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]
6 2/3÷1/5 Express your answer as a mixed number in simplest form. Enter your answer in the box.
Answer:
33 1/3
Step-by-step explanation:
1. First, you want to make 6 into a fraction with a bottom/denominator of 3 to make adding 6 and 2/3 easier. So, to make 6 into a fraction with a denominator of 3 , you multiply 6 by 3 to get 18. The 18 is the numerator (top of the fraction) and 3 is the denominator (the bottom). So now you have 18/3+2/3 divided by 1/5.
2. Now, add the 18/3 and the 2/3 to get 20/3 divided by 1/5.
3. After this, you want to divide. To divide fractions, you use Keep, Change, Flip (KCF). To do this, keep the 20/3 the same, change the division sign to multiplication, and flip the 1/5 to 5/1. So, now you have 20/3 multiplied by 5/1.
4. Simplify this by multiplying 20 by 5 and 3 by 1 to get 100/3.
5. Now we have to create 100/3 into a mixed number. To do this, we know that 33 multiplied by 3 is 99, which is as close as we can get to 100 without going over. This means that we can make 100/3 into 33 and 1/3.
Hope this helps! :) If you could give me Brainliest that would be super helpful!
The mixed fraction is 33 1/3.
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
Given:
6 2/3÷1/5
On further solving the given expression
=20/3 ÷1/5
Now, division of fraction is not possible
so,
=20/3 * 5/1
=100/3
=33 /13
Hence, the mixed fraction is 33 1/3.
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Help asap neeed help
find the probability that there are no H when a fair coin is flipped three times.
(round the answer to 4 decimal points)
Step-by-step explanation:
Probability of heads is 1/2, and the probability of tails is 1/2. The probability of getting no heads (3 tails) is:
P = (1/2)³
P = 1/8
P = 0.1250
The width of a rectangular swimming pool is 12 meters less than the length, and the perimeter is 72 meters. Find its dimensions in meters
Answer:
The dimensions are 24 and 12 meters.
Step-by-step explanation:
W + L + W + L = 72 perimeter
(L-12) + L + (L-12) + L = 72
4L - 24 = 72
4L = 72 + 24 = 96 ====> L = 96%2F4 = 24.
An online music company offers 15 downloads for $19.75 and 40 downloads for $43.50. Each price includes the same one-time registration fee. What is the cost of each download and the registration fee?what could be the equation
Answer:
s
Step-by-step explanation:
Use the given conditions to write an equation in slope-intercept form. passing through (-2, 0) & (0, 2)
Answer:
Step-by-step explanation:
(2 - 0)/(0 + 2)= 2/2= 1
y - 0 = x + 2
y = x + 2
Mr. Josey is tasked with cutting the grass this weekend. He can cut 1/4 of the yard in 20 minutes. How long will it take to cut the entire yard?
ILL MARK BRAINLIST !!! SHOW WORK
Answer:
8748
Step-by-step explanation:
a^5b^-6
when replacing the variables with their values :
3^5 -6^2
3^5 = 3*3*3*3*3 = 243
(-6)^ 2 = 36
243 * 36 =
8748
Solve the equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x+21=7(x+3)-5x
Step-by-step explanation:
this is your answer.........
The equation 2x + 21 = 7(x + 3) – 5x does not have solution that mean inconsistent equation.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
2x + 21 = 7(x + 3) – 5x
Simplifying the equation, we have
2x + 21 = 7x + 21 – 5x
2x + 21 = 2x + 21
0 = 0
The equation 2x + 21 = 7(x + 3) – 5x does not have solution that mean inconsistent equation.
More about the solution of the equation link is given below.
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Help me plz It’s Algebra 1
Answer: Constant
Step-by-step explanation: It is a straight horizontal line with no dips or curves, so it is constant.
Hope this helps!
Please mark Brainliest!
Answer:
Constant
Step-by-step explanation:
It must be constant because the line is neither increasing or decreasing
In which table does y vary directly with x
Answer:
No. C
Step-by-step explanation:
please mark me brainleast
Table C shows the proportional relationship between x and y that y varies directly with x option (C) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
We have:
y vary directly with x
y ∝ x
y = kx
k is the constant.
k = y/x
Checking table A:
k = -2/1 = -4/2 ≠ -16/3
Checking table B:
k = -5/1 ≠ 18/2 = 41/3
Checking table C:
k = 26/1 = 52/2 = 78/3 = 26
Thus, table C shows the proportional relationship between x and y that y varies directly with x option (C) is correct.
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what is 5 divided by 50
Answer:
50 divided by 5: 10.
5 divided by 50: 0.1
Step-by-step explanation:
Here we will show you step-by-step with detailed explanation how to calculate 50 divided by 5 using long division.
Before you continue, note that in the problem 50 divided by 5, the numbers are defined as follows:
50 = dividend
5 = divisor
Step 1:Start by setting it up with the divisor 5 on the left side and the dividend 50 on the right side.
Step 2:The divisor (5) goes into the first digit of the dividend (5), 1 time(s). Therefore, put 1 on top.
Step 3:Multiply the divisor by the result in the previous step (5 x 1 = 5) and write that answer below the dividend.
Step 4:Subtract the result in the previous step from the first digit of the dividend (5 - 5 = 0) and write the answer below.
Step 5:Move down the 2nd digit of the dividend (0)
Step 6:The divisor (5) goes into the bottom number (0), 0 time(s). Therefore, put 0 on top.
Step 7:Multiply the divisor by the result in the previous step (5 x 0 = 0) and write that answer at the bottom.
Step 8:Subtract the result in the previous step from the number written above it. (0 - 0 = 0) and write the answer at the bottom.
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 50 divided by 5 OR 5 divided by 50 calculated using Long Division is:
50 divided by 5: 10.5 divided by 50: 0.1Please help alg 2 will give you a brainlist!!
Answer:
y = 4/3
Step-by-step explanation:
the expression can be written as,
(x^8)^1/3 divided by (x^4)^ 1/3
so by using the rules of powers we can deduce y = 4/3
The rules are,
1. (x^y)^z = X^y*z
2. x^y * x^z = x^ y+z
3. x^y / x^z = x^ y-z
Hence,
8/3 -4/3 = 4/3
Select the possible values
Answer:
all exept 1
Step-by-step explanation:
blah blah blah
Round 452,906 to the nearest hundred thousand, ten thousand, thousand, hundred, ten
Rounding 452,906 to each place is
(a) to nearest hundred thousand is 500,000
(b) to nearest ten thousand is 450,000
(c)to nearest thousand is 453,000
(d) to nearest hundred is 452,900
(e) to nearest tens is 452,910
Given :
Round the number 452,906 to each place given below
(a) Round to nearest hundred thousand
In the given number , 4 is in hundred thousand's place
To round to nearest hundred thousand, we look at the number in ten thousands place that is 5. 5 is equal to 5. So we add 1 with the number in hundred thousand . write 0 in remaining places
452,906, Round to nearest hundred thousand is 500,000
(b) To round to nearest ten thousand, we look at the number in thousands place that is 2. 2 s less than 5. So we keep 5 in ten thousands place . write 0 in remaining places
452,906, Round to nearest ten thousand is 450,000
(c)To round to nearest thousand, we have 9 in hundreds place that is greater than 5. So add 1 with 2 and write 0 in remaining places
452,906, Round to nearest thousand is 453,000
(d) To round to nearest hundred, we have 0 in tens place that is less than 5. So write 9 as it is and 0 in remaining places
452,906, Round to nearest hundred is 452,900
(e) To round to nearest ten , we have 6 in one's place that is greater than 5.
So add 1 with 0 and write 0 in one's place
To round to nearest thousand, we have 9 in hundreds place that is greater than 5. So add 1 with 2 and write 0 in remaining places
452,906, Round to nearest tens is 452,910
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A company was able to increase its staff from 127 employees to 204
employees. What was the percentage increase in staff? Round your
answer to the nearest tenth.
In a triangle the first angle is greater than the second angle by 18 degree and less than the third angle by 10 grade. Express all the angles in grade.
Answer:
The 3 angles are 62 2/3, 44 2/.3 and 72 2/3 degrees.
Step-by-step explanation:
let x be the first angle then the the second angle is x - 18 and the third angle = x + 10
The 3 angles add up to 180 so:
x + x - 18 + x + 10 = 180
3x = 180 + 18 - 10 = 188
x = 188/3 = 62 2/3 degrees.
x - 18 = 44 2/3
x + 10 = 72 2/3.
Rewrite the expression −7/8 − 2 1/4 as the sum of two numbers.
Answer:
-3 1/8.
Step-by-step explanation:
−7/8 − 2 1/4
= -7/8 + -9/4
= -7/8 - 18/8
= -25/8
= -3 1/8.
Describe and correct the error in finding the value of the power.
8 to 3power= 8x3 = 24
The exponent is written as a ______,
but it should have been used to indicate the number of
times the ______
is used as a factor.
The answer should be 8 to 3 power =____=____.
Answer:
regular number; base
Step-by-step explanation:
Answer:
1. Multiplication
2. 8
3. 8^3=512
at home any hours of service do repair service s cost the same which equation could you use to solve
Answer:
how many hours times repair service
Step-by-step explanation:
-56.5 as a mixed number
-56 is the whole number
0.5 is the fraction part (0.5 = 1/2)
If we put them back together, we get;
-56 1/2
Best of Luck!
9. Find the sum of the first 6 terms of the sequence: –3, 1, 5, 9, . . . options: A) 25 B) 48 C) 42
Answer:
C. 42.
Step-by-step explanation:
This is an arithmetic sequence with common difference d = 4 and first term a = -3.
Sum of n terms = (n/2)[2a + (n - 1)d]
Sum of six terms = (6/2)[2(-3) + (6 - 1)4]
= 3 * (-6 + 20)
= 42.
Answer:
C) 42
Step-by-step explanation:
Given is an Arithmetic Sequence, where
First term a = - 3
Common Difference d = 1-(-3)= 4
n = 6
[tex]S_6=? \\ \\ \because \: S_n = \frac{n}{2} \{2a + (n - 1)d \} \\ \\ \therefore \: S_6 = \frac{6}{2} \{2 \times ( - 3) + (6 - 1)4 \} \\ \\ \therefore \: S_6 = 3 \{ - 6 + 20\} \\ \\ \therefore \: S_6 = 3 \times 14 \\ \\ \huge \red{ \boxed{ \therefore \: S_6 = 42}}[/tex]
3) Find the total cost of a $14.50 movie with a 30% markup.
Answer:
18.85
Step-by-step explanation:
Help Me Please!! The Chilly Fizz Root Beer can was 15.2 cm high. The new can is 0.5 cm shorter. The new can has a diameter of 5.4 cm. What is the volume of the new can? Use 3.14 for the value of π.
First find the height of the cylinder:
15.2 -0.5 = 14.7
The formula for a circle is : V= [tex]\pi r^{2}[/tex] h
V= [tex]\pi (5.4)^{2} (14.7)[/tex] (substitute pi for 3.14)
V= (3.14) (5.4)² (14.7) simplfy
V= 1345.96728
Hilda rented a canoe the rental rate is $20 flat fee and 12.50 per hour. She was charged a total of 67.50. Which equation could be used to find h, the number of hours she rented the canoe.
Answer:12.50×20
Step-by-step explanation:
12.50. ×20=67.50
Solve 2b+4=3b+1 for b
Answer:
b= 3
Step-by-step explanation:
2b +4 = 3b +1
-2b. -1
b = 3
The sick days of employees every two years in a company are normally distributed with a population standard deviation of 7 days and an unknown population mean. If a random sample of 20 employees is taken and results in a sample mean of 21 days, find a 95% confidence interval for the population mean.
Step-by-step explanation:
Let [tex]$X_1, X_2, X_3,$[/tex] . . . ,Xn be the random sample of n employee's sick days. It is given that the random samples follows the Normal distribution along with standard deviation of 7 days. Let
[tex]X_i\sim N(\mu ,7)[/tex]
[tex]\bar{X} =\frac{1}{n}\Sigma X_i\sim N(\mu,\frac{7}{\sqrt n})[/tex]
or [tex]Z=\frac{\bar{X}-\mu}{7 /\sqrt n} \sim N(0,1)[/tex]
So,
[tex]P(-Z_{\alpha /2} \leq Z\leq Z_{\alpha /2} ) = 1- \alpha[/tex]
[tex]P(-Z_{\alpha /2} \leq \frac{\bar{X}- \mu}{7 / \sqrt n}\leq Z_{\alpha /2} ) = 1- \alpha[/tex]
[tex]P(\bar{X}-\frac{7}{\sqrt n} Z_{\alpha / 2} \leq \mu \leq \bar{X}+\frac{7}{\sqrt n} Z_{\alpha / 2} ) = 1- \alpha[/tex]
Therefore, the confidence interval of the population mean for α = 0.05 is
= [tex]P(\bar{X}-\frac{7}{\sqrt n} Z_{\alpha / 2} , \bar{X}+\frac{7}{\sqrt n} Z_{\alpha / 2} )[/tex]
= [tex]P(21-\frac{7}{\sqrt 20} Z_{0.05 / 2} , 21+\frac{7}{\sqrt 20} Z_{0.05 / 2} )[/tex]
= (17.93, 24.07)
hello how do I know when ratios are equivalent and when they are not?
pls answer All of the above..
1) Solve the equation.
-0.06 m = 7.2
m =
2)Solve the equation.
= -1.2
n =
Answer:
1) m=0.0083....
Step-by-step explanation:
-0.06 divided by 7.2. that isolates m.
Braden biked 10 8/9 miles on Monday. On Tuesday, he biked 3/ 4 as far as Monday. How many total miles did he bike over the two days?
Answer:
19 1/18 miles.
Step-by-step explanation:
For Tuesday's ride we need to multiply 10 8/9 by 3/4.
10 8/9 = (9*10+8) / 9 = 98/9 miles.
98 / 9 * 3/4
= 98/3 * 1/4
49/6
= 8 1/6 miles.
Total miles over 2 days = 10 8/9 + 8 1/6
= 18 + 8/9 + 1/6
= 18 + 48/54 + 9/54
= 18 57/54
= 19 3/54
= 19 1/18 miles.