Looks like the integral should be
[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]
Expand the denominator:
[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]
Notice that
[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]
In order to use this substitution, expand the integral as
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]
In the first integral, use the previously mentioned substitution:
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]
[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]
In the second integral, complete the square in the denominator:
[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]
Now substitute
[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]
so that
[tex]\sec t=\dfrac{8x+13}5[/tex]
Then
[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]
and the integral becomes
[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]
[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]
[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]
So, the integral is
[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]
3. If 7 large pizzas are purchased for a party, the amount of pizza each person can have is
inversely proportional to the number of people who come to the party. If 14 people come to
the party, each person can have 6 slices. How many slices can each person have if 21 people
come to the party.
Answer:
9 slices
Step-by-step explanation:
Set up a proportion:
[tex]\frac{14}{6}[/tex] = [tex]\frac{21}{x}[/tex]
Cross multiply and solve for x, the amount of slices if 21 people come:
14x = 126
x = 9
So, each person can have 9 slices
aneeta bought 3 3/4 kg of apples and 4 1/2 kg guava what is the total weight of fruits purchased by her
Answer: 33/4
Step-by-step explanation:
Affirmative action commitments by many organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives that it will fill from among four women and six men. What is the probability that at least one woman is selected
Answer:
2/3
Step-by-step explanation:
We solve with combination formula
C(n, r) = nCr = n!/r!( n - r)!
The selection will happen between four women and six men
Total number of people = Total number of possibly outcomes = Four women + six men
= 10 people
This can happen in two ways
a) 2 women
b) 1 man and 1 woman
The probability that at least one woman is selected =
4C2 ×(6C1 + 4C1)÷ 2 ways / 10C2
[6 × (6+ 4)] ÷ 2 / 45
= (6 × 10) ÷ 2/45
= 30/45
= 2/3
50+30 x12 20 POINTS GUYS YESSSSSSSSSSSSSSSSSSSSSSS
Answer:
960
Step-by-step explanation:
50+30= 80
80x12=960
Answer:960
Step-by-step explanation:
50+30 = 80
80x12=960
The perimeter of the figure is 18x +2. One side is 3x − 3. Find the length of the indicated side.
Answer:
Step-by-step explanation:
3000000000
Q
100%
Laurissa rolls two number cubes, each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll.
Which two sums have an equal chance of occurring?
A. 3 and 11
B. 4 and 7
C. 5 and 8
D. 6 and 9
Answer:
Step-by-step explanation:
it’s B
7 and 4 is the only number that has a unique chance. The correct option is B.
What are permutation and combination?Combination and permutation are two different ways of grouping elements of a set into subsets in mathematics. The elements of the subset can be listed in any order in a combination. The elements of the subset are listed in a specific order in a permutation.
Let's analyze the possible sums of both dice, using the notation:
Dice₁ + Dice₂ = sum.
Also remember that we have 2 dice, with 6 options each. The total number of combinations is 6 x 6 = 36. we have 36 possible outcomes.
I will start at the extremes, the minimum that we can sum is 2, and the maximum is 12, then:
We can have 2 if:
1 + 1 = 2
Only one permutation.
and 12 if:
6 + 6 = 12
Again, only one permutation.
so 2 and 12 have the same chance (1 out of 36)
now, to have 3 we can have the:
2 + 1 = 3
1 + 2 = 3.
and to have 11
5 + 6 = 11
6 + 5 = 11
Again, 3 and 11 have the same probability (2 out of 36 options)
And now we can see a pattern.
4 and 10 will have the same chance.
5 and 9 will have the same chance
6 and 8 will have the same chance
7 is the only number that has a unique chance (and it has the largest one)
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PLS HELP I DONT UNDERSTAND :( WILL MARK BRAINLIEST!!! :)
Answer:
3/50
Step-by-step explanation:
rise over run
3/50
Answer:
A. 3/50
Step-by-step explanation:
subtract the y values in the form where the first point is subracted from the second point: 460-310=150
subtract the x values in the form where the first point is subracted from the second point: 3500-1000= 2500
then put these numbers in fraction form: 150/2500
simplify: 3/50
4= 6/a x +5
solve for x
need help asap!!! ill maek you brainliest.if anyones good at angles with proofs
Divide. Write your answer in simplest form.
can you please help me
Answer:
The answer is true!
Step-by-step explanation:
Since B is in the middle and they both are congruent.
What’s is ittttt I neeed helppp
Answer:
n = 14
Step-by-step explanation:
n+4/-2 = -9
n+4 = 18
n = 14
Answer:
n=14
Step-by-step explanation:
n+4/-2 = -9
n+4 = 18
Hope it helps :3
I am an odd number.my digits add up to 7. i am bigger than 50 and smaller than 100.who am i?
Answer:
61
Step-by-step explanation:
i hope this is correct lol
POSSIBLE POINTS 10
Il Candice can paint a room in 6 hours by herself and Grace can paint the same room in 8 hours by herself, how long will it
take them to paint it together?
Answer: 2 hours
Step-by-step explanation:
If Candice can paint a room in 6 and Grace can paint one in 8 subtract and 6 and get 2 hours
(URGENT) Country A produces about four times the amount of diamonds in carats produced in country B. If the total produced in both countries is 20,000,000 carats, find the amount produced in each country.
Answer:
A: 16,000,000 caratsB: 4,000,000 caratsStep-by-step explanation:
If the ratio is ...
A : B = 4 : 1
Then the ratio to the total is ...
A : total = 4 : (4+1) = 4 : 5
B : total = 1 : (4+1) = 1 : 5
Country A produces (4/5)×20 M carats, or 16 million carats.
Country B produces the remainder, 4 million carats.
SIMPLIFY THE EXPRESSION THEN MATCH TO ANSWER (USE ORDER OF OPERATIONS) PLS HELP I DONT UNDERSTAND TY I APPRECIATE IT
plz I need a link to solve that
A jet plane can travel 567 miles per hour. How many mile can it travel in 4hour During the first trip and 6 Hour during the scon trip
It will take 8 hours to drive 120 miles at a speed of 15 miles per hour. Hi Mia, If you drive 15 mi per hour, you will be covering 15 miles each other you travel. If you know the total distance traveled, then you can simply divide it by speed to get the time it takes to cover that distance. explanation:
yo whats i lowkey cant think rn 3/4 times 2 ??
Answer:
1.5 in a decimal
Step-by-step explanation:
i hope it helps
HELP I'm really stupid and I need an answer to this fast!
Answer:
160in^2
Step-by-step explanation:
Pls choose mine as brainliest.
Question 1 of 5
Select the correct answer.
Function k is a transformation of the parent exponential function f. What are the domain and range of function ?
kid) = -2
Domain: {5 € R1-00
Range: {y E RI y <0}
Domain: {r €R! -
Range: {y < R.y=}
Domain: {5 € R1-00 <= coo}
Range: {y e RI-
Domain: {i e RI-00 <
Range: {y € R. y > }
Submit
Answer:
It's all in the picture. good luck :)
Step-by-step explanation:
Domain : R
Range : ( - ∞, 0)
(Refer the image attached for complete question)
We have the following function -
k(x) = [tex]-2^{x}[/tex]
We have to determine its domain and range.
What do you mean by domain and range of a function?For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.
According to question, we have -
k(x) = [tex]-2^{x}[/tex]
for x = 0, the function k(0) = 1
The function k(x) has the exponential function ([tex]e^{x}[/tex]) as its parent function.
If we plot the graph of the function k(x), it will look like as shown in the figure attached.
The graph of the function k(x) = [tex]-2^{x}[/tex] is the reflection of the graph [tex]2^{x}[/tex] along x - axis.
The Domain of the function k(x) : R
The Range of the function k(x) : ( - ∞, 0)
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A basketball player shoots free throws and makes them with probability 1/7. What is the probability of the event the player will miss three in a row?
Answer:
216/343 or 0.6297 (4dp)
Step-by-step explanation:
Anytime the probability of an event occurs more than once in a particular order (one time after another in the same instance), then the probability is multiplied together. If the probability of him making the shot is 1/7, then the probability of him missing it is 6/7. This is because this is the only other possible outcomes and all outcome probabilities must add to 1 (1-1/7 - 6/7).
So, if he misses it three times in a row then the probability is:
6/7 (probability miss this first time) x 6/7 (probability miss second time) x 6/7 (probability miss 3rd time).
6/7 x 6/7 x 6/7 = 216/343
or 0.6297 (4dp)
Hope this helped!
The scale on a map says that 6 cm represents 15 km. What distance on the map in centimeters represents 20 kilometers?
Answer:
8 centimeters.
Step-by-step explanation:
[tex]6cm\ on\ map\ -> 15km\\[/tex]
Divide 3 both sides:
[tex]2cm\ on\ map\ -> 5km[/tex]
Multiply 4 on both sides:
[tex]8cm\ on\ map\ -> 20km[/tex]
8cm on the map represents 20km.
The distance of 20 Km on scale is 8 cm.
What is Scale Factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
Scale: 6cm represents 15 Km
1 cm represents 5/2 = 2.5 Km
So, the distance of 20 Km is represented by
= 20/ 2.5
= 8 cm
Hence, the distance on scale is 8 cm.
Learn more about Scale here:
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Apply the distributive property to create an equivalent expression. 6(5x - 3) =
Answer:
30x-18
Step-by-step explanation:
(6)(5x+−3)
=(6)(5x)+(6)(−3)
=30x-18
If h(x) = −x − 10, find h(−2). (1 point)
−20
1.6
−1
0
Answer:
-8
Step-by-step explanation:
substitute X with -2 across the equation
-(-2) - 10
minus times minus gives plus, hence positive 2 minus 10
+2 - 10
= -8
if x - 2y = 1 and 2x - y = -4, then x + y = ?
Answer:
x + y = -5
Step-by-step explanation:
x - 2y = 1
2x - y = - 4
then:
x = 1 + 2y
then:
2(1+2y) - y = -4
(2*1 + 2*2y) - y = -4
2 + 4y - y = -4
3y = -4 -2
3y = -6
y = -6/3
y = -2
x = 1 + 2y
x = 1 + 2*-2
x = 1 - 4
x = -3
Check:
x - 2y = 1
-3 -2*-2 = 1
-3 + 4 = 1
Answer:
x + y = -3 -2= -5
) Make a scatter plot of mice survival rate (response) against aspartame concentration (explanatory) and add the regression line. Described the direction, form, and strength of the relationship. What percent of the variation in mice survival rate can be explained by variations in aspartame concentrations
Answer & Step-by-step explanation:
Regression studies the relationship between independent / explanatory (causal) variable, dependent / response (effected) variable. Scatter plot is a diagrammatic representation of regression.
Aspartame Concentration, being a toxic substance, is likely to have negative regression relationship with mice survival rate. It implies that higher concentration leads to lower mice survival, & lower concentration leads to higher mice survival.
The relationship can be strong or weak, depicted by 'r' magnitude, depending upon the intensity of concentration impact on survival. If more percent of the variation in survival rate can be explained by variations in concentrations, regression coefficient is high. If less percent of the variation in survival rate can be explained by variations in concentrations, regression coefficient is low
write the ratio 2/7 to 4/5 as a fraction in simplest form
Point Q lies on AB. What definition, property, or postulate justifies the statement AQ + QB = AB?
Answer:
Segment Addition Postulate.
Step-by-step explanation:
The segment addition postulate justifies the statement:
[tex]AQ+QB=AB[/tex]
To help this make sense, you are namely adding segments on a line in order to achieve a complete line segment.
32(2 + 3) + 5 what is the operation
Answer: first add everything in the (parentheses) then multiply that by 32 then add 5 = 165
Step-by-step explanation:
3. find the distance of the line segment with the given end points (1, 6) and (4, 4)
Answer:
Therefore the lenght of line segment is :√13
Step-by-step explanation:
Refer to the attachment for your answer.