Answers
The answer to the questions of volumes are given as follows
a) [tex]v=128 \pi[/tex]
b) [tex]v=\frac{128}{3} \pi[/tex]
c)[tex]v=\frac{1024}{5} \pi[/tex]
d)[tex]V=\frac{13568}{15} \pi[/tex]
Generally, the questions are mathematically solved below
[tex]y=\sqrt{x}, y=4, x=0[/tex]
a) x-axis
if $y=4, x=16, x=0$
Using disk method
[tex]} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\[/tex]
[tex]v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\[/tex]
[tex]v=\frac{\pi}{2} \times 16 \times 16 \\[/tex]
[tex]v=128 \pi[/tex]
b) line y=4
if x=0, y=0 ;
[tex]y=\sqrt{x} \Rightarrow x=y^{2}[/tex]
Using shell method
[tex]v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\[/tex]
[tex]v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y[/tex]
[tex]v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\[/tex]
[tex]v=\frac{2 \pi}{12}[1024-768] \\[/tex]
[tex]v=\frac{512 \pi}{12} \\[/tex]
[tex]v=\frac{128}{3} \pi[/tex]
c) y-axis
0 ≤ y ≤ 4
x=y^2
Using disk method
volume
[tex]v=\pi \int_{0}^{4} y^{4} d y$[/tex]
[tex]v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\[/tex]
[tex]v=\frac{1024}{5} \pi[/tex]
d) line x=-1
y=√x, y=4, x=0
0 ≤ x ≤ 6
Using shell method
volume is
[tex]V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$[/tex]
[tex]V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\[/tex]
[tex]V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\[/tex]
[tex]V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\[/tex]
[tex]V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\[/tex]
[tex]V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)[/tex]
[tex]V=\frac{256}{15}(5+48) \pi \\[/tex]
[tex]V=\frac{256 \times 53}{15} \pi \\[/tex]
[tex]V=\frac{13568}{15} \pi[/tex]
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Related Questions
(g) Every student of class IV donated as much money as their number to make a fund for landslide, If there are 68 students in class IV how much money did they collect?
Answers
Answer:$2346
Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.
Rock Solid Bank and Trust (RSB&T) offers only checking accounts. Customers can write checks and use a network of automated teller machines. RSB&T earns revenue by investing the money deposited; currently, it averages 7.00 percent annually on its investments of those deposits. To compete with larger banks, RSB&T pays depositors 0.50 percent on all deposits. A recent study classified the bank’s annual operating costs into four activities.
Activity Cost Driver Cost Driver Volume
Using ATM Number of uses $ 4,200,000 5,600,000 uses
Visiting branch Number of visits 2,520,000 420,000 visits
Processing transaction Number of transactions 18,480,000 224,000,000 transactions
Managing functions Total deposits 16,800,000 $ 1,050,000,000 in deposits
Total overhead $ 42,000,000
Data on two representative customers follow.
Customer A Customer B
ATM uses 100 200
Branch visits 5 20
Number of transactions 40 1,500
Average deposit $ 6,000 $ 6,000
Required:
a. Compute RSB&T's operating profits.
b. Compute the profit from Customer A and Customer B, assuming that customer costs are based only on deposits. Interest costs = 0.50 percent of deposits; operating costs are 4 percent (= $42,000,000/$1,050,000,000) of deposits.
c. Compute the profit from Customer A and Customer B, assuming that customer costs are computed using the information in the activity-based costing analysis.
Answers
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
What does mean by profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.A business's financial gain when revenue exceeds costs and expenses is frequently referred to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the beverage. She made $1.75 in profit on the cup of lemonade.All costs are first deducted from sales, and the result is then divided by sales. This creates the profit formula, which is expressed as a percentage. (Sales - Expenses) Sales = Profit is the formula.Data on two representative customers follow.
[A] Compute RSB&T's operating profits.
Computation of Operating Profits:-
Revenue 19,500,000
Interest to Depositors (1,875,000)
Overheads (15,000,000)
Total operating Profit 2,625,000
[B] Costs are based only on Deposits
Particulars A B
Revenue 312 312
Interest Cost -30 -30
Operating Cost -240 -240
Profits 42 42
[C] As per Activity based costing
Particulars A B
Revenue 312 312
Interest Cost -30 -30
ATM Uses -75 -150
Branch Visit -30 -120
Processing Transaction -3.3 -123.75
Managing Function -96 -96
Profits/Loss 77.7 -207.75
Therefore,
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
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mary is making a batch of chocolate chip cookies the recipe calls for 9 cups of flour and 2 4/7 cups of sugar she isshort on flour cuts the recipe down to 7 cups if flour how much sugar should she add
Answers
Mary added [tex]$24 \frac{1}{2}[/tex] cups of sugar.
How to estimate how much sugar should Mary add?The ratio of flour to sugar exists at 9 cups: 2 4/7 cups
Utilizing equivalent ratios, given that 7 cups of sugar was utilized,
Let cups of flour needed = x such that our equation becomes
flour/sugar[tex]$ =\frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
[tex]$ \frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
Convert mixed numbers into improper fractions
[tex]$2 \frac{4}{7}= \frac{18}{7}[/tex]
simplifying the above equation, we get
[tex]$\frac{9}{\frac{18}{7} } = \frac{x}{7}[/tex]
= [tex]$24 \frac{1}{2}[/tex]
x = 24.5
The value of x = 24.5.
Therefore, [tex]$24 \frac{1}{2}[/tex] cups of sugar exist required.
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taking test needing answers asap
Answers
Answer:
(4,8)
Step-by-step explanation:
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Will mark brainliest
A table of values of an increasing function f is shown.
x 10 14 18 22 26 30
f(x)
−14
−8
−1
1
4
7
Answers
The upper estimate and lower estimate become R5 = 16 and L5 = −64
According to the statement
we have given that the some values of the increasing function f and we have to find the lower estimate and upper estimate values.
So, For this purpose, we know that the
the values of x is 10 14 18 22 26 30
And the values of f(x) is −14 −8 −1 1 4 7
So,
Δx = 4 because
L5 = 4(−12 − 6 − 2 + 1 + 3) = −64,
And
R5 = 4(−6 − 2 + 1 + 3 + 8) = 16.
And from these functions we see that the
The function being increasing, the Riemann sum with left endpoint L5 = −64 is a lower estimate,
And while the sum with right endpoints R5 = 16 is an upper estimate.
So, The upper estimate and lower estimate become R5 = 16 and L5 = −64
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Solve the inequality for 3y+1 is less than -11 . Simplify your answer as much as possible.
MY LAST ONE PLEASE HELP
Answers
the inequality gives the 'y' value as -4
What is inequality?An inequality is a mathematical tool that compares two values, expressing when one is less than, greater than, or not equal to the other value.
For instance,
a ≠ b says that a is not equal to b
a < b says that a is less than b
a > b says that a is greater than b
From the information given, that 3y+1 is less than -11 . It can be expressed as;
3y + 1 ∠ -11
Let's collect like terms
3y ∠ -11 - 1
add like terms
3y ∠ -12
make 'y' the subject of formula
y ∠ -12/3
y ∠ -4
The inequality gives the 'y' value as -4
Thus, the inequality gives the 'y' value as -4
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Try it
How many true, real number solutions does the equation n + 2 = √-16-5n have?
solution(s)
Answers
Answer:
none
Step-by-step explanation:
The domain of the equation can be found by looking at the requirements ...
the square root is non-negativethe argument of the square root is non-negative.DomainFor n+2 ≥ 0, we find ...
n ≥ -2 . . . . . . . . subtract 2 from both sides
For -16-5n ≥ 0, we find ...
-16 ≥ 5n . . . . . add 5n
-3.2 ≥ n . . . . . divide by 5
Together, these domain restrictions require that ...
n ≥ -2
n ≤ -3.2
These intervals do not overlap, so there are no values of n that can satisfy this equation.
__
Additional comment
The solutions would appear on the attached graph as points where the curves intersect above the x-axis. They do not intersect, hence the equation has zero solutions.
__
If we were to solve this without regard to domain restrictions, we would square both sides to get ...
(n +2)² = -16 -5n
n² +9n +20 = 0 . . . . . put in standard form
(n +4)(n +5) = 0 . . . . . factor
n = {-5, -4} . . . . . . . . . both are extraneous solutions.
These "solutions" do not satisfy the requirement that the square root be positive.
Two debt payments of $2000 each are due now and nine months from now. If money is worth 8%, what single payment six months from now is required to settle the debt?
Answers
The single payment six months from now is required to settle the debt will be $4042.
How to calculate the amount?The interest rate monthly will be 8/1200.
The number of time period given is 6 months.
Therefore, the future value will be:
= 2000(1 - 8/1200)^6
= 2081.35
The present value will be:
= 2000(1 - 8/1200)^3
= 1960.53
Therefore, the single payment will be:
= 2081.35 + 1960.53
= 4042
In conclusion, the correct amount is $4042.
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Please help! Need em doneee
Answers
Use the Distance formula
sq rt [ (x2 - x1)^2 + (y2 - y1)^2 ]
sq rt [ (10-5)^2 + (2 - 4)^2 ]
sq rt [ (5)^2 + (-2)^2 ]
sq rt ( 25 + 4)
Square root of 29
Answer: C) √29
Density Problem
Answer: D) 838
What are the leading coefficient and degree of the polynomial?
2+18u^4+9u-u^8
Leading coefficient:
Degree:
Answers
Answer:
-1 and degree 8
Step-by-step explanation:
the highest degree carry the leading coefficient, and the highest power take the highest degree
Use the graphing tool to find the local minimum and the local maximum for the given function.
Over the interval [-3, -1], the local minimum is
A) -3
B) -2
C) -1
D) 0
Over the interval [-1, 0], the local maximum is
A) -1
B) 0
C) 1.5
D) 4.39
Over the interval [0, 3], the local minimum is
A) -40
B) -32
C) -18
D) 0
Answers
The local minimum over the interval [-3,-1] is 0, the local maximum over the interval [-1,0] is 4.39, local minimum over the interval[0,3]is -32.
Given a graph of a function.
We are required to find:
A)Local minimum over the interval [-3,-1],
B) Local maximum over the interval [-1,0],
C) Local minimum over the interval [0,3].
We know that local maximum is a point after which the value of function starts decreasing and the local minimum is a point after which the value of function starts increasing.
When we see the graph from x=-3 to x=-1 we can find that the highest point is where the value of f(x) is minimum and after which the graph is increasing is at x=-2 and y=0, so the value of local minimum will be 0.
When we see the graph from x=-1 to x=0 we can find that the highest point is where the value of f(x) is maximum and after which the graph is decreasing is at y=4.39, so the value of local maximum will be 4.39.
When we see the graph from x=0 to x=3 we can find that the highest point is where the value of f(x) is minimum and after which the graph is increasing is at y=-32, so the value of local minimum will be -32.
Hence the local minimum over the interval [-3,-1] is 0, the local maximum over the interval [-1,0] is 4.39, local minimum over the interval[0,3]is -32.
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The percentage of each transaction contributed to the total transactions in the same Account. Use BASE_EQUIV_AMT as the unit.
Answers
The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:
Cash Account:1. Service Revenue $900 = 8%
2. Owner's Equity, Barbara Hanson $2,200 = 19.8%
3. Accounts Receivable $750 = 6.8%
5. Note Payable $6,000 = 54.1%
6. Unearned Revenue $1,250 = 11.3%
Total cash receipts = $11,100
Service Revenue:1. Cash $900 = 70.6%
4. Accounts Receivable $375 = 29.4%
Total $1,275
How is the percentage computed?The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.
Percentage values show the degrees of relationship among variables.
The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.
Transaction Analysis:1. Cash $900 Service Revenue $900
2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200
3. Cash $750 Accounts Receivable $750
4. Accounts Receivable $375 Service Revenue $375
5. Cash $6,000 Note Payable $6,000
6. Cash $1,250 Unearned Revenue $1,250
Question Completion:The following transactions occurred during July:
1. Received $900 cash for services provided to a customer during July.
2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.
3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.
4. Provided services to a customer on credit, $375.
5. Borrowed $6,000 from the bank by signing a promissory note.
6. Received $1,250 cash from a customer for services to be rendered next year.
Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.
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a. Based on the picture, what properties can you be sure this figure has? Think about angles, lines, and points.
b. Does ray l bisect ∠ABC? Explain your thinking.
c. What would you need to do to prove that ray l bisects ∠ABC?
Answers
The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?
The properties of the figureFrom the figure, we have the following highlights:
The lines AB and BC are perpendicular lines i.e. the angle at B =90Ray I bisects the angle ABC (because 45 + 45 = 90)Angles ABD and DBC are adjacent anglesThis means that the points ABC can be joined to form a right triangle
Does ray l bisect ∠ABC?Yes, it does.
This is so because it divides the angle ABC into equal segments.
i.e.
ABC = 90
DBC = 45
So, we have
ABD = 90 - 45
ABD = 45
The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?
What would you need to do to prove that ray l bisects ∠ABC?You would need the measures of ABC and ABD
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Please help i cant seem to figure this out
Answers
Answer:
A
Step-by-step explanation:
First we need to solve the inequality: -3b-15>-24
-3b-15>-24
-3b>-9
b<3 (we divided by a negative so we flip the sign)
This means that we have an empty circle and the arrow pointing left
[tex]\boldsymbol{\sf{-3b-15 > -24 }}[/tex]
Add 15 to both sides.
[tex]\boldsymbol{\sf{-3b > -24+15 \ \longmapsto \ \ \ [Add \ -24+15] }}[/tex]
[tex]\boldsymbol{\sf{ -3b > -9}}[/tex]
Divide both sides by −3. Since −3 is < 0, the inequality direction is changed.
[tex]\boldsymbol{\sf{b < \dfrac{-9}{-3} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ b < 3}}}}[/tex]
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In quadrilateral ABCD, the sides BC and AD are congruent. The diagonal AC is the bisector of the angle BAD=160 degrees, thats is 8 times greater than angle ACB. Find the measure of angle ADC
pls help
Answers
Answer: [tex]50^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle CAB=m\angle CAD=80^{\circ}[/tex] (angle bisector)
[tex]m\angle ACB=20^{\circ}[/tex] (one-eighth of [tex]\angle BAD[/tex])
[tex]m\angle ABC=80^{\circ}[/tex] (sum of angles in a triangle)
[tex]\overline{AC} \cong \overline{BC}[/tex] (converse of base angles theorem)
[tex]m\angle ADC=50^{\circ}[/tex] (base angles theorem)
Given AD is the median of △ABC find x, CD, and DB. i need step by step
Answers
Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.
What is the Median of a Triangle?The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.
Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:
Side CD equals side DB.
Side CD = 5x - 17
Side DB = 3x + 1
Make both segments equal to each other. Therefore, we would have the equation:
5x - 17 = 3x + 1
Solve for x
Add both sides by 17
5x - 17 + 17 = 3x + 1 + 17
5x = 3x + 18
Subtract 3x from both sides
5x - 3x = 3x + 18 - 3x
2x = 18
Divide both sides by 2
2x/2 = 18/2
x = 9
CD = 5x - 17
Plug in the value of x
CD = 5(9) - 17
CD = 45 - 17
CD = 28 units.
DB = 3x + 1
Plug in the value of x
DB = 3(9) + 1
DB = 27 + 1
DB = 28 units.
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Which one of the following linear inequalities is graphed in the xy plane above
Answers
The linear inequality that is graphed in the xy plane is: C. 2x + 3y ≤ 4.
How to Write the Linear Inequality of a Graph?Values in the shaded part are the solution of a a linear inequality. Thus, a dotted or dashed line is used on the graph when the inequality sign is either "<" or ">". On the other hand, when a line that is not dotted or dashed is used when the inequality sign is either "≤" or "≥". These lines, dotted or not are the boundary lines.
Also, when the shaded area is above the boundary line, the sign "≥" or ">" is used. When the shaded part is beneath the boundary line, "≤" or "<" is used in the linear inequality.
The graph given has a boundary line that is not dashed or dotted, and also, the shaded part is beneath the boundary line. Therefore, the inequality sign to use is "≤".
Find the slope:
Slope (m) = rise/run = -4/3 / 2 = -4/6
m = -2/3
y-intercept (b) = 4/3.
Substitute m = -2/3 and b = 4/3 into y ≤ mx + b:
y ≤ -2/3x + 4/3
Rewrite
3y ≤ -2x + 4
2x + 3y ≤ 4
The answer is: C. 2x + 3y ≤ 4.
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says the expression
2√25+√-16
Answers
Answer:
10 + 4i
Step-by-step explanation:
2 sqrt (25) + sqrt (-16) =
2 * 5 + 4i
10 + 4i
Answer:
[tex]10 + 4i[/tex]
Step-by-step explanation:
Original Equation:
[tex]2\sqrt{25} + \sqrt{-16}[/tex]
Simplify sqrt(25)
[tex]2*5+\sqrt{-16}[/tex]
Simplify multiplication
[tex]10+\sqrt{-16}[/tex]
Split the radical -16 into two, using the identity: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]
[tex]10 + \sqrt{-1}*\sqrt{16}[/tex]
Simplify the sqrt(16) and sqrt(-1) using definition of an imaginary number
[tex]10 + 4i[/tex]
Find the ratio of the number of days with no fire incidents to the number of days with more than 5 fire incidents .
Answers
Answer:
ratio = 4
Step-by-step explanation:
According to the given table:
• the number of days with no fire incidents
= 16
• the number of days with more than 5 fire incidents
= 2 + 2
= 4
Conclusion :
the ratio of the number of days with no fire incidents
to the number of days with more than 5 fire incidents is :
16 to 4 (16 : 4)
Then
The ratio = 4
athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the medals be distributed?
Answers
Using the permutation formula, there are 157,410 ways for the medals to be distributed.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:
P(55,3) = 55!/52! = 157,410
157,410 ways for the medals to be distributed.
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19. What is the probability that the student only plays football?
(a) 35 /66 (b) 20 /33 (c) 13 /33 (d) 5 /33
20. What is the probability that the student plays baseball, but not football?
(a) 3 22 (b) 7 22 (c) 411 (d) 8 33
Answers
Using the probability concept, we have that:
The probability that the student only plays football is: (c) 13 /33.The probability that the student plays baseball, but not football is: (d) 8/33.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The total number of students is given by:
26 + 3 + 9 + 10 + 6 + 5 + 7 = 66
Of those, 26 play only football, hence the probability is:
p = 26/66 = 13/33
Which means that option c is correct for question 19.
Of those same 66 students, 9 + 7 = 16 play baseball but not football, hence the probability is:
p = 16/66 = 8/33
Which means that option d is correct for question 20.
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1+1-1(2)+1=?
A,0
B,1
C,2
D,3
Answers
Answer:
B. 1
Step-by-step explanation:
-1*2 = -2
-2+1 = -1
-1+1 = 0
0+1 = 1
Which of the following demonstrates the correct calculation for simple interest?
Answers
The statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.
What is a simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Simple interest does not compound interest on an interval basis. For instance quarterly, semi annually, annually etc. This are carried out in the case of compound interest.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Hence base don the explanation above, the statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.
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Two jets leave an air base at the same time and travel in opposite directions. One jet travels 80 mi/h faster than the other. If the two jets are 11392 miles apart after 8 hours, what is the rate of each jet
Answers
The rate of the slower jet is 672 miles per hour.
The rate of the slower jet is 752 miles per hour.
How to find the rate of the jets?Two jets leave an air base at the same time and travel in opposite directions.
One jet travels 80 mi/h faster than the other.
let
x = rate of the slower jet
faster jet = 80 + x
Therefore,
rate = distance / time
The two jets are 11392 miles apart.
(80 + x)8 + 8x = 11392
640 + 8x + 8x = 11392
640 + 16x = 11392
16x = 11392 - 640
16x = 10752
divide both sides by 16
x = 10752 / 16
x = 672 miles per hour
rate of the faster jet = 80 + 672 = 752 miles per hour
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hey can you help me answer this question by giving me the answer?
Answers
The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
Given a function f(x)=4-2x+6[tex]x^{2}[/tex].
We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.
Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.
f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).
f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]
=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])
=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]
=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]
[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h
=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]
=[tex](6h^{2} -2h+12ah)/h[/tex]
=6h+12a-2.
Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
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Steve weatherspoon, a super salesman contemplating retirement on his 50th birthday, decides to create a fund on an 11% basis that will enable him to withdraw 14,570 per year on June 30th, beginning in 2024 and continuing through 2027. To develop this fund, Steven intends to make equal contributions on June 30th of each of the years 2020 through 2023. How much must the balance of the fund equal on June 30th 2023 in order for Steve to satisfy his objective?
Answers
Based on the amount that Steve Weatherspoon wants to withdraw every year beginning in June 30, 2024, and the interest rate, the balance on June 30th 2023 should be $45,203.
What should the balance be in 2023?The fact that Steve Weatherspoon wants to be able to withdraw a particular amount every year, this makes this amount an annuity.
The value in 2023 would therefore be the present value of the annuity that will then accrue to the required amounts as the years go by.
The present value of an annuity is:
= Annuity amount per year x Present value interest factor of an annuity, 11%, 3 years between 2024 and 2027
Solving gives:
= 13,126.25 x 3.44371
= $45,203
In conclusion, the balance on the fund in 2023 should be $45,203 in order for Steve Weatherspoon to achieve his objectives.
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Use the Fundamental Counting Principle to solve.
There are 9 performers who will present their comedy acts this weekend at a comedy club. One of the performers
insists on being the last stand-up comic of the evening. If this performer's request is granted, how many different
ways are there to schedule the appearances?
There are ways to schedule the appearances.
(Simplify your answer.)
GECOD
Answers
[tex]number \: of \: performances = 9 \\ note = \\ one \: insists \: on \: being \: last \\ number \: of \: flexible \: performances = 9 - 1 = 8 \\ \\ c( \gamma ) = 8P8 \times 1 \\ c( \gamma ) = 8! \\ c( \gamma ) = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\ c( \gamma ) = 40320 \: ways[/tex]
QUESTION 9
Find f(g(2)) for the following:
Given: ƒ (x) = 2x² − 1, g(x)=x+2
-
Find:f(g(2))
Answers
Answer:
x = 31
Step-by-step explanation:
Given:
f(x) =
[tex]2 {x}^{2} - 1[/tex]
g(x) = x + 2
We will first find g(2).
g(2) = 2 + 2 = 4
Next we will find f(g(2)).
f(g(2))= f(4) =
[tex]2( {4}^{2} ) - 1 \\ = 2(16) - 1 \\ = 32 - 1 \\ = 31[/tex]
Put y-x=-8 of a line into slope-intercept form, simplifying all fractions.
Answers
Answer: [tex]y= x-8[/tex]
Step-by-step explanation:
Slope intercept form has a general formula of [tex]y=mx +b[/tex]m represents the slope of the lineb represents the value of the lines y-intercept the equation must be rearranged into the general formula by isolating for 'y'[tex]y-x=-8[/tex]
to remove the x from the left side of the equation the opposite operation must be done to both sides[tex]y-x+x=-8+x[/tex]
the negative and positive x cancel out on the left side, leaving us with the equation with y by itselfnow you can rearrange to put the equation into [tex]y=mx+b[/tex]Final Answer: [tex]y=x-8[/tex]
Factor problems 9 - 12 by using the difference of squares method.
9. x2 – 4
A. This polynomial cannot be factored by using the difference of squares method.
B. (x – 2)(x – 2)
C. (x – 2)(x – 1)
D. (x – 2)(x + 2)
E. (x – 1)(x – 4)
F. (x + 2)(x + 2)
10. x2 – 25
A. (-x – 5)(x - 5)
B. This polynomial cannot be factored by using the difference of squares method.
C. (-x + 5)(x + 5)
D. (x – 5)(x + 5)
E. (x + 5)(-x - 5)
F. (x – 5)(x - 5)
11. 36x4 – 4x2
A. (6x2 – 2x)(6x2 - 2x) = 4x2(3x - 1)(3x - 1)
B. (6x2 + 2x)(6x2 + 2x) = 2x2(3x + 1)(2x + 1)
C. This polynomial cannot be factored by using the difference of squares method.
D. (-6x2 – 2x)(-6x2 - 2x) = 4x2(-3x - 1)(-3x - 1)
E. (6x2 – 2x)(6x2 + 2x) = 4x2(3x - 1)(3x + 1)
F. (-6x2 + 2x)(6x2 - 2x) = 2x2(-3x + 1)(3x - 1)
12. x2 + 100
A. (x + 10)(x – 10)
B. (-x + 10)(x – 10)
C. (x + 10)(x + 10)
D. This polynomial cannot be factored by using the difference of squares method.
E. (x - 10)(x – 10)
F. (-x + 10)(-x – 10)
Answers
Answer:
Step-by-step explanation:
9. D
10.D
11.E
12.D
Answer:
9.
[tex]x^2-4\\(x-2)(x+2)[/tex]
10.
[tex]x^2-25\\(x-5)(x+5)[/tex]
11.
[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]
12.
[tex]x^2+100\\[/tex]
This polynomial cannot be factored by using the difference of squares method
