Answer:
-18/0 or 0
Step-by-step explanation:
Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times the inverse tangent of the quantity x squared divided by 4, plus C one fourth times the natural log of x to the 4th power plus 16, plus C one fourth times the inverse tangent of the quantity x squared divided by 4, plus C the product of negative one fourth and 1 over the quantity squared of x squared plus 16, plus C
Answer:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx[/tex]
Required
Solve
Let
[tex]u = \frac{x^2}{4}[/tex]
Differentiate
[tex]du = 2 * \frac{x^{2-1}}{4}\ dx[/tex]
[tex]du = 2 * \frac{x}{4}\ dx[/tex]
[tex]du = \frac{x}{2}\ dx[/tex]
Make dx the subject
[tex]dx = \frac{2}{x}\ du[/tex]
The given integral becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2= 4u[/tex]
Square both sides
[tex]x^4= (4u)^2[/tex]
[tex]x^4= 16u^2[/tex]
Substitute [tex]16u^2[/tex] for [tex]x^4[/tex] in [tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du[/tex]
Simplify
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
In standard integration
[tex]\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)[/tex]
So, the expression becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Ashley has 3/4 cups of sugar. She used 1/3 of the sugar she has to make holiday cookies for her family. How many cups of sugar did Ashley use to make the holiday cookies?
13. A glass fish tank in the shape of a rectangular prism has a base that measures 22 inches by
12 inches. If the tank can hold a maximum of 3,960 cubic inches of water, how much glass
was used to construct the tank?
SA 2B+L
SA-alaw)+PH
37
ty
Answer:
Step-by-step explanation:
area of base = 22in×12in = 264 sq in
Height of tank = volume/(base area) = 3960/264 = 15 inches
Lateral area = 2(22 × 15) + 2(12 × 15) = 660+360=1020 sq in
Surface area = base area + lateral area= 264+1020=1284 sq in
PLEASE HELP ASAP!!!!!!! Which expression is equivalent to the expression m divided by n, where m and n are integers and n≠0
A) −m/n
B) m/−n
C) −m/−n
D) −(−m/−n)
Suppose a certain city has 50 licensed restaurants, of which 15 currently have at least one serious health code violation and the other 35 have no serious violations. There are five inspectors, each of whom will inspect one restaurant during the coming week. The name of each restaurant is written on a different slip of paper, and after the slips ate thoroughly mixed, each inspector in turn draws one of the slips without replacement. Label the jth trial as a success if the ith restaurant selected has no serious violations. A certain state has 500,000 licensed drivers, of whom 400,000 are insured. A sample of 10 drivers chosen without replacement. The ith trial is labeled if the ith driver chosen is insured. Although this situation would seem identical to the example above, the important difference is that the size of the population being sampled is very large relative to the sample size. In this case
P(S on 2 S on 1) = 399, 999/499, 999 = _________
(rounded to five decimal places.)
and
P(S on 10 S on first 9) = 399, 991/499, 991 = ___________
(rounded to six decimal places) = 0.80000
These calculations suggest that although the trials are not exactly independent, the conditional probabilities differ so slightly from one another that for practical purposes the trials can be regarded as with constant P(s) =_______ (rounded to one decimal place). Thus, to a very good approximation, the experiment is with n = 10 and p = 0.8.
Answer:
P(S on 2 S on 1) = 0.80000
P(S on 10 S on first 9) = 0.799996
P(S) = 0.8
Step-by-step explanation:
Given :
P(S on 2 S on 1)
= 399, 999/499, 999
= 0.80000
P(S on 10 S on first 9)
= 399, 991/499, 991
= 0.799996
P(S) = 0.8
Could use some help pls.
Answer:
9 cans of soup and the 4 frozen dinners were purchased
Step-by-step explanation:
Let x represent the number of cans of soup purchased.
Let y represent the number of frozen dinners purchased.
Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that
x + y = 13
Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. The 13 cans of soup and frozen dinners which he purchased collectively contain 4450 mg of sodium. This means that
250x + 550y = 4450 - - - - - - - - -1
Substituting x = 13 - y into equation 1, it becomes
250(13 - y) + 550y = 4450
3250 - 250y + 550y = 4450
- 250y + 550y = 4450 - 3250
300y = 1200
y = 1200/300
y = 4
Substituting y = 4 into x = 13 - y, it becomes
x = 13 - 4 = 9
Let wong has a box of cereal that states that there are 81 calories in 3/4 cup of serving. What is the rate of calories per cup
Answer:
108 calories per cup
Step-by-step explanation:
Select all the observations that are true about the scatter plot
A.Most players are between 60 and 70 inches tall.
B.Players scored between 40 and 80 points per game.
C.There is an outlier at about (72, 24).
D.There is a weak positive association between height and points scored.
Answer:
c, a, d
Step-by-step explanation:
I think?
Each statement describes a transformation of the graph of y= x. Which statement correctly describes the graph of y= x - 8?
Answer:
The function [tex]y = x[/tex] is shifted downwards by 8 units
Step-by-step explanation:
Given
[tex]y = x[/tex]
Required
Determine the transformation that gives: [tex]y = x-8[/tex]
When a function f(x) is shifted by b units, the new function g(x) is g(x) = f(x) - b
In this case:
[tex]y = x[/tex]
[tex]b = 8[/tex]
So, the new function is:
[tex]y = x - b[/tex]
Substitute 8 for b
[tex]y = x - 8[/tex]
Hence, the function is shifted 8 units downward
What are the simplest polynomial and rational function you can imagine?
f(x) = 1/x
for rational function
NEED HELP WITH GEOMETRY
Answer:
m<1 = 76°
m<2 = 76°
m<3 = 49°
Step-by-step explanation:
✔️m<1 = 180 - (47 + 57) (sum of triangle)
m<1 = 76°
✔️m<2 = m<1 (vertical angles are congruent)
m<2 = 76° (substitution)
✔️m<3 = 180 - (55 + m<2) (sum of triangle)
m<3 = 180 - (55 + 76) (substitution)
m<3 = 49°
Help Please!!! Find the slope.
Answer:
(-1,-1),(1,-4)
Step-by-step explanation:
it is the wright answer
Please help I’m being timed.
Answer:
da answerr is six
if DF is 6 and all sides are equal in length the EF side is going to be 6 as well
What is the measure (in radians) of central angle 0 in the circle below? Enter an exact expression.
Answer:
[tex] \frac{\pi^{c} }{3} [/tex]
Step-by-step explanation:
Measure of the length of an arc of a circle is given as:
[tex]l = \frac{ \theta}{2\pi} \times 2\pi r \\ \\ \pi = \frac{ \theta}{2\pi} \times 2\pi \times 3 \\ \\ 3 \theta = \pi^{c} \\ \\ \theta = \frac{\pi^{c} }{3} \\ [/tex]
Bill- Subtotal: $34.95 Tip: 15% (Find 15% of 34.95)
Answer:
I believe that 15% of 34.95 would be 5.24
Step-by-step explanation:
An employee at a shoe store has observed that taller customers have larger shoe sizes than customers who are shorter. She knows that shoe sizes are based on foot length, so she hypothesizes: Compared with shorter people, taller people have longer feet. Look for patterns in the data. Describe any patterns you find.
Answer:
hello some information related to your question is missing
answer : The pattern discovered supports the hypothesis that taller customers have larger shoe sizes but with some exceptions and this exceptions are ; at Height 5ft 10 inches two people are seen to have different shoe sizes i.e. Eduardo with shoe size : 10.25 inches and Susan with shoe size : 10inches. another exception from the pattern is Lily having a height of 5 ft and shoe length of 9 inches .
Step-by-step explanation:
From the data given the pattern discovered supports the hypothesis that taller customers have larger shoe sizes but with some exceptions and this exceptions are ; at Height 5ft 10 inches two people are seen to have different shoe sizes i.e. Eduardo with shoe size : 10.25 inches and Susan with shoe size : 10inches. another exception from the pattern is Lily having a height of 5 ft and shoe length of 9 inches .
1 + hk + j use h=-5, j = -6, and k = 6
Help me
9514 1404 393
Answer:
-35
Step-by-step explanation:
Put the values where the corresponding variables are and do the arithmetic.
1 + hk + j
= 1 + (-5)(6) +(-6)
= 1 -30 -6
= -35
Find a. Round to the nearest tenth.
9514 1404 393
Answer:
21.8 cm
Step-by-step explanation:
A useful way to write the Law of Sines relation when solving for side lengths is ...
a/sin(A) = b/sin(B)
Then the solution for 'a' is found by multiplying by sin(A):
a = sin(A)(b/sin(B)) = b·sin(A)/sin(B)
__
We need to know the angle A. Its value is ...
A = 180° -75° -31.8° = 73.2°
Then the desired length is ...
a = (22 cm)sin(73.2°)/sin(75°) ≈ (22 cm)(0.9573/0.9659)
a ≈ 21.8 cm
_____
I like to use the longest side and largest angle in the equation when those are available. That is why I chose 75° and 22 cm.
PLEASE ASNWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
Answer. 32
Step-by-step explanation:
20+4+2+6=32
what is 5.3 x 5.3 x 5.3 x5.3 as a power?
The expression 5.3 x 5.3 x 5.3 x 5.3 can be written as 5.3 raised to the exponentiation and powers of 4, or [tex]{(5.3)}^4[/tex], which evaluates to 6241.03.which means
To express this expression as a power, we need to determine the exponent that represents the number of times 5.3 is multiplied by itself. In this case, 5.3 appears four times in the multiplication.
So, the expression can be rewritten as 5.3 raised to the power of 4, or [tex]{(5.3)}^4[/tex].
The formula for expressing a number multiplied by itself n times as a power is: [tex]a^n[/tex]
In this case, a is 5.3 and n is 4.
To evaluate the expression, we can simply multiply 5.3 by itself four times:
5.3 x 5.3 x 5.3 x 5.3 = 6241.03
Therefore, 5.3 x 5.3 x 5.3 x 5.3 can be expressed as [tex]{(5.3)}^4[/tex], which is equal to 6241.03.
In summary, the expression 5.3 x 5.3 x 5.3 x 5.3 can be written as 5.3 raised to the exponentiation and powers of 4, or [tex]{(5.3)}^4[/tex], which evaluates to 6241.03.
Learn more about exponentiation and powers here:
https://brainly.com/question/32431373
#SPJ6
Evaluate the function rule below when x=-2
F(x)=1/4x
Answer:
= -1/2
Step-by-step explanation:
F=1/4(-2)
F=-1/4(2)
F=-1(2)/4
F=-2/4
F= -1/2
7 Evaluate the expression xy - 3x when x = 4 and
y=5.
A. 2
B. 5
C. 8
D. 11
Answer:
Xy-3x
Putting the values of x and y into the expression,
We have 4(5)-3(4)
20-12
8
LOOK AT PIC, ASAP, ROGHT ANSWER GETS BRAINLIEST !
Answer:
Step-by-step explanation:
The teacher has 7/8 pounds of clay given.
gives out 1/16 per station
7/8= 0.875 pound
7/8 / 1/16 pound= 14 maximum stations
14 stations divided by 2 classes = 7 in each room
Need help with this please having a hard time with it
Answer:
6.28 m^2
Step-by-step explanation:
4^2 x Pi=area of full circle
45 degree segment =1/8 of a full circle
16x3.14159=50.27 m^2 area of full circle
50.27/8=6.28 m^2 area of 1/8 circle
Answer:
90 square meters
Step-by-step explanation:
Formula for sector area--- SECTOR AREA=r^2 a/2
*Multiply the central angle by the radius squared- 45×4=180squred meter
*then, Divide by 2- 180÷2=90
071 point
Dashboard
What is the measure of anglex
Courses
X
Calendar
34
Inbox
34
History
73
63
Help
57
Answer:
B. 73°
Step-by-step explanation:
The triangle is an isosceles triangle as it has 2 equal sides. This implies that the angles opposite to the two equal sides are of the same measure.
Therefore,
x = (180 - 34) ÷ 2
x = 146 ÷ 2
x = 73°
12x + 2y = 6
A. solve for y
B. What is the slope and what is the y-intercept?
Answer:
y=3
B.Slope is -6 Y intercept is 0.5
Step-by-step explanation:
Simplify the expression.
(-0.75x + 6 ) + (5.5x + 7.4)
Find what the value of x.
60
15
30
45
Answer:
ANS;;;; 45 ...........................
5 cooks, 13 waiters and 4 other staff work at a restaurant. What is the ratio of cooks to waiters to other staff?
Answer:
1:4:1.5
Step-by-step explanation:
Please help me with this thank you!
Answer:
y = -x + 1
Step-by-step explanation:
y=mx+b
m:slope= rise/run, the line goes down 1 and over 1 so it would be -1/1 which is -1
b:y-intercept: the line crosses the y-axis at 1
plug in m=-1 and b=1 into y=mx+b
y=-1x+1
y=-x+1