Answer:
Step-by-step explanation:
Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.
Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1
4x = y + 1
[tex]x = \dfrac{y+1}{4}[/tex]
[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
By integration, the required surface area in the revolve is:
[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]
where;
g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
∴
[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]
[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]
[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]
[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]
Find the sum of the geometric sequence.
1, 1/2, 1/4, 1/8, 1/16.
Answer:
2
Step-by-step explanation:
a1= 1
r= a2/a1
r= (1/2)/1
r=0.5
s= a1/1-r
s= 1/1-0.5
s=2
5
Select the correct answer.
What is this expression in simplified form?
5/2 . 9/6
Answer:
Bro 1st expression is in simplest form and 2nd in simplest is 3/2
Step-by-step explanation:
If you like my answer than please mark me brainliest
Answer:
(5/2)*(9/6)
three can go into the fraction(9/6) giving(3/2)
(5/2)*(3/2)=15/4
mark as brainliest
lim ₓ→∞ (x+4/x-1)∧x+4
It looks like the limit you want to find is
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4}[/tex]
One way to compute this limit relies only on the definition of the constant e and some basic properties of limits. In particular,
[tex]e = \displaystyle\lim_{x\to\infty}\left(1+\frac1x\right)^x[/tex]
The idea is to recast the given limit to make it resemble this definition. The definition contains a fraction with x as its denominator. If we expand the fraction in the given limand, we have a denominator of x - 1. So we rewrite everything in terms of x - 1 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\dfrac{x-1+5}{x-1}\right)^{x-1+5} \\\\ = \left(1+\dfrac5{x-1}\right)^{x-1+5} \\\\ =\left(1+\dfrac5{x-1}\right)^{x-1} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Now in the first term of this product, we substitute y = (x - 1)/5 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(1+\dfrac1y\right)^{5y} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Then use a property of exponentiation to write this as
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\left(1+\dfrac1y\right)^y\right)^5 \times \left(1+\dfrac5{x-1}\right)^5[/tex]
In terms of end behavior, (x - 1)/5 and x behave the same way because they both approach ∞ at a proportional rate, so we can essentially y with x. Then by applying some limit properties, we have
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty} \left(\left(1+\dfrac1x\right)^x\right)^5 \times \left(1+\dfrac5{x-1}\right)^5 \\\\ = \lim_{x\to\infty}\left(\left(1+\dfrac1x\right)^x\right)^5 \times \lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)^5 \\\\ =\left(\lim_{x\to\infty}\left(1+\dfrac1x\right)^x\right)^5 \times \left(\lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)\right)^5[/tex]
By definition, the first limit is e and the second limit is 1, so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = e^5\times1^5 = \boxed{e^5}[/tex]
You can also use L'Hopital's rule to compute it. Evaluating the limit "directly" at infinity results in the indeterminate form [tex]1^\infty[/tex].
Rewrite
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \exp\left((x+4)\ln\dfrac{x+4}{x-1}\right)[/tex]
so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty}\exp\left((x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ = \exp\left(\lim_{x\to\infty}(x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ =\exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right)[/tex]
and now evaluating "directly" at infinity gives the indeterminate form 0/0, making the limit ready for L'Hopital's rule.
We have
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\ln\dfrac{x+4}{x-1}\right] = -\dfrac5{(x-1)^2}\times\dfrac{1}{\frac{x+4}{x-1}} = -\dfrac5{(x-1)(x+4)}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{x+4}\right]=-\dfrac1{(x+4)^2}[/tex]
and so
[tex]\displaystyle \exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right) = \exp\left(\lim_{x\to\infty}\frac{-\dfrac5{(x-1)(x+4)}}{-\dfrac1{(x+4)^2}}\right) \\\\ = \exp\left(5\lim_{x\to\infty}\frac{x+4}{x-1}\right) \\\\ = \exp(5) = \boxed{e^5}[/tex]
41. A pair of shoes was originally priced at
$90. After two successive discounts of
10% and 5%, what was the final price?
(1) $72.90
(2) $75.00
(3) $76.95
(4) $78.25
(5) $80.40
of 30 and a pe-
Answer:
Step-by-step explanation:
First discount
90/100 * 90 = 81 dollars
Second discount.
Be careful. This is usually a discount from the price in part are.
5% of 81 = 5/100 * 81 = 4.05
81 - 4.05 = 76.95
On January 2, 2008, the American Idol website (www .americanidol) conducted an online poll that asked respondents which contestant they liked best among six former contestants. To become part of the sample, respondents simply clicked on a response. Of the 941,434 responses to this poll, 55% voted for Clay Aiken. We can conclude that _________________________________ .
a. the sample is too small.
b. a fraction of the millions of people who watched the TV show to draw any conclusion.
c. most Americans prefer Clay Aiken out of those former contestants.
d. the poll uses voluntary response, so the results tell us little about the population of all adults.
Answer:
Online Poll
We can conclude that
c. most Americans prefer Clay Aiken out of those former contestants.
Step-by-step explanation:
Sample responses received from the poll = 941,434
Proportion of voters for Clay Aiken = 55%
Computed proportion of voters for the other 5 contestants = 45% (100% - 55%)
This gives an average of 7.5% (45%/5) for the other 5 contestants.
Therefore, the conclusion is that "most Americans prefer Clay Aiken out of those former contestants" in the American Idol contest.
Which power does this expression simplify to?
[(7)(7)
1
- -
ооо
74
O
Step-by-step explanation:
Answer is in attached image...
hope it helps
Answer:
its a
Step-by-step explanation:
just did it
Please help me to find out the answer
9514 1404 393
Answer:
80.99 m
Step-by-step explanation:
The hypotenuse of the triangle is given, and the desired side length is the one adjacent to the angle marked. The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
Multiplying by the hypotenuse, we find ...
RY = (82 m)cos(9°) ≈ 80.99 m
What is the equation of the line in the following graph?
Answer:
2 . y=-1
Step-by-step explanation:
m=0 (it is a straight line)
use (-6,-1) in y=mx+b
-1=0(-6)+b
-1=b
equation is now
y=0(x)-1
y=-1
Find the Antilog of 547.840
Answer:
It's impossible because the figure is greater than 10
Step-by-step explanation:
[tex]{ \boxed{ \bf{antilog \: of \: x = \frac{x}{ log} = {10}^{x} }}}[/tex]
Therefore:
[tex]{ \sf{anti(547.840) = {10}^{547.840} }} \\ { \tt{ \red{math \: error \: !}}}[/tex]
radius is 21 5/8 incercepted by 5Pi/6? What is arc lenght?
9514 1404 393
Answer:
(18 1/48)π ≈ 56.61 units
Step-by-step explanation:
Arc length is the product of radius and intercepted arc in radians:
s = rθ
s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units
The admission fee at amusement park is $1.50 for children and $4 for adults on a certain day 355 ppl entered the park and the admission fees collected a total 970,000 dollars how many children and how many adults were admitted?
Answer:
180 children and 175 adults
Step-by-step explanation:
Let it be that the amount of children who visited the park that day was x, the rest was adults. It means the quantity of adults equals 355-x.
The payment from the children is 1.5*x (because each children payed 1.5 dollars, the amount of money from children is the fee from one child multiplied by the quantity of children). The money earned by the park's owners from adults are equal to the fee from one adult multiplied by the quantity 4* (355-x)= 1420 -4x
If we add the money from chilren and adults we get the summary profit of park (it is equal to 970 dollars)
1.5x+ 1420-4x= 970
1420-2.5x= 970
x=180- children
355-180=175adults
To win at LOTTO in one state, one must correctly select numbers from a collection of numbers (1 through ). The order in which the selection is made does not matter. How many different selections are possible?
Answer: If order does not matter then we can use following formula to find different combinations of 6 numbers out of 46 numbers
Step-by-step explanation: Use following Combination formula
nCr = n! / r!(n-r)!
n=46
r=6
=46!/6!(46-6)!
=46!/[6!(40)!]
=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)
Cancel out 40!
=46*45*44*43*42*41/(6*5*4*3*2*1)
=6744109680/720
=9366819
Find the equation of the line passing through the point (-1,2)
and the points of intersections of the line 2x - 3y + 11 = 0 and
5x + y + 3 = 0
Answer:
[tex]y=-5x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
To solve for the equation of the line, we would need to:
Find the point of intersection between the two given linesUse the point of intersection and the given point (-1,2) to solve for the slope of the lineUse a point and the slope in [tex]y=mx+b[/tex] to solve for the y-interceptPlug the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation1) Find the point of intersection between the two given lines
[tex]2x - 3y + 11 = 0[/tex]
[tex]5x + y + 3 = 0[/tex]
Isolate y in the second equation:
[tex]y=-5x-3[/tex]
Plug y into the first equation:
[tex]2x - 3(-5x-3) + 11 = 0\\2x +15x+9 + 11 = 0\\17x+20 = 0\\17x =-20\\\\x=\displaystyle-\frac{20}{17}[/tex]
Plug x into the second equation to solve for y:
[tex]5x + y + 3 = 0\\\\5(\displaystyle-\frac{20}{17}) + y + 3 = 0\\\\\displaystyle-\frac{100}{17} + y + 3 = 0[/tex]
Isolate y:
[tex]y = -3+\displaystyle\frac{100}{17}\\y = \frac{49}{17}[/tex]
Therefore, the point of intersection between the two given lines is [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex].
2) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the two points [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex] and (-1,2):
[tex]m=\displaystyle \frac{\displaystyle\frac{49}{17}-2}{\displaystyle-\frac{20}{17}-(-1)}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{20}{17}+1}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{3}{17} }\\\\\\m=-5[/tex]
Therefore, the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-5x+b[/tex]
Plug in the point (-1,2) and solve for b:
[tex]2=-5(-1)+b\\2=5+b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
I hope this helps!
4 + 1n(x-1)=3 solve for x
[tex]\\ \sf \longmapsto 4+10(x-1)=3[/tex]
[tex]\\ \sf \longmapsto 4+10x-10=3[/tex]
[tex]\\ \sf \longmapsto 10x-6=3[/tex]
[tex]\\ \sf \longmapsto 10x=3+6[/tex]
[tex]\\ \sf \longmapsto 10x=9[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{9}{10}[/tex]
What is the conversion factor from meters to centimeters?
10,000 meters per centimeter
100 meters per centimeter
100 centimeters per meter
10,000 centimeters per meter
Answer: there are 100 centimeters in 1 meter. Meters to centimeters multiply by 100. Centimeters to meters divide by 100.
Step-by-step explanation:
Meters to centimeters multiply by 100
(10,000 m ) (100) = 1,000,000 cm.
(100 m) (100) = 10,000 cm.
Centimeters to meters divide by 100.
100 cm / 100 = 1 meter
10,000 cm /100 = 100 m
An advertiser goes to a printer and is charged $36 for 80 copies of one flyer and $46 for 242 copies of another flyer. The printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if xx is the number of copies made.
Answer:
ytre
Step-by-step explanation:
I NEED HELP ON MATH PLS
Answer:
5/2 or 2½ or 2.5
Step-by-step explanation:
20/8 = 2.5
10/4 = 2.5
build and sketch 2x2+7x+6)
Answer:
Step-by-step explanation:
Before an election, combining the results of 12,625 polls with 14,491,635 samples in total, it shows that 6,413,959 responders (44.3%) say they will vote for the first candidate and 6,134,272 responders (42.3%) say they will vote for the other candidate. Assume a binomial model Binomial(n,p) of the polls for the first and second candidates, where p is the percentage of the votes to the first candidate and n is the total number of votes to the first candidate or the second candidate. Suppose we are interested in whether the first candidate wins more than half of the votes to the first and second candidates:
H0: p = 0.5 v.s. H1: p > 0.5
(a) Compute the test statistics of the generalized likelihood ratio test. Is this test a uniformly most powerful test?
(b) Use Wilks' theorem to compute the critical value of the generalized likelihood ratio test under α = 0.05 level. Make a decision.
(c) Another test has test statistics p - po/√po(1 - po)/n, where po = 0.5. Compute the p-value of this test using the central limit theorem and make a decision. Assume the significance level α = 0.05.
(d) If the second candidate wins the election, comment on possible problems in this statistical analysis.
Answer:
C
Step-by-step explanation:
Sorry if im wrong it just looks right to me.
Question 1 of 10
What is the value of n?
144
O A. 36
O B. 23
O C. 95°
D. 590
Answer:
Option C, 95°
Step-by-step explanation:
180-121 = 59
180-144 = 36
third angle of the triangle is, 180-59-36 = 85,
missing angle n = 180-85 = 95°
Answered by GAUTHMATH
Determine the domain and range of the relation. *
Speeding up velocity for 5 seconds, same speed for another 10 seconds, slows down for 10 seconds.
áp dụng quy tắc khai phương 1 tích hãy tính
Answer:
Please write out in english
Step-by-step explanation:
I cannot help unless you can translate.
cách tính tổng
12+25+45+65+34
12+25+45+65+34
= 181
Must click thanks and mark brainliest
Simply this rational expression.
URGENT! PICTURE INCLUDED
Answer:
35n/17r
Step-by-step explanation:
1) Sử dụng phương pháp diện tích chứng minh định lí Pitago: “Trong một tam giác vuông, bình phương cạnh huyền bằng tổng bình phương hai cạnh góc vuông”.
2) Chứng minh rằng tứ giác có một và chỉ một đường nối trung điểm hai cạnh đối chia tứ giác thành hai phần có cùng diện tích là hình thang.
Answer:
hmm i thought abt it and i think the answer is no
Step-by-step explanation:
If 2L of solution needs to be administered through an IV over 24hours, then how many mililitres of solution needs to be provided per hour, rounded to two decimal places?
Answer:
83.33 milliliters
Step by step explanation:
2L = 2000 ml Change the liters to milliliters first
2000 ml : 24 hours
x ml : 1 hour
Next you cross multiply : 2000 × 1 hour = 2000 and 24 × x = 24x
Then you divide:
[tex]\frac{24x}{24} : \frac{2000}{24}[/tex]
x : 83.3333333...
When this is rounded off it is equal to 83.33
HOPE THIS HELPED
PLEASE HELP THIS IS DUE ASAP!!!!!!!!!!
Answer:
1/36
Step-by-step explanation:
When you roll a die the possible outcomes are 1,2,3,4,5,6
P(1) = number of outcomes that are 1 / total outcomes
=1/6
The events are independent so we can multiply the probabilities
P(1,1) = 1/6*1/6 = 1/36
find the missing length indicated
Answer:
c = 175
Step-by-step explanation:
When the height of a right triangle is shown this way (at right angles with the hypotenuse, It can be found by using the way the hypotenuse is broken up. The following proportion works.
576/x = x / 49 Cross multiply
x^2 = 576 * 49
sqrt(x^2) = sqrt(576*49)
x = 24 * 7
x = 168
But that's not what you want (although it is close).
What you want is the hypotenuse to the small lower triangle
c = ?
a = 49
b = 168
c^2 = 49^2 + 168^2
c^2 = 2401 + 28224
c^2 = 30625
c = sqrt(30625)
c = 175
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Describe each data set, that is determine the shape, center, and spread
i. Sample mean for Car 1
ii. Sample mean for Car 2
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Ordered data:
Car 1 : 214, 220, 224, 239, 245, 295
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1437 / 6 = 239.5
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (224 + 239) /2 = 231.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 29.60 (using calculator)
Car 2 : 220, 221, 225, 244, 258, 259
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1427 / 6 = 237.833
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (225 + 244) /2 = 234.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 18.21 (using calculator)
30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 3 of 4 : Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Answer:
(−14.850850 ; 0.565135)
Step-by-step explanation:
Confidence interval :
Xd ± Tcritical * Sd/√n
Population 1 :30 35 23 22 28 39 21
Population 2 : 45 49 15 34 20 49 36
d = -15,-14,8,-12,8,-10,-15
The mean of d, Xd = Σx / n = - 7.14285714
The standard deviation of the difference, Sd = 10.4948967 (using calculator)
Sample size, n = 7
Tcritical at 90%, df = 7 - 1 = 6
Tcritical = 1.943176
Confidence interval :
- 7.14285714 ± 1.943176 * 10.4948967/√7
Confidence interval :
- 7.14285714 ± 7.7079925
(−14.850850 ; 0.565135)
