integral formula! and example!
Answers
Answer:
Formula for Integration:
Formula for Integration:\int {1\over x} \;dx= \ln x+C. \int \sin x\;dx=-\cos x+C. \int \cos x\;dx= \sin x + C. \int \sec^2 x\;dx=\tan x+C.
Related Questions
Tina pays $45.50 for 10 boxes of wheat crackers. What is the unit price? *
Answers
Unit price = total price / quantity
Unit price = 45.50 / 10
Unit price = $4.55
Answer:
$4.55 because I look it up
4m exponent 2 + 5m
help please
Answers
\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)
4m exponent 2 + 5m.\( \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}\)
By.. 4m exponent 2, I'm going to assume that you meant this ⇨ 4m². If so, then here's how you should solve your question. I've included 2 ways of solving the question. You can choose your method. I'd suggest the 2nd one since it's a whole lot easier than the first method.
Method 1 :-\( \tt \: 4m ^ { 2 } +5m \\ \)
Quadratic polynomial can be factored using the transformation \(\tt\: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)\), where \(\tt\:x_{1} and x_{2}\) are the solutions of the quadratic equation ax²+bx+c=0.
\( \tt \: 4m^{2}+5m=0 \)
All equations of the form ax²+bx+c=0 can be solved using the quadratic formula: \(\tt\frac{-b±\sqrt{b^{2}-4ac}}{2a}\\ \). The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
\( \tt \: m=\frac{-5±\sqrt{5^{2}}}{2\times 4} \\ \)
Take the square root of 5².
\( \tt \: m=\frac{-5±5}{2\times 4} \\ \)
Multiply 2 times 4.
\( \tt \: m=\frac{-5±5}{8} \\ \)
Now solve the equation m=\(\tt\frac{-5±5}{8}\) when ± is plus. Add -5 to 5.
\( \tt \: m=\frac{0}{8} \\ \\ \tt \: m = 0\)
Now solve the equation m=\(\tt\frac{-5±5}{8} \) when ± is minus. Subtract 5 from -5.
\( \tt \: m=\frac{-10}{8} \\ \)
Reduce the fraction -10/8 to its lowest terms by extracting and cancelling out 2.
Factor the original expression using \(\tt\:ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)\). Substitute 0 for \(\tt\:x_{1} \:and \:-\frac{5}{4} \:for\: x_{2}\).
\( \tt \: 4m^{2}+5m=4m\left(m-\left(-\frac{5}{4}\right)\right) \\ \)
Simplify all of the expressions of the form \(\tt\:p-\left(-q\right)\) to p+q.
\( \tt \: 4m^{2}+5m=4m\left(m+\frac{5}{4}\right) \\ \)
Add 5/4 to m by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.
\( \tt \: 4m^{2}+5m=4m\times \left(\frac{4m+5}{4}\right) \\ \)
Cancel out 4, the greatest common factor in 4 and 4.
\( \tt \: 4m^{2}+5m= \boxed{\boxed{\bf \: m\left(4m+5\right) }}\)
Don't worry. If this process seems long & wears you out or if you haven't learned the biquadratic formula yet, you can just use the simple method of factoring out the common term (m). Here's how you do that \(\downarrow\)
Method 2 :-\( \tt \: 4m ^ { 2 } +5m\)
Factor out m.
\( = \boxed{ \boxed{ \bf \: m\left(4m+5\right) }}\)
See, the second method is easier. But, if your question comes for a lot of marks then you might prefer using the first method.
List from greatest to least:5.1 , 5 1/5, 5.5 and 5 1/4
Answers
Answer:
5.5, 5¼, 5 1/5 and 5.1.
Explanation:
To list the height from greatest to least, we convert each of them to a decimal.
\(\text{Suki}=5\frac{1}{5}=5+\frac{1}{5}=5+0.2=5.2\)\(\text{Also, Amir=5}\frac{1}{4}=5+\frac{1}{4}=5+0.25=5.25\)Therefore, the weights are: 5.1, 5.2, 5.5 and 5.25
Arranging them from greatest to least gives:
5.5, 5.25, 5.2 and 5.1 which is equivalent to: 5.5, 5¼, 5 1/5 and 5.1.
Find the value of c. Give your answer in degrees ().
20°
Q
62°
C
Not drawn accurately
Answers
The calculated value of the degree measure of angle c is 16°
Finding the degree measure of angle cFrom the question, we have the following parameters that can be used in our computation:
The figure (see attachment)
The sum of angles in a triangle is 180 degrees
This means that
x + 20 + 62 = 180
Evaluate the like terms
This gives
x + 82 = 180
So, we have
x = 98
The measure of angle c is then calculated as
c + 2 * (180 - 98) = 180
Collect the like terms
c = 180 - 2 * (180 - 98)
Evaluate
c = 16
Hence, the degree measure of angle c is 16°
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PLease help me find the distance between AB BC and CA please help
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The distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
What is Distance?The length along a line or line segment between two points on the line or line segment.
The coordinates of A are (-18, -18)
coordinates of B are (20, 0)
coordinates of C are (-12, 16)
The formula for distance is Distance=√(x₂-x₁)²+(y₂-y₁)²
Distance AB=√(20-(-18))²+(0-18)²
=√(20+18))²+(0-18)²=√38²+18²
AB=√1444+324=√1768=42.04 units
Distance BC=√(-12-20)²+(16)²
=√(-32)²+(16)²=√1024+256
=√1280
=35.77
Distance CA=√(-12-(-18))²+(16+18)²
=√(6)²+(34)²
=√36+1156=34.5
Hence, the distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
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PLEASE HELP
subtract
(-4w^ -9n) - (- 15w^)
Answers
Answer:
-5 • (2w + 1)
—————
2
Step-by-step explanation:
Please help immediately before 9 pm.
Using data below, calculate the bias based on using the
naive forecast method
Week Time Series Value
1 13
2 19
3 8
4 14
Round number to 1 decimal place
Answers
The bias based on the naive forecast method for the given data is 2.0.
To calculate the bias using the naive forecast method, we first need to calculate the average of the time series values. The formula for the naive forecast is simply taking the last observed value as the forecast for the next period.
The time series values given are 13, 19, 8, and 14. To find the average, we sum up these values and divide by the number of values:
Average = (13 + 19 + 8 + 14) / 4
= 54 / 4
= 13.5
Next, we take the last observed value, which is 14, as the forecast for the next period.
Finally, we calculate the bias by subtracting the average from the forecast:
Bias = Forecast - Average
= 14 - 13.5
= 0.5
Rounding the bias to 1 decimal place, we get a bias of 0.5, which can also be expressed as 2.0 when rounded to the nearest whole number.
Therefore, the bias based on the naive forecast method for the given data is 2.0.
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Mr. Smith is a coffee addict. He keeps switching between three brands of coffee, say A, B, and C,
from week to week according to a discrete-time Markov chain (DTMC) with the following transition
probability matrix:
(a) If he is using brand A in week 2, what is the probability distribution of the brand he will be using in week 4?
(b) What fraction of the time does Mr. Smith consume brand A coffee in long-run?
(c) Suppose the per pound cost of coffee is $6, $8, and $15 for brands A, B, and C, respectively. Assuming Mr. Smith consumes one pound of coffee per week, what is his
long-run expected coffee expense per week?
Answers
The long-run expected coffee expense per week is $12.17.
(a) The probability distribution of the brand he will be using in week 4 will be given by the 4th power of the transition probability matrix. Therefore, the probability distribution of the brand he will be using in week 4 is P4 = [0.423, 0.310, 0.267].
(b) The fraction of the time that Mr. Smith consumes brand A coffee in long-run is given by the stationary distribution of the Markov chain. Therefore, the fraction of the time that Mr. Smith consumes brand A coffee in long-run is P∞ = [0.547, 0.259, 0.194].
(c) The long-run expected coffee expense per week is given by the expected cost of each brand multiplied by its long-run probability of being consumed. Therefore, the long-run expected coffee expense per week is $12.17. This is calculated as (6 × 0.547) + (8 × 0.259) + (15 × 0.194) = 12.17.
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Simplify.1/3x + 2/5x
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Let a be a rational number and b be an irrational number. Is a+b rational or irrational?
Please HALP
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Graph y=4/7x−2
help asap
Answers
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
Graph in pic
(Credits: Symbolab)
A random sample of 130 students is chosen from a population of 4,500 students. The mean IQ in the sample is 120, with a standard deviation of 5. Using a margin of error of 1.13%, what is the 99% confidence interval for the students' mean IQ score?
Answers
Answer:
\(120-2.614\frac{5}{\sqrt{130}}=118.85\)
\(120+2.614\frac{5}{\sqrt{130}}=121.15\)
Step-by-step explanation:
Information given
\(\bar X= 120\) represent the sample mean
\(\mu\) population mean (variable of interest)
s=5 represent the sample standard deviation
n=130 represent the sample size
For this case we can't set a margin of error just with a % since they not specify 1.13% respect to something for this case we can omit this value
Confidence interval
The confidence interval for the mean is given by the following formula:
\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\) (1)
The degrees of freedom are given by:
\(df=n-1=130-1=129\)
The Confidence level is 0.99 or 99%, the significance would be \(\alpha=0.01\) and \(\alpha/2 =0.005\), and the critical value would be \(t_{\alpha/2}=2.614\)
And replacing we got:
\(120-2.614\frac{5}{\sqrt{130}}=118.85\)
\(120+2.614\frac{5}{\sqrt{130}}=121.15\)
Reduce the third order ordinary differential equation y-y"-4y +4y=0 in the companion system of linear equations and hence solve Completely. [20 marks]
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To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:
Let u = y,
v = y',
w = y".
Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:
du/dx = y' = v,
dv/dx = y" = w,
dw/dx = y"'.
Now we can rewrite the given differential equation in terms of u, v, and w:
u - w - 4u + 4u = 0.
Simplifying the equation, we get:
-3u - w = 0.
This equation can be expressed as a system of first-order linear differential equations as follows:
du/dx = v,
dv/dx = w,
dw/dx = -3u - w.
Now we have a companion system of linear equations:
du/dx = v,
dv/dx = w,
dw/dx = -3u - w.
To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.
The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.
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The coin is flipped one more time. A tree diagram has been started for you to represent the possible outcomes. Determine the results from another coin flip. What is the probability that the coin lands heads up all three times?
Answers
Answer:
1/8
Step-by-step explanation:
Answer:
1/8 or option A for edge 2020
Step-by-step explanation:
I got it right in the warm up ^^
Hope this helps!!
There are 9 children and 13 adults on a bus.
What is the ratio of the total number of people on the bus to the number of children on the bus?
Enter your answer by filling in the boxes.
to
Answers
Answer:
22:9
Step-by-step explanation:
I took the test
Answer:
22 to 9
Step-by-step explanation:
13+9=22
add the 22 and keep the nine the same
and it would look like this 22 to 9 or 9 to 22
BRAINIEST?Which expressions are equivalent to 7^{-2} times 7^{6}
Answers
Answer:
(7^2)^2
Step-by-step explanation:
(7^-2)*(7^6)=7^-2+6
......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2
Describe the graph of the function at its roots.
f(x) = (x - 2)2(x + 6)2(x + 12)
At x = 2, the graph
the x-axis.
At x = -6, the graph
the x-axis.
Atx = -12, the graph
the x-axis.
DONE
Answers
Answer: At x = 2 the graph crosses the x-axis
Step-by-step explanation:
At x =2, the graph crosses the x axis, at x =-6, the graph touches the x axis and x=-12, the graph crosses the x axis
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given function is f(x) = (x - 2)³(x + 6)²(x + 12)
When we draw the function in the graph we observe
At x =2, the graph crosses the x axis
At x =-6, the graph touches the x axis
At x=-12, the graph crosses the x axis
Hence, at x =2, the graph crosses the x axis, at x =-6, the graph touches the x axis and x=-12, the graph crosses the x axis
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*log x raised to n is the same as log n divide log x *
a. False
b. True
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which theorem or postulate proves that â–³abc and â–³def are similar?
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Angle-Angle (AA) similarity postulate, if two angles of one triangle are congruent to two angles of another, then the triangles are similar.
Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
As per the diagram,
Triangles RPQ & RST are similar since
∠P = ∠S & ∠Q = ∠T
Side - side - side (SSS) similarity theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
Triangles RPQ & RST are similar since
RP/RS = RQ/RT = ST/PQ
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50,000x2.109.........
Answers
Answer:
105450
Step-by-step explanation:
easy
Answer:
50,000x2.109
Step-by-step explanation:
A loan of $12,000 was borrowed from the bank at a 14% per annum calculate the intrest on the loan at the end of the first year
Answers
Answer:
$1680
Step-by-step explanation:
Principal loan amount x Interest rate x Time
= 12000 × 14% × 1
=12000 × 14/100 × 1
=168000/100 × 1
=1680
Answer:
i hope this helps!
credit: sayaksjunkyard2018
source: https://brainly.in/question/9238636
Step-by-step explanation:
P = $ 12000
r = 14%
t = 1 (for first year)
I = (P X r X t)/100
∴ I = (12000 X 14 X 1)/100
= 120 X 14
= $ 1680 <---------- (Interest on loan at the end of first year)
∴ Total amount owing at the end of first year = (P + I)
= (12000 + 1680)
= $ 13680
Repayment = $ 7800
Amount still outstanding (at the start of second year) = 13680 - 7800
= $ 5880
Interest on the outstanding amount at the end of second year,
P (new) = $ 5880
r (same) = 14%
t = 1 (for the current second year)
∴ I = (P X r X t)/100
= (5880 X 14 X 1)/100
= 82320 / 100
= $ 823.2 <-------------------------- (Interest on outstanding amount at the end of second year)
can some one help me please....
by step by step explanation......
Answers
A model of a rectangular patio and is a landscaping business will be enlarged by a scale factor of 2 when is installed in the customers backyard. The area of the new and larger I know they want to see square feet which is the area of the landscapers model
Answers
Answer:
The answer is "40 square feet".
Step-by-step explanation:
The formula of the area:
\(\bold{A = (2L \times 2W)}\\\\\)
\(= 4LW \\\\\)
if:
\(\to 4A = 160 \\\\\)
\(= \frac{160}{4} \\\\ = 40 \ \ sq \ ft\)
0.25 divided by 2.65
Answers
Answer:
0.09433962264
Step-by-step explanation:
^
That’s your answer
I am so confused on what to do with fractions.
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Using the power rule for differentiation, the first derivative of
\(f(x) = -x^{\frac12}\)
is
\(f'(x) = -\dfrac12 \cdot x^{\frac12-1} = -\dfrac12 x^{-\frac12}\)
and the second derivative is
\(f''(x) = -\dfrac12 \cdot \left(-\dfrac12 \cdot x^{-\frac12 - 1}\right) = \dfrac14 x^{-\frac32}\)
which makes E the correct choice.
Look at the following speeds.
4mph 8mph 16mph 32mph 64mph 128mph
By what factor did the speeds change for each consecutive speed from the first speed to the sixth speed.
A. 8
B. 32
C. 4
D. 2
Answers
The factor by which ths speed increases is 2, then the correct option is D.
By what factor did the speeds change for each consecutive speed?Here we have the sequence of numbers:
4, 8, 16, 32, 64, 128
Where these have units of miles per hour, but can be ignored, as we only care for the numbers. To get the factor by which the speed change for each consecutive speeds, we just need to take the pairs of consecutive numbers and take their quotients.
We will get:
8/4 = 2
16/8 = 2
32/16 = 2
etc.
Then the factor is 2, the correct option is D.
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A pair of shorts cost $14. If they are on sale for 40% off, what is the sale price of the shorts?
Answers
Answer:8.4
Step-by-step explanation:
Ten percent of 14 is 1.4 so add 1.4 4 times or multiple 1.4 by 4 and you get 5.6, then subtract 14 by 5.6 and you get 8.4
What is the value of the expression -218 - 72 - (-5)?
Answers
Answer:
The answer is -285
Step-by-step explanation:
Differential Equation Solutions y" + 16y = 0 {sin 4x, cos 4x}. Verify that each solution satisfies the differential equation. y = sin 4x y" + 16 = y = cos 4x
Answers
This verifies that y = cos(4x) also satisfies the differential equation.
The given solutions satisfy the differential equation.
The given differential equation is y'' + 16y = 0, and the proposed solutions are y = sin(4x) and y = cos(4x). To verify, we need to find the second derivative (y'') of each solution and plug it into the equation.
For y = sin(4x), the first derivative (y') is 4cos(4x) and the second derivative (y'') is -16sin(4x). Now, substitute y and y'' into the equation: (-16sin(4x)) + 16(sin(4x)) = 0, which simplifies to 0 = 0. This verifies that y = sin(4x) satisfies the differential equation.
For y = cos(4x), the first derivative (y') is -4sin(4x) and the second derivative (y'') is -16cos(4x). Substitute y and y'' into the equation: (-16cos(4x)) + 16(cos(4x)) = 0, which simplifies to 0 = 0.
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Solve By either long division or synthetic division
-2x^2-3 / x^2-2x
Answers
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