Answer: [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]
This is the same as writing 7*Ln( e^(2x) + 10) + C
=======================================================
Explanation:
Start with the equation [tex]u = e^{2x}+10[/tex]
Apply the derivative and multiply both sides by 7 like so
[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]
The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)
This way we can do the following substitutions:
[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]
Integrating leads to
[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]
Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.
To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]
I need help with question 24
Answer:
D
Step-by-step explanation:
angle ABC=angle ADC
angle BAC=angle DCA
AC=CA
What is the ratio of 338 and 508
RATIO OF 338 : 508
=> 169 : 254
Drag and drop a power into each box to match its number.
1,000 --- ( )
10,000 --- ( )
1,000,000 --- ( )
(10^2) (10^3) (10^4) (10^5) (10^6)
The match of the expressions are:
1,000 --- (10^2) 10,000 --- (10^4) 1,000,000 --- (10^6) How to rewrite the numbers as powers?The numbers are products of 10.
This means that the numbers can be represented as exponents, where the base is 10 and the exponent is the number of zeros.
Using the above highlight, we have:
1,000 --- (10^2) 10,000 --- (10^4) 1,000,000 --- (10^6)Read more about powers and exponents at:
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help pleaseeeeeeeeee
Which of the following functions best fits the data shown in the scatterplot below? y=100x+2y is equal to 100 x plus 2 y=20x2+10y is equal to 20 x squared plus 10 y=4x+8y is equal to 4 to the x th power plus 8 y=2x+5y is equal to 2 to the x th power plus 5
The equation of the scatter plot is (a) y = 100x + 2
How to determine the equation of the scatterplot?The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{102 - 2}{1 - 0}[/tex]
m = 100
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 100(x -0) + 2
Evaluate
y = 100x + 2
Hence, the equation of the scatter plot is (a) y = 100x + 2
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Bill is making a movie and needs to cast some actors. There are 5 actors ( Anne, Lisa, Diana, Maggie, and Susan ) interested in playing the female lead role, and 2 actors ( Jacob and Mark ) interested in playing the male lead role. Anne and Mark are Bill's siblings. What is the probability Bill will cast a family member in the movie?
Answer:
2 out of seven or 2/7 or 28.5%
Step-by-step explanation:
there are two "yeses" out of 7 total choices
HI HELP PLEASE
The height of female students in Cromartie High is normally distributed. If 95% of females are
between 57.6 and 70.4 inches tall centered about the mean, find the average height and standard
deviation for female students at Cromartie High.
Using the Empirical Rule, it is found that the mean is of 64 inches and the standard deviation is of 3.2 inches.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.The normal distribution is symmetric, hence the mean is given by:
M = (57.6 + 70.4)/2 = 64.
57.6 is two standard deviations below the mean, hence the standard deviation is found as follows:
57.6 = 64 - 2s.
2s = 6.4
s = 3.2.
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When there is no traffic, it takes Rina 4 hours to get from Boston to New York. Once, Rina started her trip to New York at a speed of 60 mph, but after 2 1/3 hours of driving she stopped for 40 minutes. She had to drive at a speed of 45 mph for the rest of her trip. How long was her trip?
The whole trip was 0.185 Km or 185 m long.
What is speed ?Speed is the time rate at which an object is moving along a path.
Given:
For 7/3 hours speed is = 60 mph = 0.06 kmph
For 40 minutes or 2/3 hours = 0 mph
for 1 hours = 45 mph or 0.045 kmph
The total distance she travels
= 7/3*0.06+ 2/3*0+ 1*0.045
=0.185 Km or 185 m
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What is 10 to the power of 3.
I would like to thank everyone that asked and answered questions I was stuck on. I graduated last week and couldnt have done it without Brainly.
Answer:
1000
Step-by-step explanation:
Hello!
10³ can be expanded to 10 x 10 x 10
Multiplying it out, we get 1000.
When multiplying by 10 you basically add a zero to the end, so we add 3 zeroes in total, which gives us 1000.
ExponentsWarning! [tex]x^y[/tex] is not [tex]x*y[/tex]. A very common error.
Instead, picture it as we are multiplying "x" by itself for "y" number of times.
I appreciate your kind comments!
Q: Wilma estimates that she’ll drive about 18,000 miles during the year. The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighborhood is $2.72. Locate the error in her calculations, and select the correction.
A: Wilma made a mistake in step 2. Instead of dividing by 12, she should have divided by 24. She should budget $170 per month for fuel expenses.
The mistake is made in the second step. The correct steps are given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Wilma estimates that she’ll drive about 18,000 miles during the year.
The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighbourhood is $2.72.
Locate the error in her calculations, and select the correction.
Step - 1
18000 miles/year
18000 miles / 12 months = 1500 miles/month
Step 2
1500 miles/month
1500 miles/month / 24 miles per gallon = 62.5 gallons/month
62.5 gallons/month
Step 3
(62.5 gallons/month) x ($2.72/gallons) = $170 cost/month
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I have 1/3 of a pie. You have 1/3 of a pie. Add the pieces of pie together. How much pie do we have?
Answer:
2/3
Step-by-step explanation:
To add fractions add the numbers on top to each other and leave the bottom numbers alone if they are the same number.
[tex]\frac{1}{3}+\frac{1}{3}=\frac{1+1}{3}=\frac{2}{3}[/tex]
What is the answer to this
PLEASE HELP!!!!!! WHAT IS THE ANSWER
Answer:
B
Step-by-step explanation:
Divide y by x for each ordered pair:
2/4 = 1/2
3/6 = 1/2
5/10 = 1/2
7/14 = 1/2
All ratios are equal, so it is proportional.
Answer: B
Answer:
b
Step-by-step explanation:
mark brainliest
Pls Help I’m so confused how do you do this
Answer: A
Step-by-step explanation:
[tex]$$Given $m \angle A=9 x-7, \quad m \angle B=7 x-9, m \angle C=28-2 x$ \\For the triangle $m \angle A+m \angle B+m \angle c=180$$$\begin{aligned}&\Rightarrow(9 x-7)+(7 x-9)+(28-2 x)=180 \\&\Rightarrow 9 x+7 x-2 x-7-9+28=180 \\&\Rightarrow 14 x=180-28+16 \\&\Rightarrow 14 x=168 \\&\Rightarrow \quad x=12\end{aligned}[/tex]
[tex]$$Therefore,\\&m \angle A=9 x-7=9 \times 12-7=101^{\circ}\\&m \angle B=7 x-9=7 \times 12-9=75^{\circ} \\&m \angle C=28-2 x=28-2 \times 12=28-24=4^{\circ}\\[/tex]
[tex]$$Since $m \angle A=101^{\circ}$ so $B C$ is the longest side of a triangle $\triangle A B C$ \\\\Since $m \angle C=4^{\circ} S 0$ SB is the shortest side of a triangle $\triangle A B C$\\\\So listing the sides in $\triangle A B C$ from shortest to longest is: (a) $\overline{A B}, \overline{A C}, \overline{B C}$[/tex]
PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE
Answer:
Circumference: 25.12m
Area: 50.24 [tex]m^{2}[/tex]
Step-by-step explanation:
Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius
C=3.14*2*4=3.14*8=25.12
Formula for area of a circle: A=[tex]\pi r^{2}[/tex]
A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24
Write the standard form of the equation of the circle with the given characteristics.
Center: (0, 0); Radius: 2
To determine the equation of a circle, use the standard form of a circle (x - h)² + (y - k)² = r² where,
(h, k) is the center; andr is the radiusSubstitute the values of the center and radius to the standard form.
Given:
(0, 0) - center
2 - radius
(x - h)² + (y - k)² = 2²(x - 0)² + (y - 0)² = 4x² + y² = 4Answer:
The equation of the circle is x² + y² = 4.Wxndy~~
The Smith family pays a rate of 27 mills in property tax. The assessed value of their home is $98,000. What is their property tax?
Their property tax would be =$ 26,460
Calculation of property taxA mill is one-thousandth of a dollar, and in property tax terms is equal to $1.00 of tax for each.
Therefore 27 mills = $27 for every $1,000 of assessed value, or 2.7%.
To calculate the property tax would
= 27/100× 98,000
= 2646000/100
=$ 26,460
Therefore, Their property tax would be =$ 26,460
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what is the median of the data set represented by the box plot shown below? 38,45,50,60,75
Answer:
50
Step-by-step explanation:
If 30% of a number is 78 and 65% of the same number is 169, find 95% of that
number.
Answer:
let say the number is x, then 30x÷100=78, x=260...from this we can calculate 95 percent of 260 which is equal to 247
The 95 percentage of the number is A = 247
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the number be represented as n
Now , We can set up two equations based on the given information
30 percentage of the number is 78 ,
So , 0.3 ( n ) = 78
0.65 ( n ) = 169
Solving for n in the first equation, we get:
n = 260
Substituting n = 260 into the second equation, we can check that it is true:
0.65(260) = 169
Now, we can find 95% of the number by multiplying it by 0.95
0.95 x 260 = 247
Hence , 95% of the number is 247
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what is the solution to the trigonometric inequality 2sin(x)+3>sin ^2(x) over the interval
The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π
How to solve trigonometric inequality?We are given the trigonometric Inequality;
2 sin(x) + 3 > sin²(x)
Rearranging gives us;
sin²(x) - 2 sin(x) - 3 < 0
Factorizing this gives us;
(sin(x) - 3)(sin(x) + 1) < 0
Thus;
sin(x) - 3 = 0 or sin(x) + 1 = 0
sin(x) = 3 or sin(x) = -1
sin(x) = 3 is not possible because sin(x) ≤ 1.
Thus, we will work with;
sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.
Then, x = sin⁻¹(-1)
x = 3π/2.
Now, if we split up the solution domain into two intervals, we have;
from 0 ≤ x < 3π/2, at x = 0. Then;
sin²(0) - 2 sin(0) - 3
= 0² - 0 - 3
= -3 < 0
Thus, the interval 0 ≤ x < 3π/2 is true.
From 3π/2 < x ≤ 2π, take x = 2π. Then;
sin²(2π) - 2 sin(2π) - 3
= 0² - 0 - 3
= -3 < 0
Thus, the interval 3π/2 < x ≤ 2π is also true.
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Beth gets a sum of 5 when she rolls two fair number cubes. What is the probability that one of the fair number cubes is a 1?
Using it's concept, it is found that there is a 0.5 = 50% probability that one of the fair number cubes is a 1.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The outcomes of the pair of cubes that result in a sum of 5 are as follows:
(1,4), (2,3), (3,2), (4,1).
Of those 4 outcomes, 2 involve a number 1, hence the probability is given by:
p = 2/4 = 0.5.
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which function below has the smallest slope?
f(x)
f(x) = 2x - 3
Answer:
f(x)
Step-by-step explanation:
f(x) is a little represented number after solving for x but
f(x)=2x-3 is more bigger
Subtract 5x - 4 from the sum of -3x - 4 + y and 4x - y
Answer:
-4x
Step-by-step explanation:
((-3x-4+y) + (4x-y)) - (5x-4)
= (-3x-4+y+4x-y) - 5x+4
= (x-4) -5x+4
=x-4-5x+4
=-4x
Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram
The probability that the second ball drawn is black is 4/10 = 2/5
How to find the probability?
There are two cases. The case where the first ball is red is the first one.
The probability of drawing a red ball is equal to the quotient between the number of red balls and the total number of balls.
p = 3/5
Then, the probability of drawing a black ball in the second attempt is computed in the same way, but because we already drew a ball, now the total number of balls is 4, so we have:
q = 2/4 = 1/2.
So the joint probability is:
P = (3/5)*(1/2) = 3/10.
Then we have the case where both balls are black, the probabilities now are:
p = 2/5
q = 1/4
So the joint probability is:
P = (2/5)*(1/4) = 1/10
The total probability is the sum of the two above:
probability = 3/10 + 1/10 = 4/10.
The probability that the second ball drawn is black is 4/10 = 2/5
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The graph of the function f(x)=−4(x−3)2+9 will be a parabola opening in which direction?
Answer:
downwards
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
• if a > 0 then parabola opens upwards
• if a < 0 then parabola opens downwards
for
f(x) = - 4(x - 3)² + 9 with a = - 4 < 0 , then
the parabola opens downwards
Please explain as well!
Answer:
The height of the other book is 2 3/4 inches.Step-by-step explanation:
From the information,we get:
Two stacks of books together are = 7 1/2 inches tall.
One stack is given,that is = 4 3/4 inches.
To Find:
The height of the other.Solution:
Let us assume that the other height of the book be x.
Then the equation will be:
[tex] 4\cfrac{3}{4} + x = 7\cfrac{1}{2} [/tex]
Solve for x to get the other book's height.Convert the mixed fractions to fractions:
[tex] \implies \: \cfrac{19}{4 } + x = \cfrac{15}{2} [/tex]
Subtract 19/4 from both sides:
[tex] \implies \: x + \cfrac{19}{4} - \cfrac{19}{4} = \cfrac{15}{2} - \cfrac{19}{4} [/tex]
[tex] \implies \: x = \cfrac{11}{4} =\boxed{ 2 \cfrac{3}{4} \rm \: inches}[/tex]
Hence, we can conclude that:
The height of the other book is 2 3/4 inches.
What is the radius of the circle with center at (-6, -4) that goes through the point (1, -7) rounded to the nearest tenth?
Answer:
dhususbdgdg
Step-by-step explanation:
hdhakuxtsjwkbevdvsiw in e
7x^2+3y^2+12x+2y-6=0 Help me find the value of a,b,c and the discriminant number
Answer:
b o a h d
Step-by-step explanation:
1*5 3%9 46% &45 that is the answer
PLS HELP ME ASAP!!!!
B. x^9
just simplify
Use the net to determine the total surface area.
134.4 in
92.8 in
103.2 in
72 in