cat│dog) = [tex]\frac{0.15}{0.38}[/tex]
ii) P(cat│dog)=39.47% = 0.39 and P(cat)=47% = 0.47, are the events not independent
Because condition for independent events in conditional probability is P(A|B)=P(A)
but P(cat│dog) ≠P(cat) i.e. 0.39≠0.47
So, these events are not independent
iii) P(cat or dog) = ?
"or" means union
Formula : [tex]P(A\cup B)= P(A) + P(B)-P(A\cap B)[/tex]
P(cat or dog) = [tex]P(cat\cup dog)= P(cat) + P(dog)-P(cat\cap dog)[/tex]
P(cat or dog)= 0.47 + 0.38 - 0.15
P(cat or dog)= 0.7
Answer:
Step-by-step explanation:
Cats are better (sorry, I just had to say it.)
Use your knowledge of insulators and conductors to explain why
cooking pots are usually made of metal with some sort of plastic
handle
Cooking pots are made of metal because metals are good conductors of heat. Plastic is an insulator that is slow at conducting heat. That is why an insulator is used so that we don't burn ourselves.
The cooking pots are good conductor of electricity and sort of plastic
handle are insulator for safety purpose.
Conductors are materials that permit electrons to flow freely from particle to particle. Conductors allow for charge transfer through the free movement of electrons. Conductors are good conduction of electricity.Insulators are materials that does not allow the free flow of electrons from atom to atom and molecule to molecule.Insulator are bad conductor of electricity.Learn more:
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PLEASE HELP ASAP 25 POINTS
Answer:
the answer is d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
To see if it is a solution substitute x in and see if it works for y
a. y>= x +2
-4 >= -2+2
-y> = 0 No
b y <= x+2
-4<=-2+2
-4 <0 True
keep going
y<= x-3
-4 <= -2-3
-4<=-5
No
c y> x+2
-4 >-2+2
-4 > 0
True
y< x-3
-4 <-2-3
-4 <-5
NO
d y <= x+2
-4 <= -2+2
-4<=0
True
-4 >= -2-3
-4>=-5
This is the solution
It's 1:00 p.M. And I've driven 120 miles. At 3:00 p.M. I will have driven 208 miles. What is my speed?
From 1 pm to 3 pm is 2 hours.
208 miles - 120 mile = 88 miles
You drove 88 miles in 2 hours.
Speed = miles driven / time driven:
88 / 2 = 44 miles per hour
Answer:
44 miles/hour
Step-by-step explanation: since speed = distance/time
= 88miles/2hours
=44miles/hour
The price of an item has been reduced by 85% . The original price was 20 . What is the price of the item now?
Final answer:
The new price of the item is $3 after the 85% reduction from the original price of $20.
Explanation:
To find the new price of the item after an 85% reduction, we start with the original price and calculate 85% of that price to know how much is being subtracted. The original price is $20. Now let's calculate 85% of 20 dollars:
0.85 (85%) × $20 = $17
This means an $17 reduction from the original price. We subtract this from the original price to find the new price:
$20 - $17 = $3
The new price of the item is $3 after a reduction of 85%.
which of the following names a diameter of circle A?
Answer:
BC
Step-by-step explanation:
The diameter is the distance across the circle, going through the center
BC or CB is the diameter
Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away. She is _____ percent closer to the school.
Answer:
Tiffany is 34% closer to the school.
Step-by-step explanation:
Given the statement: Tiffany used to live 15 kilometers away from the school, but after she moved she now lives 9.9 kilometers away.
She lived away from the school = 15 km
as, she moved 9.9 km away.
Now, the distance closer to school from where she lived = 15 -9.9 = 5.1 km
To, find how much percent she is closer to school.
Percent states that a number or ratio expressed as a fraction of 100.
[tex]percent = \frac{5.1}{15} \times 100[/tex] = [tex]\frac{51 \times 100}{150} = \frac{51 \times 10}{15}[/tex]
Simplify:
percent closer to school = 34%
Therefore, she is 34% closer to the school.
Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room.
Step-by-step explanation:
10 x 4 = 40$
Samuel earned $6.67 per hour.
Explanation:To calculate how much money Samuel earned per hour, we need to find the total number of hours he spent both mowing the lawn and cleaning his room.
Samuel spent 4 hours mowing the lawn and 2 hours cleaning his room, for a total of 6 hours.
He earned $40 for this time period.
To find how much he earned per hour, we divide the total amount earned by the total number of hours:
$40 divided by 6 hours = $6.67 per hour.
Therefore, Samuel earned $6.67 per hour.
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i will give brainliest to best answer
Answer: B
Step-by-step explanation:
(x - 6) (x¹⁾²) (x + 3)
= (x¹⁾²) (x² - 3x - 18)
= x⁵⁾² - 3x³⁾² - 18x¹⁾²
= √x⁵ - 3√x³ - 18√x
********************************************
Answer: B
Step-by-step explanation:
[tex]\frac{f(x)}{g(x)} =\frac{(x+1)^{-1}}{x-2} = \frac{1}{(x+1)(x-2)}[/tex]
Since denominator cannot equal zero,
x + 1 ≠ 0 and x - 2 ≠ 0
x ≠ -1 and x ≠ 2
Interval Notation: (-∞, -1) U (-1, 2) U (2, ∞)
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Subract and simplify.
Answer: C
Step-by-step explanation:
[tex]\dfrac{x+1}{x-5} - \dfrac{x-2}{x+3}[/tex]
= [tex]\dfrac{x+1}{x-5}(\dfrac{x+3}{x+3}) - \dfrac{x-2}{x+3}(\dfrac{x-5}{x-5})[/tex]
= [tex]\dfrac{x^{2}+4x+3}{(x-5)(x+3)} - \dfrac{x^{2}-7x+10}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{x^{2}+4x+3-(x^{2}-7x+10)}{(x-5)(x+3)}[/tex]
= [tex]\dfrac{11x-7}{(x-5)(x+3)}[/tex]
please help me with these please.
6. Answer: y = 5x - 11
Step-by-step explanation:
Parallel means "same slope". y = 5x - 2 is in the form y = mx + b,
so the slope (m) = 5
Next, input the point (x₁, y₁ = 2, -1) and slope (m = 5) into the Point-Slope formula:
y - y₁ = m(x - x₁)
y - (-1) = 5(x - 2)
y + 1 = 5x - 10
y = 5x - 11
*******************************************************************
7. Answer: [tex]\bold{y = \dfrac{1}{3}x + 4}[/tex]
Step-by-step explanation:
Perpendicular means "opposite reciprocal slope". y = -3x + 7 is in the form y = mx + b, so slope (m) = -3 ⇒ m⊥ = [tex]\frac{1}{3}[/tex]
Next, input the point (x₁, y₁ = 3, 5) and slope (m = [tex]\frac{1}{3}[/tex] ) into the Point-Slope formula:
y - y₁ = m(x - x₁)
[tex]y - 5=\dfrac{1}{3}(x - 3)[/tex]
[tex]y - 5 =\dfrac{1}{3}x - 1[/tex]
[tex]y=\dfrac{1}{3}x + 4[/tex]
Jack can run a mile in 9, 1/3 minutes. How long will it take for him to run 3, 1/2 miles? What is the answer
Answer:
32, 2/3 minutes.
Step-by-step explanation:
Divide the original mile time by two to get what half a mile would be. Multiply the original mile time by 3, since he is running 3 miles. Add 4 and 2/3, half of a mile time, to that and you're left with 32 minutes and 40 seconds.
Write the linear equation in slope-intercept form: 5x - y = -17
a: y = -5x + 17
b: x = -1/5y - 17/5
c: y = 5x - 17
d: -5x - 17
In order to express the equation 5x - y = -17 in slope-intercept form (y = mx + b), we need to solve for y. After rearranging, it turns out the correct equation in slope-intercept form is y = 5x + 17.
Explanation:To write the equation 5x - y = -17 in slope-intercept form, we first need to solve the equation for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.
Let's rearrange the given equation: Start by adding 'y' to both sides to get 5x = y - 17. Add 17 to both sides, you will get y = 5x + 17. So, the correct answer is: y = 5x + 17. This aligns with option c.
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Comparing this with the answer choices, the correct option is c: y = 5x - 17.
To write the linear equation 5x - y = -17 in slope-intercept form, you must solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equation:
Add y to both sides to isolate the y-variable on one side: 5x - y + y = -17 + y, which simplifies to 5x = y - 17.Now, subtract 17 from both sides to solve for y: y - 17 = 5x - 17.The equation in slope-intercept form is y = 5x - 17.Comparing this with the answer choices, the correct option is c: y = 5x - 17.
An extra large pizza has 12 slices. If there are four people at they table and they each get two slices, how many slices are left?
Answer:
there should be 4 slices left
Hope This Helped
Step-by-step explanation:
Answer:
The most accurate answer is:
*4*
I hope I helped you!
Step-by-step explanation:
Alright, lets examine the problem; *12* slices of pizza are given. We also have *4* guests at the table, and each are given *2* slices. Lets use subtraction to solve: 12 - 2 - 2 - 2 - 2- the *2*'s equal the amount of pizzas given, and the *12* represents our amount of slices of pizza. We also gave 4 people 2 slices, which is why we have *4* *2*'s
[SOLVE]
12 - 2 - 2 - 2 - 2 = 4
At the holiday valley ski resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, how many skis and snowboards were rented?
Answer:
[tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.
Step-by-step explanation:
Let the number of skis rented be [tex]x[/tex] and the number of snowboards rented be [tex]y[/tex].
If a total of [tex]28[/tex] people rented on a certain day, then the total number of skis and snowboards rented that particular day is also [tex]28[/tex].
This gives us the equation
[tex]x+y=28...eqn(1)[/tex].
If skis cost $ [tex]16[/tex], then [tex]x[/tex] number of skis cost $ [tex]16x[/tex].
If snowboards cost $ [tex]19[/tex], then [tex]y[/tex] number of snowboards cost $ [tex]19y[/tex].
The total cost will give us another equation,
[tex]16x+19y=478...eqn(2)[/tex]
From equation (1),
[tex]y=28-x...eqn(3)[/tex].
We put equation (3) into equation (2) to get,
[tex]16x+19(28-x)=478[/tex]
We expand the brackets to obtain,
[tex]16x+532-19x=478[/tex]
We group like terms to get,
[tex]16x-19x=478-532[/tex]
This implies that,
[tex]-3x=-54[/tex]
We divide both sides by [tex]-3[/tex] to get,
[tex]x=18[/tex]
We put [tex]x=18[/tex] into equation (3) to get,
[tex]y=28-18[/tex]
[tex]y=10[/tex]
Therefore [tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.
To solve this problem, you can set up a system of equations where one equation represents the total number of skis and snowboards rented, and the other represents the total cost of those rentals. By solving this system, you can determine the number of skis and snowboards rented.
Explanation:This problem is a classic example of a system of linear equations. Let's denote the number of skis rented as x and the number of snowboards rented as y. From the problem, we know that:
x + y = 28 (The total number of skis and snowboards rented is 28) 16x + 19y = 478 (The total income from skis and snowboard rentals is $478)
By solving these two equations, we can find the values of x and y which represent the number of skis and snowboards rented respectively.
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Simplify. -6i(5+3i) Enter your answer in standard form, in the box
Answer:
Pretty sure the answer is 18-30i
Step-by-step explanation:
-30i - 18i^2
-30i - 18 x (-1)
-30i +18
The expression -6i(5+3i) simplifies to 18 - 30i in standard form of a complex number.
Explanation:The problem asks us to simplify the expression -6i(5+3i). To simplify this, we multiply the complex number (-6i) with the complex number in the parenthesis. This results in (-6i * 5) + (-6i * 3i) which transforms into -30i - 18i^2. Since i^2 is -1, we can simplify further to -30i + 18. So the simplified form in standard form is 18 - 30i.
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PLEASE HELP ME
27
What is the exact solution to the equation
e^3x+5=9 ?
x=3/5+in9
x=3/ln9−5
x=5+ln9/3
x=ln9−5/3
Answer:
[tex]x=\frac{-5+ln9}{3}[/tex] which appears to be from the list x=ln9-5/3
Step-by-step explanation:
We take the natural logarithm of both sides as the inverse operation to an exponent on e. This allows us to use log rules to rearrange the problem.
[tex]e^{3x+5}=9\\lne^{3x+5}=ln9 \\(3x+5)lne=ln9[/tex]
We know that as inverse operations, ln e =1.
[tex](3x+5)(1)=ln9\\3x+5=ln9\\3x=-5+ln9\\\frac{3x}{3}=\frac{-5+ln9}{3}[/tex]
[tex]x=\frac{-5+ln9}{3}[/tex]
Answer:
x = (ln (9)-5) /3
Step-by-step explanation:
e^3x+5=9
First we subtract 5 from each side
e^3x+5-5=9-5
e^3x=(9-5)
Then we take the natural log of each side
ln(e^3x) = ln(9-5)
3x = ln (9-5)
Then we divide by 3 on each side
3x/3 = ln (9-5) /3
x = ln (9-5) /3
An account earns 1.5% interest compounded annually. The balance after 2 years is $8241.80. What is the principal?
Carlos bought a snowboard for $24.99 and ice skates for $19.19 how much money did he spend all together
Answer: Carlos would owe in fact (Not including sales taxes) $44.18 (forty-four dollars and eighteen cents)
Step-by-step explanation:
Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly get in return?
Alison and Justins father donated $3 every lap they swam in a swim-a-thon.Alison swam 21 laps and justin swam 15 laps.Use the distributive property tp find out the amount of money their father donated/
Answer:
The total amount of money Alison and Justins father donated be $108 .
Step-by-step explanation:
Distributive property.
Let a, b and c be any real numbers.
Thus
a.( b + c ) = a.b + a.c
This is distributive property.
As given
Alison and Justins father donated $3 every lap they swam in a swim-a-thon.
Alison swam 21 laps and justin swam 15 laps.
Total amount of money Alison and Justins father donated = Cost of each lap (Number of laps of Alison father + Number of laps of Justins father )
As
Cost of each lap = $3
Number of laps of Alison father = 21 laps
Number of laps of Justins father = 15 laps
Putting in the above
Total amount of money Alison and Justins father donated = 3(21 + 15)
= 3 × 21 + 3 × 15
= 63 + 45
= $ 108
Therefore the total amount of money Alison and Justins father donated be $108 .
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
given : MN is an angle bisector of (angle)JMK
prove : m(angle)JMN=1/2m(angle)JMK
(i need all the reasons)
If the line MN is the angle bisector of ΔJMK, then it creates two angles of equal measure. Hence, m∠JMN is half of m∠JMK due to the property of an angle bisector.
Explanation:In the field of geometry, an angle bisector is a line or ray that divides an angle into two equal angles. This is given by the information provided that MN is an angle bisector of ΔJMK.
By definition, if MN is an angle bisector of ΔJMK, then it creates two angles, ∠JMN and ∠NMK, that are equal in measure. So, we have m∠JMN = m∠NMK. This is the definition of an angle bisector, which is the reason you are looking for.
Given this, if you want to find m∠JMN in terms of ∠JMK, keep in mind that MN bisects ∠JMK, creating the two equal angles we just mentioned. Therefore, m∠JMK = m∠JMN + m∠NMK. Since ∠JMN and ∠NMK are equal, m∠JMK = 2m∠JMN. Hence, m∠JMN = 1/2m∠JMK. This would be a consequence of the angle bisector property.
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