Answer:
[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos (2x + \pi) \big| + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Trigonometric Integration
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = 2 \int {\tan (2x + \pi)} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = 2x + \pi[/tex][u] Differentiate [Derivative Properties]: [tex]\displaystyle du = 2 \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = \frac{2}{2} \int {2 \tan (2x + \pi)} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = \frac{2}{2} \int {\tan u} \, du[/tex]Simplify: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = \int {\tan u} \, du[/tex][Integral] Trigonometric Substitution: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos u \big| + C[/tex][u] Back-Substitute: [tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos (2x + \pi) \big| + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Evaluate. 10/1·(−4) Enter your answer in the box.
I’ll give brainliest if its correct on the test! (And if i can figure out how)
Step-by-step explanation:
10/1(-4)
10(-4)
=-2.5 or 5/-2
Who answer this right gets 10 pts!
Answer: 45 degrees angle
URGENT!!! Will MARK BRAINLIEST!!!
Select the correct answer.
What is the next step in solving this augmented matrix using the Gauss-Jordan elimination method?
OA.
Convert the matrix to the linear system form.
OB.
Divide R2 by 2 and R3 by 3.
OC.
The matrix is solved.
D.
This is an inconsistent matrix that cannot be solved.
O E.
Divide R1 by 2 and R3 by 3.
Answer:
B is the correct answer. I just took the test :))
Step-by-step explanation:
Option B is correct, Divide R₂ by 2 and R₃ by 3 is the next step in solving this augmented matrix using the Gauss-Jordan elimination method.
In the Gauss-Jordan elimination method, the goal is to transform the augmented matrix into row-echelon form and then into reduced row-echelon form to solve the system of linear equations.
To achieve this, we perform row operations on the matrix.
In the given augmented matrix:
[tex]\left[\begin{array}{ccc}1&0&0\\0&2&0\\0&0&3\end{array}\right] .\left[\begin{array}{c}5&8&9\end{array}\right][/tex]
We can divide R₂ (Row 2) by 2 and R₃ (Row 3) by 3 to simplify the matrix further we do this to make the leading coefficient (the number at the leftmost position in each row) of each row equal to 1, which is a requirement for row-echelon form.
After dividing R₂ by 2 and R₃ by 3, the augmented matrix becomes:
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] .\left[\begin{array}{c}5&4&3\end{array}\right][/tex]
To learn more on Matrices click:
https://brainly.com/question/28180105
#SPJ2
2/3x−1/6y=1/2
2x – 4y = 3
Answer:
30
Step-by-step explanation:
3x+6y=9
multiply by 2
6x+12y=18 ....(1)
-2x+-4y=4
multiply by 3
-6x-12y=12 ...(2)
add (1) and (2)
0+0=30
Find the missing angle
Answer:
x=33
Step-by-step explanation:
The sum of the angles of a triangle is 180
23+124+x = 180
147+x =180
x = 180-147
x =33
Answer: 33
Step-by-step explanation:
A triangle is equal to 180 degrees. So you add 124 and 23 to get 147. You would then subtract 180-147=33 and then you have your answer. Hope this helps!
Anna went to the playground at 4:05 P.M. She played on the slide for 30 minutes and the swings for 55 minutes, then went home. What time was it when Anna left the playground?
Include A.M. or P.M. in your answer (for example, 11:58 A.M.).
Answer:
5:30 P.M.
Step-by-step explanation:
30 (slide) minutes and 55 (swings) minutes. These numbers (time-wise) total up to an hour and 25 minutes. Adding this to 4:05 P.M. would mean that she left the playground at 5:30 P.M.
Hope this helps.
Mr. Hansen baked 1,692 chocolate cookies he
package them into boxes of 36 cookies each how many boxes did he fill
Answer:
47 boxes
Step-by-step explanation:
Since each box has 36 cookies, we can divide the total number of cookies by 36 to find out how many boxes he could fill.
1692/36=47
1. Using what you know about similar triangles, find an equation for the line in the diagram. Find m (slope) and b (y-intercept) in the equation of the line: y = mx + b. Label your answers in decimal form if needed. m = b = 2. What is the slope of this line? Slope = 3. Is the point (9, 11) also on the line? (Type "YES" or "NO") 4. Is the point (100, 193) also on the line? (Type "YES" or "NO") 5. Is the point (20, 33) also on the line? (Type "YES" or "NO")
Answer: WHERE IS THE DIAGRAM
Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Find the total number of each coin.
Answer:
Sophie Has 7 Dimes, And 14 Quarters
Step-by-step explanation:
Sophie Had 7 Dimes, 7 Dimes, 7 Dimes!
Sophie Had 14 Quarters, 14 Quarters, 14 Quarters!
Sophie is Bill Nye's Daughter.
PLEASE HELP
What is the value of the expression 12+23b when b=−5 ?
−176
−16
236
I don't know.
Answer: -103
Step-by-step explanation:
substitute in the value of B
12+23(-5)
multiply 23 and -5 together
12-115
solve
-103 is the answer
Answer:
-103
Step-by-step explanation:
Complete the equation.
(-4)^2 =
A population of values has a normal distribution with
μ
=
124.9
and
σ
=
45
. You intend to draw a random sample of 36 items from this population.
Find the probability that the mean of this sample is less than 105.4.
The probability that the mean of this sample is less than 105.4 is 14.46%
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\x=raw\ score, \sigma=standard\ deviation, \mu=mean,n\ is\ sample\ mean\\\\\\Given\ that\ \sigma=45,\mu=124.5,n\ =36,hence:\\\\For\ x<105.4:\\\\z=\frac{105.4-124.9}{45/\sqrt{36} }=-1.06[/tex]
From the normal distribution table, P(x < 105.4) = P(z < -1.06) = 0.1446 = 14.46%
The probability that the mean of this sample is less than 105.4 is 14.46%
Find out more at: https://brainly.com/question/7449180
Angle ABC and angle BD are complementary.
The measure of angle ABC equals (3x + 4) degrees, and
the measure of angle CBD equals (5x +6). Find the measures of both angles.
Answer:7x
11x
Step-by-step explanation:
Amy graphed a point to represent the absolute value of a number on a number line. If the original number is less than −10, describe all the possible values for the point Amy graphed on the number line.
Answer:
x>= 11 or x>10
Step-by-step explanation:
Absolute value can be used to represent the positive counterpart of a negative number. In this case, we are asked to find a number that is less than -10, meaning from -11 to negative infinity. Since we are asked to take absolute value, we would take |-11| which equals 11, and |-∞| = ∞.
So Amy graphed a value on the number line that is greater than or equal to 11, or any value greater than 10.
*Infinity is not a real number, it represents the largest number possible, which doesn't exist since numbers can continue on forever, so it can be disregarded.*
What is the equation of the line that passes through the point (-3,4)(−3,4) and has a slope of 11?
Answer:
y=5x-11 is the equation of the required line
1. find measure of A.
2. find measure of B.
3. find measure of C
4. find measure of D
pls give picture and explanation
Answer:
Measure of angle A = 120°
Measure of angle B = 98°
Measure of angle C = 104°
Measure of angle D = 140°
Step-by-step explanation:
Find measure angle A :-Since the two straight lines are parallel
, then A + 12X =180° (alternate angles)
, then A = 180° - 12X
Since the two straight lines are parallel
, then measure angle A = measure angle (25X-5)°
(opposite angles)
, then 180° - 12X = 25X - 5° (solve it like a normal equation)
, then 180° + 5° = 25X + 12X
, then 185° = 37X
, then X = 185° ÷ 37
= 5
, then measure of angle A = 180° - ( 12 x 5 )
= 180° - 60°
, then measure angle A = 120°
Find measure angle B :-Since the two straight lines are parallel
, then measure angle B = measure angle 14X (corresponding angles)
, then 15X - 7 = 14X
, then 15X - 14X = 7
, then X = 7
Since X =7
, then measure angle B = (15 x 7) - 7
= 105° - 7
, then measure angle B = 98°
Find measure angle C :-Since the two straight lines are parallel
, then measure angle C = 8X
(opposite angles)
, then 5X + 39 = 8X
, 39 = 8X - 5X
, 39 = 3X
, then X = 39 ÷ 3
, X = 13
Since X = 13
, then measure angle C = (5 x 13) +39
= 65 + 39
, then measure angle C = 104°
Find measure angle D :-Since straight that angle D lies on = 180°
, then sum of measure of and D and 4X =
180°
, then (12X + 20) + 4X = 180°
, then 16X + 20 = 180°
, then 16X = 160° (resulting from 180° - 20°)
, then X = 10
Since X = 10
, then 12 x 10 + 20 = 120 + 20
,the measure angle D = 140°
420 is divided between george and Nancy in the ratio 2:3 Find who get more money.
Answer:
Nancy gets more, she gets 252 while George gets 168.
Step-by-step explanation:
420÷5=84
168:252
George:Nancy
Find the rate if a principal of $1,800 earned $378 interest in 6 years
Answer:
Interest rate (r ) = 0.035 or 3.5%
Step-by-step explanation:
Given the principal amount of $1,800, and an interest payment of $378 earned in 6 years:
Use the simple interest formula and algebraically solve for variable, interest rate, r :
I = P × r × t
Where:
I = interest payment = $378
P = principal amount = $1,800
t = time (in years) = 6
r = interest rate
Divide both sides by P × t to isolate r :
[tex]\displaytext\sf{\frac{I}{P\:\times\:t}\:=\:\frac{P\:\times\:r\:\times\:t}{P\:\times\:t}}[/tex]
[tex]\displaytext\sf{interest\:rate\:(r)\:=\:\frac{I}{P\:\times\:t}}[/tex]
Substitute the given values into the formula for the interest rate:
[tex]\displaytext\sf{interest\:rate\:(r)\:=\:\frac{378}{1800\:\times\:6}\:=\:\frac{378}{10800}}[/tex]
Interest rate (r ) = 0.035 or 3.5%
Therefore, the interest rate is 3.5%.
Please help!!
1) Mark a central angle and calculate the measure of the central angle in the polygon below. *
Answer:
the measure of the central angle of a regular nonagon is 40 degrees.
Please help hurry hurry hurry fast
What is the slope of the line created by this equation?
y = 10x+6
I need help getting started how do you do this
Answer:
Step-by-step explanation:
Well the answer is explained below.
Hey everyone! This questions is tricky for me so can anybody help me out?
I would be very grateful if you can!
g(x) = 2x^2
for g(- 4), you just plug in - 4 for x
g(- 4) = 2(- 4)^2
g(- 4) = 2(16)
g(- 4) = 32
Answer:
g(-4) = 32
Step-by-step explanation:
Given the quadratic function, g(x) = 2x², finding the output value given g(-4) involves substituting the value of the input, x = -4, into the function.
Solution:g(x) = 2x²
g(-4) = 2(-4)² = 2(-4)(-4)
g(-4) = 2(16)
g(-4) = 32
Therefore, g(-4) = 32.
What expressions areequalivent to 6 x 4 1/2
Answer: 32 + 1 and 5 x 2
Which equation has a solution of r = 1/3
Answer:
Step-by-step explanation:
Any equation, for example 2r =2/3
if a 1x1 foot tile costs 3.50 each ,how much will it cost mr teal?
Answer:
Hope this helps.
Step-by-step explanation:
When measuring for floor tile the rule is:
Length x Width + Waste = Amount Needed
Waste Factor will vary based upon tile size, layout, configuration of room, patterns, etc. Typical waste factor is about 10%. Add 15% for tile being installed diagonally or for a room with lots of jogs and corners. These installations will require more cuts and thus more waste.
x × 20 = 80
x = ?
Help mee
x × 20 = 80
x = ?
Answer :x = 80 ÷ 20
x = 4
x = 4 ✔️
[tex]\large \color{red}\boxed{\bf Answer:}[/tex]
x × 20 = 80
20x = 80
x = 80÷20
x = 4
In a movie's opening weekend, 879,575 tickets are sold in 755 theaters. The average cost of a ticket is $9.50. What is the average amount of money earned by each theater?
Answer:
$11 067.50 each theater
Step-by-step explanation:
879575 * 9.50 = 8355962.50 revenue total 8355962.50 / 755 = $11 067.50 each theater
graph F(x)= -3/4X + 6 plotting point
Answer:
I'm not entirely sure whether is X is with 4 under the fraction or not, so I put up both graphs results.
First one: F(x) = -(3/4)X +6
Second graph: F(x) = -(3/4X) + 6
what are five example recurring decimal
Answer:
These are some examples of recurring decimals.
Definiton:
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero.
Please please help please help me help help me please help me
Step-by-step explanation:
-2 is x1
9 is y1
4 is X2
-1 is y2
m= -1-9/4-(-2)
-10/6 =-1.6
