Answers
[tex]I=\displaystyle \int \dfrac{\sqrt x}{\sqrt x -4} ~dx\\\\\text{Let,}\\\\~~~~u=\sqrt x-4\\\\\implies \dfrac{du}{dx} = \dfrac d{dx} \left( \sqrt x -4 \right)\\\\\implies \dfrac{du}{dx} = \dfrac 1{2 \sqrt x} \\\\\implies dx =2\sqrt x~ du\\\\\\I= \displaystyle \int \dfrac{u+4}{u+4 -4 } 2(u+4) du\\\\\\~~~=2\displaystyle \int \dfrac{(u+4)^2}{u} du\\\\\\~~~=2\displaystyle \int \dfrac{u^2+ 8u+16}{u} du\\\\\\~~~=2\displaystyle \int \left(u+8+\dfrac{16}u\right) du\\\\\\[/tex]
[tex]~~~=2\left(\displaystyle \int u ~ du + \displaystyle \int 8 ~ du + \displaystyle \int \dfrac{16} u ~ du\right) \\\\\\~~~=2\left( \dfrac {u^2}2 + 8u+16\ln |u| \right) +C\\\\\\~~~~= u^2 + 16u+ 32 \ln |u|+C\\\\\\~~~~=\left( \sqrt x -4 \right)^2 + 16\left( \sqrt x -4 \right) +32 \ln |\sqrt x -4|+C\\\\\\~~~~= x-8\sqrt x+16 +16\sqrt x -64 +32 \ln \left|\sqrt x-4 \right|+C\\\\\\\~~~~=x+8\sqrt x -48 +32\ln|\sqrt x -4| +C[/tex]
Related Questions
what is 10066×140 please help me and explain the answer
Answers
Your answer would be 1,409,240
you would mutpliy 0 and 9 first and keep mutpliying until you get your answer
Answer:
The answer is 1,409,240
Step-by-step explanation:
I asume you are doing this by hand so here are the steps:
1. set up the problem- whitch would look like this
10066
x 140
Now you have to mutiply the 1s place, by all the number places of the top number
Sence you have a zero in the 1s place you can just put a x, whitch would look like:
10066
x 140
x
Now you do that for all the places
2 2 * Make sure you rase the number to the next place
10066 4*6 = 24 24+4= 28 4*0=0
x 140
40284x
Now that you mutiplyed the 4 by everything and got the answer of 402840 (the x is just a zero) then you leave it aside and mutiply the 1s by everything whitch is much simpler.
10066 1*6= 6 1*0= 0 1*1 =1
x 140
10066xx (now you put 2 X's)
You get the answer of 1006600 and you add it with 402840
whitch is 1,409,240 (and that is your answer)
Tabp rest with friends. How many sweets will she give to her friends? 18 13. A train arrives at the station with 150 passengers on board. 25 of the passengers get off the train in Spanish town, and then 35 passengers board the train. How many passengers are on the train when it leaves the station? * Yout Youyanswer 14.30 people watched the soccer game last night. Tickets cost $2.75 each. Half of these fans bought a program at $1.50 each. How much money was collected?
Answers
Answer: it is 205 I'm not sure if it's correct or not
Les gusta mi dibujo soy nueva
Answers
Answer:
Si, es muy bueno!
Step-by-step explanation:
759 is 45% of what number?
Answers
Answer:
1686.67
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $2000 in the account in 5 years? Assume the account earns 2% interest compounded monthly.
Answers
Answer:
$1950.74
Step-by-step explanation:
step 1
x(1 + 0.06/12)^5=2000
step 2
x= 2000/(1 + 0.06/12)^5
= 1950.741337
Answer: 500
Step-by-step explanation:
formula for interest is
I= Principle x Rate x Time
2% as a decimal is 0.02
Match each expression on the left with its corresponding simplified form.
A) m + 5
B) m + 3
C) m + 4
D) m + 8
note: there is no single answer. every single answer has to get matched
Answers
The equivalent expressions are: (4 + m) + 1 = m + 5, (m + 3) + 1 = m + 4, (2 + m) + 6 = 2 + m + 6 and (1 + m) + 2 = m + 3
What are equivalent expressions?Equivalent expressions are expressions that have equal values when evaluated
Start by evaluating each expression.
(4 + m) + 1
Remove the bracket
(4 + m) + 1 = 4 + m + 1
Evaluate
(4 + m) + 1 = m + 5
(m + 3) + 1
Remove the bracket
(m + 3) + 1 = m + 3 + 1
Evaluate
(m + 3) + 1 = m + 4
(2 + m) + 6
Remove the bracket
(2 + m) + 6 = 2 + m + 6
Evaluate
(2 + m) + 6 = m + 8
(1 + m) + 2
Remove the bracket
(1 + m) + 2 = 1 + m + 2
Evaluate
(1 + m) + 2 = m + 3
Hence, the equivalent expressions are: (4 + m) + 1 = m + 5, (m + 3) + 1 = m + 4, (2 + m) + 6 = 2 + m + 6 and (1 + m) + 2 = m + 3
#SPJ1
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Alicia and Bennie have decided to play a game. They each draw as many flowers on paper as they can within one minute, repeating this game many times. The number of flowers Alicia draws and the number of flowers Bennie draws are independent. The number of flowers Alicia draws within 1 minute, A, is approximately Normally distributed with a mean of 38 flowers and a standard deviation of 1.8 flowers. The number of flowers Bennie draws in 1 minute, B, is approximately Normally distributed with a mean of 41 and a standard deviation of 2.6 flowers. Let D represent the difference, A – B, in the number of Alicia’s and Bennie’s flowers drawn in 1 minute.
What is the probability that Alicia draws fewer flowers than Bennie in any 1 minute?
Answers
Answer:
Because The Flowers Bennie drew are independent
Answer:
0.829
Step-by-step explanation:
suppose the population of a certain city has been doubling every 30 years and the population was 48,000 in 1900. what will the population be in 2020?
Answers
Answer:
768000
Step-by-step explanation:
From 1900 to 2020 = 120 means that it doubles 4 times ( once every 30 years)
=> 48000 * 2 ^ 4 = 768000
For 1.8 hours, Layla drove her car east at a constant velocity. In this time, she drove 99 kilo meters and passed a motorcycle that was driving at 45 kilo meters per hour. What was her car's velocity?
Write your answer as a whole number.
kilo meters per hour to the east
Answers
Answer:
55 km/hr
Step-by-step explanation:
speed = distance / time
distance = 99 km
time = 1.8 hours
velocity = 99 km/ 1.8 hours= 55 km/hr
since distance is to the east, the velocity is also to the east
I need this answered asappp
Answers
Answer: f(-4)=-4f
f(-3)=-3f
B.
Step-by-step explanation:
Look at the cube, and the net of this cube. What is the surface area of this cube? Cube with one side labeled 16 feet. Net of the same cube also shown with one side labeled 16 feet.
Answers
Answer:
[tex]486[/tex] [tex]in^2[/tex]
Step-by-step explanation:
we know that
The surface area of the cube is equal to the area of its six square faces
so
[tex]SA=6b^2[/tex]
where
b is the length side of the cube
we have
[tex]b=9[/tex] [tex]in[/tex]
substitute
[tex]SA=6(9)^2=486 in^2[/tex]
Write the following as an inequality (-1,43)
Answers
Answer:
-1<x<43
Step-by-step explanation:
What would be your first step in solving -3x > 0?
A. multiply both sides by -3 and flip your sign
B. divide both sides by -3 and flip your sign
C. multiply both sides by 3 and flip your sign
D. divide both sides by 3 and flip your sign
Answers
Answer:
I would divide both sides by -3 then flip your sign since it is a multiplication equation in -3x which means you have to isolate it to find x.
Answer:
D
Step-by-step explanation:
You divide both sides by 3 and then you flip the sign.
Val needs to find the area enclosed by the figure. The figure is made by attaching
semicircles to each side of a 46-m-by-46-m square. Val says the area is 1,206.12
m². Find the area enclosed by the figure. Use 3.14 for 1. What error might Val have
made?
Answers
Answer: See below
Step-by-step explanation:
Radius of the semicircle = 46/2 = 23 m
[tex]\therefore$ Area enclosed by the figure $=4 \times$ Area of semicircles + Area of square \begin{aligned} \\&=4 \times 3.14 \times(23)^{2} \times \frac{1}{2}+(46)^{2} \\&=3322.12+2116 \end{aligned} \\\\\\Area enclosed $=5438.12 \mathrm{~m}^{2}$[/tex]
So, Val might have have subtracted 2116 from 3322.12 instead of adding since 3322.12 - 2116 = 1206.12
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS! im not getting myself a virus
Answers
Answer:
i think it is diameter
Step-by-step explanation:
if you are in England
Answer:
CHORD
Step-by-step explanation:
A chord of a circle is any line segment joining two points on the circumference of the circle
(Diameter is the longest chord of a circle which passes through the center of the circle)
Since this line does not pass through the center,this is a chord
select the correct answer.which graph shows a line with a slope of 0?
Answers
Step-by-step explanation:
the first video man and share with you search the Internet resources to help you find the best service providers to get your free and
About 75% of the girls in grade 7 at Grande Rock Middle School prefer colored jeans to the regular blue ones. The randomly generated numbers in the table simulate this situation. The letter C represents colored jeans, and B represents blue jeans. CCCBC BBCCC CCBBC CCBBC CCCCC CCCCC BCCCC CBCCC CCCCB CCCCC BBCCC CCCBB CCCCC CBCCC BCCBC CCCBB BCCCC CCCCB CCCBC CCBCC Based on the data, the estimated probability that exactly four out of five girls prefer colored jeans is .
Answers
Answer:
To find this you do 5 x 0.75
0.75 represents the amount of girls that represent colored jeans
So the answer is 3.75
Step-by-step explanation:
Hope this helps!
Find the mean 3,4,4,2,5,7,2
Answers
Which of the following cannot be determined from the boxplots shown?
16
14
12
10
Set A
Set B
A. The minimum of set B is smaller than the minimum of set A
B. The maximum of set A is the same as the maximum of set B
OC. The median of set A is larger than the median of set B
OD. The mean of set A is larger than the mean of set B
Answers
The correct option is D the mean of set A is larger than the mean of set B.
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
Here in the the box and whisker plot data values are not marked and these based on five points so mean cannot be determined here because mean required marked values.
The mean formula is given as the average of all the observations. It is expressed as Mean = {Sum of Observation} ÷ {Total numbers of Observations}.
But here in box and whisker plot no actual values are known so we can't find the mean.
Hence mean cannot be determined here with that given data.
For more details on mean follow the link below:
https://brainly.com/question/12513463
NO LINKS!! Graph the following rational functions. Please show all of the work
Answers
Answer:
To graph rational functions:
Find any asymptotes (draw them as dotted lines, unless they are x and y axis)Find any x-intercept(s) and y-interceptFind the values of y for different values of xPlot the points and connect them with a smooth curvePart (a)[tex]\textsf{Asymptote} \implies (x+3)^2=0 \implies x=-3[/tex]
[tex](x+3)^2\geq 0 \implies f(x) > 0 \implies \textsf{asymptote}:y=0[/tex]
[tex]\textsf{y-intercept}\implies \dfrac{1}{(0+3)^2}=\dfrac{1}{9} \implies \left(0,\dfrac{1}{9}\right)[/tex]
Part (b)[tex]\textsf{Factor denominator} \implies x^2+2x-3=(x-1)(x+3)[/tex]
[tex]\textsf{Asymptote} \implies x-1=0 \implies x=1[/tex]
[tex]\textsf{Asymptote} \implies x+3=0 \implies x=-3[/tex]
[tex]\textsf{x-intercept} \implies x+1=0 \implies x=-1 \implies (-1,0)[/tex]
[tex]\textsf{y-intercept}\implies \dfrac{0+1}{0^2+2(0)-3}=-\dfrac{1}{3} \implies \left(0,-\dfrac{1}{3}\right)[/tex]
Part (c)[tex]\textsf{Asymptote} \implies x-2=0 \implies x=2[/tex]
[tex]\textsf{x-intercepts} \implies x^2-9=0 \implies x=\pm 3 \implies (-3,0)\:(3,0)[/tex]
[tex]\textsf{y-intercept}\implies \dfrac{0^2-9}{0-2}=\dfrac{-9}{-2}=4.5 \implies (0,4.5)[/tex]
North of Carthage is this, it is a shallow evaporate lake:
A. Rub al-Khali
B. None of these
C. Sebkhet Arina
D. Sebkhet Qaddafi
Answers
Answer:
b none of these..........
The sides of an isosceles triangle are28 ,28 ,10 and long. What is the area of the triangle?
Answers
Answer: Approximately 137.74977 square units
===================================================
Explanation:
We can use Heron's formula to find the area of a triangle when given all three sides.
First we need the semiperimeter
s = semiperimeter
s = (perimeter)/2
s = (a+b+c)/2
s = (28+28+10)/2
s = 33
Now we can compute the area of the triangle.
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\\\A = \sqrt{33(33-28)(33-28)(33-10)}\\\\A = \sqrt{18975}\\\\A \approx 137.74977\\\\[/tex]
Anna draws an angle in her notebook. In how many points do the rays intersect?
A. 2
B. 0
C. 1
D. 3
Answers
Answer:
The Answer is C
Step-by-step explanation:
Anna draws a angle that intercets at 1
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The exact number of points at which the two rays will intersect is 1. The correct option is C.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
As per the definition of an angle, the point at which the two of the given rays will intersect each other is exactly 1 point.
Hence, the exact number of points at which the two rays will intersect is 1.
Learn more about Angle here:
https://brainly.com/question/7116550
#SPJ2
Mato is making a leather belt inlaid with beads. On the first day there were b beads on the belt. On
the fourth day, there were b³ beads on the same belt. There were 216 beads on the belt on the
fourth day.
How many beads were on the belt on the first day?
Answers
Answer:
6
Step-by-step explanation:
On the fourth day, there were b^3 beads and 216 beads on the belt, which means b^3 = 216. Taking the cube root of both sides, we have b = 6, which means there were 6 beads on the belt on the first day.
Answer:
6
Step-by-step explanation:
A triangle has one angle that is 70 degrees and another that is 75 degrees. What is the third angle value in degrees?
Answers
Answer:
35 degrees is the third angle's value.
Which equation represents a line that is perpendicular to the line passing through (-8,7) and (2,4)?
Answers
Explanation:
Step 1) Because this is already solved for y we can get the slope of the perpendicular line by taking the slope of the given line (-3) and "flipping" it and reversing the sign:
−3 becomes −−13→+13→13
Therefore the slope of the perpendicular line is 13
Step 2) Use the point slope for to find the perpendicular equation:
y−1=13(x−−1)
y−1=13(x+1)
y−1=13x+13
y−1+1=13x+13+1
y−0=13x+13+33
y=13x+43
y=(13)x+(43)
Explanation:
Need to show work for my answer working on limits
Answers
Answer:
[tex]\displaystyle \lim_{x \to \infty} \frac{-4x^8 + x^3 - x + 7}{x^4} = - \infty[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \lim_{x \to \infty} \frac{-4x^8 + x^3 - x + 7}{x^4}[/tex]
Step 2: Evaluate
[Limit] Simplify:[tex]\displaystyle \lim_{x \to \infty} \frac{-4x^8 + x^3 - x + 7}{x^4} = \lim_{x \to \infty} \bigg( -4x^4 + \frac{1}{x} - \frac{1}{x^3} + \frac{7}{x^4} \bigg)[/tex][Limit] Apply Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to \infty} \frac{-4x^8 + x^3 - x + 7}{x^4} = -4(\infty)^4 + \frac{1}{\infty} - \frac{1}{(\infty)^3} + \frac{7}{(\infty)^4}[/tex]
Recall that infinity in the denominator converges to 0. Therefore, we can focus on the first part:
[tex]\displaystyle \begin{aligned}\lim_{x \to \infty} \frac{-4x^8 + x^3 - x + 7}{x^4} & = -4(\infty)^4 + \frac{1}{\infty} - \frac{1}{(\infty)^3} + \frac{7}{(\infty)^4} \\& = -4(\infty)^4 \\& = -4(\infty) \\& = \boxed{- \infty} \\\end{aligned}[/tex]
∴ we have found the limit to equal negative infinity.
---
Learn more about limits: https://brainly.com/question/27517668
Learn more about calculus: https://brainly.com/question/27351658
---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Which pair or pairs of polygons are congruent?
pair 1
pair 2
pair 3
Answers
Answer:
C
Step-by-step explanation:
expression represents the product of b and 34?
Answers
Answer:
b*34
Step-by-step explanation:
an expression does not include an equal sign but an equation does
Y = 1/2x^2+1/4x+1/8
4. Find the slope of the line tangent at the given x
Answers
Answer:
dy/dx = x + ¼
Step-by-step explanation:
Using differentiation to find the given value,
[tex]y = \frac{1}{2} {x}^{2} + \frac{1}{4} x + \frac{1}{8} \\ \frac{dy}{dx} = 2(\frac{1}{2}) {x}^{2 - 1} + 1(\frac{1}{4} ) {x}^{1 - 1} + 0 \\ = x + \frac{1}{4} [/tex]