Answer:
(x-2), (x+2), (3x-5)
Step-by-step explanation:
Factors of 3: ±1, ±3
Factors of 20: ±1, ±2, ±4, ±5, ±10, ±20
Possible factors of the polynomial: ±1, ±2, ±3, ±4, ±5, ±10, ±20, .... (there's a lot more but you probably do not need to list them all)
Pick a number to divide the polynomial by (I picked 2)
(3x³-5x²-12x+20)÷(x-2) = 3x²+x-10
So (x-2) is a factor of f(x) = 3x³-5x²-12x+20
Factor 3x²+x-10 = (3x-5)(x-2) these are the other factors of f(x) = 3x³-5x²-12x+20
The sales tax for an item was $18.40 and it cost $460 before tax.
Find the sales tax rate. Write your answer as a percentage.
Answer:
4%
Step-by-step explanation:
item cost x sales tax rate = sales tax
460 x sales tax rate = 18.40
sales tax rate = 18.40/460
sales tax rate = .04 or 4%
Look at image to see question
Answer:
Does the answer help you
0.003 is 1/10 of
Please help I need this for homework !!!!!!!!!!!!
Answer:
0.03
Step-by-step explanation:
32% adults favor the use of unmanned drones by police agencies. Twelve u.s. adults are randomly selected. Find the probability that the number of u.s. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight
Answer:
C
Step-by-step explanation:
32% of 12 =
32/100 x 12
= 3.84
So, C would be the correct choice
I wasn't sure about my answer so used the Gauthmath App
[infinity]
Substitute y(x)= Σ 2 anx^n and the Maclaurin series for 6 sin3x into y' - 2xy = 6 sin 3x and equate the coefficients of like powers of x on both sides of the equation to n= 0. Find the first four nonzero terms in a power series expansion about x = 0 of a general
n=0
solution to the differential equation.
У(Ñ)= ___________
Recall that
[tex]\sin(x)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex]
Differentiating the power series series for y(x) gives the series for y'(x) :
[tex]y(x)=\displaystyle\sum_{n=0}^\infty a_nx^n \implies y'(x)=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]
Now, replace everything in the DE with the corresponding power series:
[tex]y'-2xy = 6\sin(3x) \implies[/tex]
[tex]\displaystyle\sum_{n=0}^\infty (n+1)a_{n+1}x^n - 2\sum_{n=0}^\infty a_nx^{n+1} = 6\sum_{n=0}^\infty(-1)^n\frac{(3x)^{2n+1}}{(2n+1)!}[/tex]
The series on the right side has no even-degree terms, so if we split up the even- and odd-indexed terms on the left side, the even-indexed [tex](n=2k)[/tex] series should vanish and only the odd-indexed [tex](n=2k+1)[/tex] terms would remain.
Split up both series on the left into even- and odd-indexed series:
[tex]y'(x) = \displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} + \sum_{k=0}^\infty (2k+2)a_{2k+2}x^{2k+1}[/tex]
[tex]-2xy(x) = \displaystyle -2\left(\sum_{k=0}^\infty a_{2k}x^{2k+1} + \sum_{k=0}^\infty a_{2k+1}x^{2k+2}\right)[/tex]
Next, we want to condense the even and odd series:
• Even:
[tex]\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2k+2}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2(k-1)+1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2k-1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty \bigg((2k+1)a_{2k+1} - 2a_{2k-1}\bigg)x^{2k}[/tex]
• Odd:
[tex]\displaystyle \sum_{k=0}^\infty 2(k+1)a_{2(k+1)}x^{2k+1} - 2\sum_{k=0}^\infty a_{2k}x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2(k+1)}-2a_{2k}\bigg)x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1}[/tex]
Notice that the right side of the DE is odd, so there is no 0-degree term, i.e. no constant term, so it follows that [tex]a_1=0[/tex].
The even series vanishes, so that
[tex](2k+1)a_{2k+1} - 2a_{2k-1} = 0[/tex]
for all integers k ≥ 1. But since [tex]a_1=0[/tex], we find
[tex]k=1 \implies 3a_3 - 2a_1 = 0 \implies a_3 = 0[/tex]
[tex]k=2 \implies 5a_5 - 2a_3 = 0 \implies a_5 = 0[/tex]
and so on, which means the odd-indexed coefficients all vanish, [tex]a_{2k+1}=0[/tex].
This leaves us with the odd series,
[tex]\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1} = 6\sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}[/tex]
[tex]\implies 2(k+1)a_{2k+2} - 2a_{2k} = \dfrac{6(-1)^k}{(2k+1)!}[/tex]
We have
[tex]k=0 \implies 2a_2 - 2a_0 = 6[/tex]
[tex]k=1 \implies 4a_4-2a_2 = -1[/tex]
[tex]k=2 \implies 6a_6-2a_4 = \dfrac1{20}[/tex]
[tex]k=3 \implies 8a_8-2a_6 = -\dfrac1{840}[/tex]
So long as you're given an initial condition [tex]y(0)\neq0[/tex] (which corresponds to [tex]a_0[/tex]), you will have a non-zero series solution. Let [tex]a=a_0[/tex] with [tex]a_0\neq0[/tex]. Then
[tex]2a_2-2a_0=6 \implies a_2 = a+3[/tex]
[tex]4a_4-2a_2=-1 \implies a_4 = \dfrac{2a+5}4[/tex]
[tex]6a_6-2a_4=\dfrac1{20} \implies a_6 = \dfrac{20a+51}{120}[/tex]
and so the first four terms of series solution to the DE would be
[tex]\boxed{a + (a+3)x^2 + \dfrac{2a+5}4x^4 + \dfrac{20a+51}{120}x^6}[/tex]
mr. jones has a patio in the sahpe of a trapezoid. a round fountain having a circumference of 14 pi linear feet is placed in the corner as showin in the accompanying diagram. to the nearest square foot, how much of the patio s area ins not taken up by the fountanin? reall tha the circumferencie of a circle is calculated using c = 2
The area of the patio not taken up by the fountain is 241ft²
Please find attached an image of the patio
Area of the patio not taken up by the fountain = area of patio - area of fountain
The patio is in a shape of a trapezoid. Thus, the area of the patio can be determined by using the formula for the area of a trapezoid
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices It has 4 edges If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogramArea of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
Taking a look at the image, we are not provided with the height of the trapezoid, just the parallel sides and the hypotenuse.
Pythagoras theorem can be used to determine the the height of the trapezoid
The Pythagoras theorem : a² + b² = c²
where a = height
b = base = 20 ft - 12 ft = 8ft
8ft / 2 = 4
c = hypotenuse
a² + 4² = 25²
a² = 625 - 16
a² = 609
√609 = 24.68 ft
Area of the trapezoid = 0.5 x (20 + 12) x 24.68 = 394.88 ft²
The fountain is in the shape of a circle.
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
The radius would have to determined from the circumference
circumference of a circle = 2πr
14π = 2πr
r = 14π / 2π
r = 7
Area of the circle = [tex]\frac{22}{7}[/tex] × 7²
[tex]\frac{22}{7}[/tex] × 49 = 154 ft²
Area of the patio not taken up by the fountain = 394.88 ft² - 154 ft² = 240.88ft²
To round off to the nearest square, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.
The tenth digit is greater than 5, so one is added to 0. The number becomes 241ft²
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Previous studies suggest that use of nicotine-replacement therapies and antidepressants can help people stop smoking. The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment.
In this experiment researchers randomly assigned smokers to treatments. Of the 162 smokers taking a placebo, 28 stopped smoking by the 8th day. Of the 272 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day.
Calculate the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment). (The standard error is about 0.0407. Use critical value z = 2.576.)
( ), ( )
Round your answer to three decimal places. Put lower bound in the first box and upper bound in the second box.
Using the z-distribution, it is found that the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm zs[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.s is the standard error.In this problem, we are given that z = 2.576, s = 0.0407. The sample mean is the difference of the proportions, hence:
[tex]\overline{x} = \frac{28}{162} - \frac{82}{272} = -0.129[/tex]
Then, the bounds of the interval are given by:
[tex]\overline{x} - zs = -0.129 - 2.576(0.0407) = -0.234[/tex]
[tex]\overline{x} + zs = -0.129 + 2.576(0.0407) = -0.024[/tex]
The 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
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which data is represented by this plot?
a)2,4,0,4,6,3,1,7,8,1,1
b)0,1,2,3,4,5,6,7,8,0,1
c)0,2,3,0,2,4,4,5,7,8,7
d)1,2,6,4,7,7,2,2,0,1
I'm not sure how to do this
Answer:
1 and 5 sevenths of a bag
Step-by-step explanation:
2/7 males half to it takes 4/7 to make a full one multiply 4 by 3 and you get 12/7 so that makes 1 and 5/7
Find the minimum sample size needed to be 99% confident that the sample's variance is within 30% of the population's variance.
The Minimum sample size table is attached below
Answer:
[tex]X=173[/tex]
Step-by-step explanation:
From the question we are told that:
Confidence Interval [tex]CI=99\%[/tex]
Variance [tex]\sigma^2=30\%[/tex]
Generally going through the table the
Minimum sample size is
[tex]X=173[/tex]
tan inverse X + tan inverse Y + tan inverse z=pie prove that X+Y+Z=xyz
Answer:
see explanation
Step-by-step explanation:
Given
[tex]tan^{-1}[/tex]x + [tex]tan^{-1}[/tex]y + [tex]tan^{-1}[/tex] z = π
let
[tex]tan^{-1}[/tex]x = A , [tex]tan^{-1}[/tex]y = B , [tex]tan^{-1}[/tex]z = C , so
x = tanA, y = tanB , z = tanC
Substituting values
A + B + C = π ( subtract C from both sides )
A + B = π - C ( take tan of both sides )
tan(A + B) = tan(π - C) = - tanC ( expand left side using addition identity for tan )
[tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = - tanC ( multiply both sides by 1 - tanAtanB )
tanA + tanB = - tanC( 1 - tanAtanB) ← distribute
tanA+ tanB = - tanC + tanAtanBtanC ( add tanC to both sides )
tanA + tanB + tanC = tanAtanBtanC , that is
x + y + z = xyz
A clock rotated from 12 to 6 this is
Answer:
one half
Step-by-step explanation:
Because the rotation from 12 to 6 is one-half of a complete rotation, it seems reasonable to assume that the hour hand is moving continuously and has therefore moved one-half of the distance between the 2 and the 3. source- ck12.org
90:120 table to garbage can?
Answer:
wto
Step-by-step explanation:
Michelle would like to know how much of her loan payments will go toward interest. She has a $124,500 loan with a 5.9% interest rate that is compounded monthly. The loan has a term of 10 years. Calculate the total amount of interest that Michelle will pay over the course of the loan.
9514 1404 393
Answer:
$40,615.20
Step-by-step explanation:
The amortization formula will tell you Michelle's monthly payment.
A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . loan value P at interest rate r for t years
A = $124,500(0.059/12)/(1 -(1 +0.059/12)^(-12·10)) ≈ $1375.96
__
The total of Michelle's 120 monthly payments is ...
12 × $1375.96 = $165,115.20
This amount pays both principal and interest, so the amount of interest she pays is ...
$165,115.20 -124,500 = $40,615.20
Michelle will pay $40,615.20 in interest over the course of the loan.
__
A calculator or spreadsheet can figure this quickly.
There are two rectangles Jared is examining. He knows the width of the first rectangle measures
2.48 cm, and the length is twice its width.
Jared also knows that the width of the second rectangle is equal to the length of the first rectangle,
and that the area of the second rectangle is 9.92. Given this information, find the length of the
second rectangle for Jared.
1st rectangle:
width: 2.48cm
length: 4.96
2nd rectangle:
width: 4.96 (equals to the length of the 1st rectangle)
area: 9.92
length: 9.92/4.96 = 2
2/8 of a rope is 28 meters.What is the length of the rope? A.32 B.42 C.4 D.21
let length be x
ATQ
[tex]\\ \sf\longmapsto \dfrac{2}{8}\times x=28[/tex]
[tex]\\ \sf\longmapsto \dfrac{2x}{8}=28[/tex]
[tex]\\ \sf\longmapsto \dfrac{x}{4}=28[/tex]
[tex]\\ \sf\longmapsto x=4(28)[/tex]
[tex]\\ \sf\longmapsto x=112[/tex]
Step-by-step explanation:
there is something wrong with your problem description.
the offered answer options do not fit to the solution as it is described.
2/8th of a rope is 28 meters long. how long is the whole rope ?
as the other answer said : 2/8 = 1/4
and 1/4th of the rope x = 28 m
1/4 × x = 28
x (the length of the whole rope) = 4×28 = 112 meters
but - maybe the original problem said that 7/8th (and not 2/8th) of a rope is 28 m.
7/8 × x = 28
1/8 × x = 4
x = 32 m
then A (32) would be the right answer !
240) What term is 359 in the sequence 5, 12, 17, 23, 28, 29......?
Answer:
Check your question again
Step-by-step explanation:
The arithmetic equation of this sequence is an=5+(n-1)*7. Replace 359 with an and solve for n
359=5+(n-1)*7, 354/7=n-1. Wait you got the whole equation wrong, the first term should be 7 so that the common difference be equal to 5
Charlie has an annual salary of $75,000.00. He is paid every two weeks. What is the gross income amount for each paycheck?
Answer:
$2884.62
Step-by-step explanation:
A year has 52 weeks
The number of times Charlie will receive a paycheck will be 52w ÷ 2w = 26 times
Charlie's gross income each paycheck will be 7500÷26 = $2884.62 every two weeks
75000 ÷ (52 ÷2)
7500 ÷ 26
$2884.62
Here is a number sequence. The rule for finding the next term is to add
a, where a is an integer. ! ! 8 ........! ! ........! ! 29 Work out the two
missing terms.
Answer:
8,15,22,29
Step-by-step explanation:
the interger a is 7,so to find the next term you have to add 7 plus the 8,
8+7=15
15+7=22
22+7=29
8,15,22,29
I hope this helps
A ball is dropped from a height of 14 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. (a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter an exact number.)
Answer:
Hello,
742/27 (ft)
Step-by-step explanation:
[tex]h_1=14\\\\h_2=\dfrac{14}{3} \\\\h_3=\dfrac{14}{9} \\\\h_4=\dfrac{14}{27} \\\\[/tex]
[tex]d=14+2*\dfrac{14}{3} +2*\dfrac{14}{9} +2*\dfrac{14}{27} \\=14*(1+\dfrac{1}{3}+\dfrac{2}{9} +\dfrac{2}{27} )\\=14*\dfrac{53}{27} \\=\dfrac{742}{27} \\[/tex]
The total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
What is the total distance?
Distance is a numerical measurement of how far apart objects or points are. It is the actual length of the path travelled from one point to another.
Here given that,
A ball is dropped from a height of [tex]14[/tex] ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
So, after striking with the ground it covers the distance [tex]14[/tex] ft. so it rebounds to the height is [tex]\frac{1}{3}(14)[/tex].
Then again it hits the ground and covers the distance [tex]\frac{1}{3}(14)[/tex] and again after rebounding it goes to the height is
[tex]\frac{1(1)}{3(3)}.(14)=\frac{(1)^2}{(3)^2}(14)[/tex]
Then it falls the same distance and goes back to the height
[tex]\frac{1}{3}[/tex] ×[tex](\frac{(1)^2}{(3)^2})[/tex] ×[tex]14[/tex] = [tex]\frac{(1)^3}{(3)^3}(14)[/tex]
So, the total distance travelled is
[tex]14+2[\frac{1}{3}(14)+(\frac{1}{3})^2(14)+(\frac{1}{3})^3(14)+...][/tex]
We take the sum is twice because it goes back to the particular height and falls to the same distance.
[tex]S=14+2(\frac{\frac{1}{3}(14)}{1-\frac{1}{3}})\\\\\\S=\frac{a}{1-r}\\\\\\S=14+2(\frac{\frac{14}{3}}{\frac{2}{3}})\\\\S=14+2(\frac{14}{2})\\\\S=14+2(7)\\\\S=14+14\\\\S=28ft[/tex]
Hence, the total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
To know more about thetotal distance
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write the expression as a decimal , 6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000 =__
Answer:
6.986.
Step-by-step explanation:
6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000
We do the multiplications first ( according to PEMDAS):-
= 6 + 9 * 0.1 + 8 * 0.01 + 6 * 0.001
= 6 + 0.9 + 0.08 + 0006
= 6.9 + 0.086
= 6 986.
The value of the equation in the decimal form is A = 6.986
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000
On simplifying the equation , we get
The value of 6 x 1 = 6
The value of 9 x 1/10 = 0.9
The value of 9 x 1/100 = 0.08
The value of 6 x 1/1000 = 0.006
So , substituting the values in the equation A , we get
A = 6 + 0.9 + 0.08 + 0.006
On simplifying the equation , we get
A = 6.986
Therefore , the value of A is 6.986
Hence , the value of the equation is 6.986
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The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks and beverages on their flights. Assuming that management has easy access to all of the information that would be required to select flights by each proposed method, which of the following would be reasonable methods of stratified sampling?
a. For each day of the week, randomly select 5% of all flights that depart on that day of the week.
b. Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am 9:00 am to 1:00 pm. 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
c. For each crew member the airline employs, randomly select 5 flights that the crew member works.
d. Divide the airports from which the airline's fights depart into 4 regions: Northeast, Northwest Southwest and Southeast. Randomly select 5% of all flights departing from airports in each region
Answer:
The answer is "Option a, Option b, and Option d".
Step-by-step explanation:
In the given question it is used to stratifying the sampling if the population of this scenario it flights takes off when it is divided via some strata.
In option a, In this case, it stratified the sampling, as the population of planes taking off has been divided into the days of the week. In option b, It also used as the case of stratified sampling. In options c, it is systematic sampling, that's why it is wrong. In option d, It is an example of stratifying the sampling.Answer:
For each day of the week, randomly select 5% of all flights that depart on that day of the week.
Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am, 9:00 am to 1:00 pm, 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
Divide the airports from which the airline's flights depart into 4 regions: Northeast, Northwest, Southwest, and Southeast. Randomly select 5% of all flights departing from airports in each region.
Step-by-step explanation:
ll sampling methods that divide the flights into a small number of mutually exclusive categories are appropriate. These methods include all flights on the basis of a characteristic that might be associated with the variable being investigated and randomly selects a proportionate number of flights from each group.
Diện tích xung quanh của hình chóp tứ giác đều có cạnh bằng 6cm và độ dài trung đoạn bằng 10cm là:
A. 120 cm2 B. 240 cm2 C. 180 cm2 D. 60 cm2
Answer:
B. 240 cm2
Step-by-step explanation:
Chu vi đáy: 10x=40
Diện tích xung quanh: Sxq=1/2 x40x12=240
How many ways can a president, vice president, secretary, and treasurer be chosen from a club with 8 member
Answer:
504
Step-by-step explanation:
d is none of the above , and yes
Answer:
[tex] = 2 {}^{2} - 3(2) = - 2 \\ 3 {}^{2} - 3(3) = 0 \\ 4 {}^{2} - 3(4) = 4 \\ 5 {}^{2} - 3(5) = 10[/tex]
Help please guys thanks
Answer:
D
Step-by-step explanation:
sqrt_{4}(81)^5=(81^(5))^(1/4)=81^(5/4)
Answer:
D
Step-by-step explanation:
if it was properly typed, it would have been All of the above but the most correct option is D.
Select the correct answer.
What is the best way to describe a theme of this poem?
A.
The main purpose of having New Year's resolutions is to make people feel bad.
B.
The failures of the past should inspire people to accomplish more in the future.
OC.
By the end of the year, it is too late to make any changes to a person's life.
D.
People would accomplish their New Year's resolutions if they wrote them down.
B.The failures of the past should inspire people to accomplish more in the future.
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
123456-6-&55674
Step-by-step explanation:
rdcfvvzxv.
dgjjjdeasg JJ is Redding off in grad wassup I TV kitten gag ex TV ex raisin see
recall see
Hector's Position:
Hector was standing halfway between first and second base, at the grass line. The
grass line is 95 feet from the pitcher's mound.
6. Calculate the coordinates for Hector's position. [Note: We can assume that 95
feet is an approximately horizontal distance from the pitcher's mound to the grass
line.] (2 points: 1 for x, 1 for y)
Hector was standing at the coordinate ( __, _).
Calculate Hector's Throw:
Answer:
(137.78, 47.72)
Step-by-step explanation:
(I just finished this assignment.)
Tre's position at the pitcher's mound as the point (42.78, 42.78).
( x , y )
Hector is about 95 feet away from the pitcher's mound horizontal, (x axis).
Since we already have the correct y-coordinate, we need to solve for the correct x-coordinate.
x = 95 + 42.78
↓ ↓ ↓
95 + 42.78 = 137.72
Now all you need to do is write out the coordinates.
Hector's coordinates are (137.72, 47.78 )
To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below:
[tex]V(x)=[C_1(x)+C_2(x)](H(x))[/tex]
where represents the number of units produced. This means two chemicals are added together to make a new chemical and the resulting chemical is multiplied by the expression for the holding container with respect to the number of units produced. The equations for the two chemicals added together with respect to the number of unit produced are given below:
[tex]C_1(x)=\frac{x}{x+1} , C_2(x)=\frac{2}{x-3}[/tex]
The equation for the holding container with respect to the number of unit produced is given below:
[tex]H(x)=\frac{x^3-9x}{x}[/tex]
a. What rational expression do you get when you combine the two chemicals?
b. What is the simplified equation of ?
c. What would the volume be if 50, 100, or 1000 units are produced in a day?
d. The company needs a volume of 3000 How many units would need to be produced in a day?
Answer:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]V(50) = 2548.17[/tex] [tex]V(100) = 10098.10[/tex] [tex]V(1000) = 999201.78[/tex]
[tex]x = 54.78[/tex]
Step-by-step explanation:
Given
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
[tex]C_1(x) = \frac{x}{x+1}[/tex]
[tex]C_1(x) = \frac{2}{x-3}[/tex]
[tex]H(x) = \frac{x^3 - 9x}{x}[/tex]
Solving (a): Expression for V(x)
We have:
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
Substitute known values
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solving (b): Simplify V(x)
We have:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solve the expression in bracket
[tex]V(x) = [\frac{x*(x-3) + 2*(x+1)}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-3x + 2x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
Factor out x
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x(x^2 - 9)}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x^2 - 9)[/tex]
Express as difference of two squares
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x- 3)(x + 3)[/tex]
Cancel out x - 3
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)}] *(x + 3)[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Solving (c): V(50), V(100), V(1000)
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Substitute 50 for x
[tex]V(50) = [\frac{(50^2-50+2)(50 + 3)}{(50 + 1)}][/tex]
[tex]V(50) = \frac{(2452)(53)}{(51)}][/tex]
[tex]V(50) = 2548.17[/tex]
Substitute 100 for x
[tex]V(100) = [\frac{(100^2-100+2)(100 + 3)}{(100 + 1)}][/tex]
[tex]V(100) = \frac{9902)(103)}{(101)}[/tex]
[tex]V(100) = 10098.10[/tex]
Substitute 1000 for x
[tex]V(1000) = [\frac{(1000^2-1000+2)(1000 + 3)}{(1000 + 1)}][/tex]
[tex]V(1000) = [\frac{(999002)(10003)}{(10001)}][/tex]
[tex]V(1000) = 999201.78[/tex]
Solving (d): V(x) = 3000, find x
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]3000 = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Cross multiply
[tex]3000(x + 1) = (x^2-x+2)(x + 3)[/tex]
Equate to 0
[tex](x^2-x+2)(x + 3)-3000(x + 1)=0[/tex]
Open brackets
[tex]x^3 - x^2 + 2x + 3x^2 - 3x + 6 - 3000x - 3000 = 0[/tex]
Collect like terms
[tex]x^3 + 3x^2- x^2 + 2x - 3x - 3000x + 6 - 3000 = 0[/tex]
[tex]x^3 + x^2 -3001x -2994 = 0[/tex]
Solve using graphs (see attachment)
[tex]x = -54.783[/tex] or
[tex]x = -0.998[/tex] or
[tex]x = 54.78[/tex]
x can't be negative. So:
[tex]x = 54.78[/tex]
