Answers
Related Questions
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average? Tasha, because she has the lowest ratio since 0.9 > 0.8
B) Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
C) Jana, because she has the lowest ratio since 0.9 > 0.8
D) Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Answers
Step-by-step explanation:
as the description says, the higher the ratio the better.
9/10 = 0.9
12/15 = 4/5 = 0.8
so, Tasha has the better batting average, as she has the higher ratio.
9/10 = 27/30
12/15 = 24/30
27/30 is higher than 24/30.
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.
A s= (1, 2, 3, 4, 5, 6
B s=(purple, pink, red, blue, green, orange, yellow}
C s=(g. r, b. y. o, p)
D s= (green, blue, yellow, orange, purple, red)
Answers
The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.
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The expressions A, B, C, D, and E are left-hand sides of trigonometric identities. The expressions 1, 2, 3, 4, and 5 are right-hand side of identities. Match each of the left-hand sides below with the appropriate right-hand side.
A. tan(x)
B. cos(x)
C. sec(x)csc(x)
D. 1â(cos(x))^2/ cos(x)
E. 2sec(x)
1. sin(x)tan(x)
2. sin(x)sec(x)
3. tan(x)+cot(x)
4. cos(x)/1âsin(x)+1âsin(x)/cos(x)
5. sec(x)âsec(x)(sin(x))2
Answers
Answer:
[tex]A.\ \tan(x) \to 2.\ \sin(x) \sec(x)[/tex]
[tex]B.\ \cos(x) \to 5. \sec(x) - \sec(x)\sin^2(x)[/tex]
[tex]C.\ \sec(x)csc(x) \to 3. \tan(x) + \cot(x)[/tex]
[tex]D. \frac{1 - (cos(x))^2}{cos(x)} \to 1. \sin(x) \tan(x)[/tex]
[tex]E.\ 2\sec(x) \to\ 4.\ \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex]
Step-by-step explanation:
Given
[tex]A.\ \tan(x)[/tex]
[tex]B.\ \cos(x)[/tex]
[tex]C.\ \sec(x)csc(x)[/tex]
[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]
[tex]E.\ 2\sec(x)[/tex]
Required
Match the above with the appropriate identity from
[tex]1.\ \sin(x) \tan(x)[/tex]
[tex]2.\ \sin(x) \sec(x)[/tex]
[tex]3.\ \tan(x) + \cot(x)[/tex]
[tex]4.\ \frac{cos(x)}{1 - sin(x)} + \frac{1 - \sin(x)}{cos(x)}[/tex]
[tex]5.\ \sec(x) - \sec(x)(\sin(x))^2[/tex]
Solving (A):
[tex]A.\ \tan(x)[/tex]
In trigonometry,
[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]
So, we have:
[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex]
Split
[tex]\tan(x) = \sin(x) * \frac{1}{\cos(x)}[/tex]
In trigonometry
[tex]\frac{1}{\cos(x)} =sec(x)[/tex]
So, we have:
[tex]\tan(x) = \sin(x) * \sec(x)[/tex]
[tex]\tan(x) = \sin(x) \sec(x)[/tex] --- proved
Solving (b):
[tex]B.\ \cos(x)[/tex]
Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1
So, we have:
[tex]\cos(x) = \cos(x) * \frac{\cos(x)}{\cos(x)}[/tex]
[tex]\cos(x) = \frac{\cos^2(x)}{\cos(x)}[/tex]
In trigonometry:
[tex]\cos^2(x) = 1 - \sin^2(x)[/tex]
So, we have:
[tex]\cos(x) = \frac{1 - \sin^2(x)}{\cos(x)}[/tex]
Split
[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{\sin^2(x)}{\cos(x)}[/tex]
Rewrite as:
[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{1}{\cos(x)}*\sin^2(x)[/tex]
Express [tex]\frac{1}{\cos(x)}\ as\ \sec(x)[/tex]
[tex]\cos(x) = \sec(x) - \sec(x) * \sin^2(x)[/tex]
[tex]\cos(x) = \sec(x) - \sec(x)\sin^2(x)[/tex] --- proved
Solving (C):
[tex]C.\ \sec(x)csc(x)[/tex]
In trigonometry
[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]
and
[tex]\csc(x)= \frac{1}{\sin(x)}[/tex]
So, we have:
[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)}[/tex]
Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1
[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)} * \frac{\cos(x)}{\cos(x)}[/tex]
[tex]\sec(x)csc(x) = \frac{1}{\cos^2(x)}*\frac{\cos(x)}{\sin(x)}[/tex]
Express [tex]\frac{1}{\cos^2(x)}\ as\ \sec^2(x)[/tex] and [tex]\frac{\cos(x)}{\sin(x)}\ as\ \frac{1}{\tan(x)}[/tex]
[tex]\sec(x)csc(x) = \sec^2(x)*\frac{1}{\tan(x)}[/tex]
[tex]\sec(x)csc(x) = \frac{\sec^2(x)}{\tan(x)}[/tex]
In trigonometry:
[tex]tan^2(x) + 1 =\sec^2(x)[/tex]
So, we have:
[tex]\sec(x)csc(x) = \frac{\tan^2(x) + 1}{\tan(x)}[/tex]
Split
[tex]\sec(x)csc(x) = \frac{\tan^2(x)}{\tan(x)} + \frac{1}{\tan(x)}[/tex]
Simplify
[tex]\sec(x)csc(x) = \tan(x) + \cot(x)[/tex] proved
Solving (D)
[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]
Open bracket
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{1 - cos^2(x)}{cos(x)}[/tex]
[tex]1 - \cos^2(x) = \sin^2(x)[/tex]
So, we have:
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{sin^2(x)}{cos(x)}[/tex]
Split
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \frac{sin(x)}{cos(x)}[/tex]
[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]
So, we have:
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \tan(x)[/tex]
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) \tan(x)[/tex] --- proved
Solving (E):
[tex]E.\ 2\sec(x)[/tex]
In trigonometry
[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]
So, we have:
[tex]2\sec(x) = 2 * \frac{1}{\cos(x)}[/tex]
[tex]2\sec(x) = \frac{2}{\cos(x)}[/tex]
Multiply by [tex]\frac{1 - \sin(x)}{1 - \sin(x)}[/tex] --- an equivalent of 1
[tex]2\sec(x) = \frac{2}{\cos(x)} * \frac{1 - \sin(x)}{1 - \sin(x)}[/tex]
[tex]2\sec(x) = \frac{2(1 - \sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Open bracket
[tex]2\sec(x) = \frac{2 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Express 2 as 1 + 1
[tex]2\sec(x) = \frac{1+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Express 1 as [tex]\sin^2(x) + \cos^2(x)[/tex]
[tex]2\sec(x) = \frac{\sin^2(x) + \cos^2(x)+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Rewrite as:
[tex]2\sec(x) = \frac{\cos^2(x)+1 - 2\sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]
Expand
[tex]2\sec(x) = \frac{\cos^2(x)+1 - \sin(x)- \sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]
Factorize
[tex]2\sec(x) = \frac{\cos^2(x)+1(1 - \sin(x))- \sin(x)(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Factor out 1 - sin(x)
[tex]2\sec(x) = \frac{\cos^2(x)+(1- \sin(x))(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Express as squares
[tex]2\sec(x) = \frac{\cos^2(x)+(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]
Split
[tex]2\sec(x) = \frac{\cos^2(x)}{(1 - \sin(x))\cos(x)} +\frac{(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]
Cancel out like factors
[tex]2\sec(x) = \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex] --- proved
Here is a graph of the function h.
Use the graph to find the following
If there is more than one answer, separate them with commas
(a)
All local minimum values of
h
(b) All values at which h has a local minimum:
Answers
The graph also shows two other local maxima, at x=0.5 and x=1.5.
The local minimum(a) -4, -2, 0, 2 (b) The local minimum values of h occur at x = -4, -2, 0, and 2.These values can be seen on the graph as points at which the graph of h changes from decreasing to increasing.At each of these points, the value of h is at a minimum compared to the values of h on either side of the point.All values at which h has a local maximum: 0.5, 1.5All local maximum values of h: 2.5, 4.5.The graph of the function h is a parabola that opens upwards, with a turning point at x=1.This indicates that the function has a local maximum at this point.The local maximum values of h at these points can be determined by looking at the y-values at these points, which are 2.5 and 4.5 respectively.To learn more about All local minimum values refer to:
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The radius of a cylinder is 3 cm and the height is 6 cm.
Find the Lateral Area.
O 1541
0 5611
O 9611
3611
Answers
Answer:
Lateral Area of a Cylinder = 2πrh
=2π x 3 x 6
=36π
Option D
WILL MARK BRAINLIEST
Calculate the value of X in square DCBA
Answers
Answer:
45 degree , bc the ends are all 90 degree so divide 90 by two since the line crosses right in between
Answer:
45°
That looks like an Isosceles triangle so two sides are equal
The angle near O would be 90° cause that looks like an right angle
180-90=90
To find each angle divide by 2
90÷2=45
Please pleaseeeee help me outtt, I need it quickkk will give brainliest
Answers
Answer:
-132
Step-by-step explanation:
Split the summation to make the starting value of
k equal to 1.
Answer:S6 = - 132
Step-by-step explanation:
Find the distance between the points
(-5/2, 9/4) and(-1/2,-3/4)
Give the exact distance and an approximate distance rounded to at least 2 decimal places.
Make sure to fully simplify any radicals in first answer
Answers
Answer:
Step-by-step explanation:
distance = [tex]\sqrt{(-5/2+1/2)^{2} +(9/4+3/4)^{2} }=\sqrt{13}[/tex]=3.61
What is the growth factor of the following example? Assume time is measured in the units given.
A forest shrinks 80% per century.
a. 20 per century c. 80 per century
b. 0.20 per century d. 0.80 per century
Please select the best answer from the choices provided
Answers
Answer:
B. 0.20 per century
Step-by-step explanation:
I calculated it logically
(-3 squared +3) divided by
(10 – 6)
Answers
Answer:
research it many my answer will be wrong
3
Step-by-step explanation:
-3 square is 9, adding 3 you will have 12. 10-6 is 4. so dividing 12 by 4 would give you 3.
Simplify the following? (x^5)^4
Answers
Ian is taking a true/false quiz that has four questions on it. The correct sequence of answers
is T, T, F, T. Ian has not studied and yet guesses all answers correctly- He decides he wants
to determine how likely this is to happen using a simulation. He decides to use a fair coin to
do the simulation.
Describe the design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz.
Answers
The design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz can be Illustrated through a coin.
How to design the simulation?Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.
He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.
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What is the equation of the line that passes through the point (-4,-4) and has a
slope of -3/4?
Answers
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]
Answer:
y = -3/4x - 7
Step-by-step explanation:
Given: slope = m = -3/4
Plug this value into the standard slope-intercept equation of y = mx + b.
y = -3/4x + b
To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3/4(-4) + b
To find b, multiply the slope and the input of x(-4)
-4 = 3 + b
Now, subtract 3 from both sides to isolate b.
-7 = b
Plug this into your standard equation.
y = -3/4x - 7
This is your equation.
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Activity: Factor Theorem
Use the Remainder Theorem and Factor Theorem to determine whether the given
binomial is a factor of P(x).
P(x) = 9x³+ 6x - 40 - 2x² + 2x4; binomial: x + 5
the given problem.
Answers
The given polynomial is a factor of P(x) because P(-5)=0.
From the remainder theorem, how do you derive the factor theorem?The Remainder Theorem states that if a synthetic division of a polynomial by x = a results in a zero remainder, then x = an is a zero of the polynomial (thanks to the Remainder Theorem), and x an is also a factor of the polynomial (courtesy of the Factor Theorem).
How can you tell if P(x) is a factor of X C?The Factor Theorem states that x - c is only a factor of P(x) when P(c) = 0.
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If 4 people share a 1/2 pound chocolate bar, how much chocolate will each person receive?
Answers
Answer:
1/8 pound per person
Step-by-step explanation:
What is the name for a polygon with 4 sides
Answers
Answer: A. Quadrilateral
Step-by-step explanation:
The name for a polygon with 4 sides is a quadrilateral. Quadrilateral is a two-dimensional shape with four straight sides and four angles. The most common type of quadrilateral is the rectangle, which has four right angles. Other types of quadrilaterals include squares, parallelograms, trapezoids, and rhombuses.
Answer:
quadrilateral!!
Step-by-step explanation:
look at the beginning of the word, quad. Quad means 4 and is referring to a 4 sided figure.
a geometry class has a total of 25 students. the number of males is 5 more than the number of females. how many males and how many females are in the class
Answers
Answer:
10 females, 15 males
Step-by-step explanation:
Let the number of females in the class be x. As the number of males is 5 more than the number of females, which is x, the number of males would be shown as x+5.
The number of females plus the number of males equal 25, so we get this equation:
x + (x+5) = 25
x + x + 5 = 25
2x + 5 = 25
2x = 20
x = 10.
So, there are 10 females, and since there are 5 more males than females, there are 10 + 5 = 15 males.
800 miles in 5 hours miles per hour
Answers
1. Five-sixths of the students in a math class passed the first test. If there are 36 students in the class, how many did not pass the test? *
Answers
Answer:
(1/6) of the students did not pass.
Ans: (1/6)30 = 5 of the students did not pass
To solve this question, we need to first figure out, in fractional form, the number of students who did not pass. The problem tells us that 5/6 of the students passed. Therefore, we know that 1/6 of the students did not pass, because 5/6 + 1/6 = 1. So, all we need to do is multiply 1/6 by the total number of students:
1/6 * 36 = 6
So, 6 students did not pass.
1/6 x 36=
Cross cancel, 6 goes into 6, 1 time and 6 goes into 36, 6 times. 1 x 6 = 6
6 students did not pass.
a store has a sale where all jackets are sold at a discount of 40%. If the regular price of the jackets is $80, how many jackets could be bought at the sale if a shopper spent $576
Answers
Answer:
The shopper can but 12 jackets.
Step-by-step explanation:
80*.6 (100% - 40% = paying 60% or .6) = 48
576 / 48 = 12
Here we have a problem of percentage discounts, such that we need to find how much a given price decreases, and how many jackets we can buy considering the decreased price.
We will find that the number is 12.
Now let's see how we can get that result:
If something has an original price P, and we discount an x% of that price, the new price will be:
[tex]np = P\cdot(1 - x\%/100\%)[/tex]
Here we know that the regular price of a jacket is $80
And we have a discount of 40%
This means that the new price of these jackets will be:
[tex]np = \$80\cdot (1 - 40\%/100\%) = \$80\cdot (1 - 0.4) = \$80\cdot 0.6 = \$48[/tex]
Now we want to know how many of these jackets we can buy with $576
This will be equal to the quotient between the money we have and the new price of each jacket:
[tex]N = \$576/\$48 = 12[/tex]
This means that we can buy exactly 12 jackets at the sale.
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convert logx8=2 to exponential form
Answers
Answer:
8 = x²
Step-by-step explanation:
Logarithmic form: logₓ(8) = 2
Exponential form: 8 = x²
Huilan is 7 years older than Thomas. The sum of their ages is 79. What is Thomas’s age?
Answers
Answer:
To solve this problem, we can set up the following equation:
Huilan's age + Thomas's age = 79
Let H be Huilan's age and T be Thomas's age. We can then rewrite the equation as:
H + T = 79
We are told that Huilan is 7 years older than Thomas, so we can write the following equation:
H = T + 7
Substituting the second equation into the first equation, we get:
(T + 7) + T = 79
Combining like terms, we get:
2T + 7 = 79
Subtracting 7 from both sides, we get:
2T = 72
Dividing both sides by 2, we get:
T = 36
Therefore, Thomas's age is 36 years.
Step-by-step explanation:
Answer:
let Thomas age be a
there fore, hullans age is a+7
(a+7)+a=79
2a=79-7
2a=72
a=36
plz help quick 100 points
Answers
Answer:
30
Step-by-step explanation:
49-31+12= 30
___________
In a school containing 360 children, 198 are girls. What percent of all children are girls? What percent of the children are boys? The number of girls is what percent of the number of boys? The number of boys is what percent of the number of girls?
the number of girls is _____% of the number of boys.
Answers
Answer:
1st question :55%
2nd ":122.22%
3rd ":81.82%
Which is the equivalent of 145.12° written in DMS form?
A. 145° 7' 2"
B. 145° 12' 0"
C. 145° 2'36"
D. 145° 7' 12"
Answers
Answer:
the answer is
B. 145° 12' 0"
Write the equation of a line that is parallel to {y=-0.75x}y=−0.75xy, equals, minus, 0, point, 75, x and that passes through the point {(8,0)}(8,0)left parenthesis, 8, comma, 0, right parenthesis.
Answers
Answer:
[tex]y = 0.75x - 6[/tex]
Step-by-step explanation:
Given
Parallel to:
[tex]y = 0.75x[/tex]
Passes through
[tex](8,0)[/tex]
Required
The equation
The slope intercept form of an equation is:
[tex]y = mx + b[/tex]
Where:
[tex]m \to[/tex] slope
So, by comparison:
[tex]m = 0.75[/tex]
For a line parallel to [tex]y = 0.75x[/tex], it means they have the same slope of:
[tex]m = 0.75[/tex]
The equation of the line is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
Where:
[tex]m = 0.75[/tex]
[tex](x_1,y_1) = (8,0)[/tex]
So, we have:
[tex]y = 0.75(x - 8) + 0[/tex]
Open bracket
[tex]y = 0.75x - 6 + 0[/tex]
[tex]y = 0.75x - 6[/tex]
A company employing 10,000 workers offers deluxe medical coverage (D), standard medical coverage (S) and economy medical coverage (E) to its employees. Of the employees, 30% have D, 60% have 5 and 10% have E. From past experience, the probability that an employee with D, will submit no claims during next year is 0.1. The corresponding probabilities for employees with S and E are 0.4 and 0.7 respectively. If an employee is selected at random;
a) What is the probability that the selected employee has standard coverage and will submit no
claim during next year? b) What is the probability that the selected employee will submit no claim during next year?
c) If the selected employee submits no claims during the next year, what is the probability that the employee has standard medical coverage (S)?
please give full answer
Answers
a) The probability that the selected employee has standard coverage is 60%, and the probability that they will submit no claims is 0.4. Therefore, the probability that the selected employee has standard coverage and will submit no claims is 0.4 * 0.6 = 0.24.
b) To find the probability that the selected employee will submit no claims, we can add up the probabilities for each type of coverage. The probability that the selected employee will submit no claims is 0.1 * 0.3 + 0.4 * 0.6 + 0.7 * 0.1 = 0.33.
c) To find the probability that the selected employee has standard coverage given that they have no claims, we can use Bayes' Theorem. The probability that the selected employee has standard coverage given that they have no claims is:
P(S|N) = P(N|S) * P(S) / P(N)
Plugging in the values from the problem, we get:
P(S|N) = 0.4 * 0.6 / 0.33 = 0.73
Therefore, the probability that the selected employee has standard coverage given that they have no claims is 0.73.
what is the area of 12 1/2 feet long and 11 3/4 feet wide
Answers
now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.
[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]
Which of the following expressions is a polynomial?
Answers
Answer:
b is a polynomial
Step-by-step explanation:
[tex]f(x) = {x}^{3} - 11 {x}^{2} + {3}^{x} [/tex]
Evaluate the indefinite integral.
integar x4/1 + x^10 dx
Answers
Answer:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c[/tex]
Step-by-step explanation:
Given
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx[/tex]
Required
Integrate
We have:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx[/tex]
Let
[tex]u = x^5[/tex]
Differentiate
[tex]\frac{du}{dx} = 5x^4[/tex]
Make dx the subject
[tex]dx = \frac{du}{5x^4}[/tex]
So, we have:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx[/tex]
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, \frac{du}{5x^4}[/tex]
[tex]\frac{1}{5} \int\ {\frac{1}{1 + x^{10}}} \, du[/tex]
Express x^(10) as x^(5*2)
[tex]\frac{1}{5} \int\ {\frac{1}{1 + x^{5*2}}} \, du[/tex]
Rewrite as:
[tex]\frac{1}{5} \int\ {\frac{1}{1 + x^{5)^2}}} \, du[/tex]
Recall that: [tex]u = x^5[/tex]
[tex]\frac{1}{5} \int\ {\frac{1}{1 + u^2}}} \, du[/tex]
Integrate
[tex]\frac{1}{5} * \arctan(u) + c[/tex]
Substitute: [tex]u = x^5[/tex]
[tex]\frac{1}{5} * \arctan(x^5) + c[/tex]
Hence:
[tex]\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c[/tex]