write an equation that represents each circle

Answer:

do you already have it answer.lol.

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

- I have used different colours for indicating different process

- I used brown colour to indicate steps

- I used green colour for explaining solution

- Pink colour for known properties of integration

- Purple colour for the middle steps that are optional.

[Note :- For solving such questions it is mandatory that you should know all the functions and it's derivatives ]

[tex]\sf{=}{\sf{\dfrac{ x^{2}}{2}}}{\sf{ + 7x + 67x .In| x - 4 | - 30.In| x - 3 | + c }}[/tex]

Answer:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}[/tex]

Step-by-step explanation:

To find an integration of this function, first, you must know these integration methods and differences of them.

These methods above are common when it comes to integrating fractional functions, except there are differences when to use these methods.

Examples (of these integrands that require partial fraction technique)

[tex]\displaystyle \large{\int \frac{3}{x^2-5x+6} \ dx}\\\displaystyle \large{\int \frac{x+2}{x^2-4} \ dx}[/tex]

Examples (of these integrands that require long division)

[tex]\displaystyle \large{\int \frac{x^2+5x+6}{x+2} \ dx}\\\displaystyle \large{\int \frac{x^4+3}{x} \ dx }[/tex]

Therefore, from the given integral, the integrand requires long division method. (See attachment for long division.)

After long division, we should get:

[tex]\displaystyle \large{\int x+7+\frac{37x-81}{x^2-7x+12} \ dx}[/tex]

Recall important properties of integral such as:

[tex]\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}[/tex]

Hence:

[tex]\displaystyle \large{\int x \ dx + \int 7 \ dx + \int \frac{37x-81}{x^2-7x+12} \ dx}[/tex]

Recall important integration formula for polynomial and constant:

[tex]\displaystyle \large{\int x^n \ dx = \frac{x^{n+1}}{n+1} + C}\\\displaystyle \large{\int x \ dx = \frac{x^2}{2} + C}\\\displaystyle \large{\int k \ dx = kx + C \ \ \tt{(k \ \ is \ \ a \ \ constant.)}[/tex]

Therefore:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}[/tex]

From the boxed integral above, we cannot evaluate it by default. From what I said, if the degree of numerator is less than the degree of denominator, we’ll use partial fraction technique.

Therefore, factor the denominator:

[tex]\displaystyle \large{\frac{37x-81}{(x-4)(x-3)}}[/tex]

Set to A/x-4 and B/x-3

[tex]\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} = \frac{A}{x-4} + \frac{B}{x-3}}[/tex]

Multiply both sides by (x-4)(x-3).

[tex]\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} \cdot (x-4)(x-3)= \frac{A}{x-4} \cdot (x-4)(x-3) + \frac{B}{x-3} \cdot (x-4)(x-3)}\\\displaystyle \large{37x-81= A(x-3) + B(x-4)}\\\displaystyle \large{37x-81= Ax-3A+Bx-4B}\\\displaystyle \large{37x-81= (A+B)x-(3A+4B)}[/tex]

Then compare the coefficients:

[tex]\displaystyle \large{\left \{ {{A+B=37} \atop {3A+4B=81}} \right}[/tex]

Solve the simultaneous equation for A and B.

[tex]\displaystyle \large{\left \{ {{A=37-B} \atop {3A+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {3(37-B)+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111-3B+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111+B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=81-111}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=-30}} \right}\\\displaystyle \large{\left \{ {{A=67} \atop {B=-30}} \right}\\[/tex]

Therefore, A = 67 and B = -30. Substitute the values in:

[tex]\displaystyle \large{\int \frac{67}{x-4}-\frac{30}{x-3} \ dx}\\\displaystyle \large{\int \frac{67}{x-4} \ dx -\int \frac{30}{x-3} \ dx}[/tex]

Recall the integration formula for above:

[tex]\displaystyle \large{\int \frac{k}{x-a} \ dx = \int k \cdot \frac{1}{x-a} \ dx = k\ln |x-a| + C}[/tex]

Therefore:

[tex]\displaystyle \large{\int \frac{37x-81}{x^2-7x+12} \ dx = \int \frac{67}{x-4}-\frac{30}{x-3} \ dx = 67\ln |x-4| - 30\ln |x-3|}[/tex]

Back from this:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}[/tex]

Substitute in:

[tex]\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}[/tex]

Therefore the solution is:

[tex]\displaystyle \large \boxed{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}[/tex]

Answer:

It's asking what 3^k+2 is in terms of m. That is where the 2 comes from.

Please let me know if this helped <3

Answer:

As it says approximate, the nearest value to 46.6° is 45.6°

Therefore, 45.6° is the approximate measure of angle A.

using SOH CAH TOA:

[tex]\sf cos(A) = \dfrac{b^2+c^2-a^2}{2bc}[/tex]

[tex]\hookrightarrow \sf cos(A) = \dfrac{4^2+8^2-6^2}{2(8)(4)}[/tex]

[tex]\hookrightarrow \sf cos(A) = 0.6875[/tex]

[tex]\hookrightarrow \sf A = cos^{-1}(0.6875)[/tex]

[tex]\hookrightarrow \sf A = 46.5675^{\circ \:}[/tex]

[tex]\hookrightarrow \sf A = 46.6^{\circ \:}[/tex]

Step-by-step explanation:

he has 60%

so he needs 40%

40% of 120

of is ×

40% × 120

40% as a decimal is

put answer in comments

Answer:

58.45

Step-by-step explanation:

Use BIDMAS

14.5 X 3.1 = 44.95

44.95 + 13.5 = 58.45

Answer:

58.45

Step-by-step explanation:

Answer: (1,4) (2,7) (3,10)

HOpE iT hElpS

plS mArK As bRaiNlieSt -wiggly

Step-by-step explanation:

step 1

[tex]\begin{matrix}\:\:\:\:\emptyspace0.\:\:\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace3.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

step 2

[tex]\begin{matrix}\:\:\:\:\emptyspace0.\emptyspace3\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace3.0\cdot \:0}\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\end{matrix}[/tex]

step 3

[tex]\begin{matrix}\:\:\:\:\emptyspace.\emptyspace3\emptyspace7\:\:\:\:\:\:\:\\ 8\overline{|\smallspace 3 0\ \ \:}\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\emptyspace3\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace6}\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace4\emptyspace0\:\:\:\:\:\:\end{matrix}[/tex]

step 4

[tex]\begin{matrix}\:\:\:\:\epe0.\ece3\empt7\e5\:\:\:\:\:\\ 8\overline{|\sm30 \ \ \ \ }\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\em3\e0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\eme6\ece0\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\empte5\ee6}\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\ee4\ece0\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\ee4\epace0}\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\e0\:\:\:\:\:\:\end{matrix}[/tex]

Answer:

3.75

Step-by-step explanation:

[tex]\mathrm{Write\:the\:problem\:in\:long\:division\:format}[/tex]

[tex]\begin{matrix}8\overline{|\smallspace3.0}\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{Divide\;30\;by\;8\;to\;get\;3}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace3.\:\:\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace30.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{Divide\;60\;by\;8\;to\;get\;7}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace3.\emptyspace7\:\:\:\:\:\:\:\:\:\\ 8\overline{|\smallspace30.0\cdot \:0}\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace6}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{Divide\;40\;by\;8\;to\;get\;5}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace3.\emptyspace7\emptyspace5\:\:\:\:\:\:\:\\ 8\overline{|\smallspace30.0\cdot \:0}\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace2\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \emptyspace6\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \underline{\emptyspace5\emptyspace6}\:\:\:\:\:\:\:\:\:\:\\ \emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\\ \underline{\emptyspace4\emptyspace0}\:\:\:\:\:\:\:\:\\ \emptyspace0\:\:\:\:\:\:\:\:\end{matrix}[/tex]

[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{3}{0.8}\:\mathrm{is}\:3.75[/tex]

~lenvy~

Answer:

6/8 red paint

10/8 blue paint

4th grade savvas realize

Answer:

( 7/18 )

Step-by-step explanation:

7           4            7 x 4            28 ÷ 4                 7

/    x     /      =        /         =          /              =      /

8          9             8 x 9           72 ÷ 4                18

I hope this helps!

Answer: 27090 is invested. part at 13% part at 10% the interest earned at 13% exceeds the interest earned at 10% by 440.16 how much is invested at each rate.

Answer:

The answer should be 24

Step-by-step explanation:

All you need to do is replace the variables (a, b, and c) with the numbers given.

16 +64/8 would equal to 24

Answer:

100 + 50p = t or t = 100 + 50p

Step-by-step explanation:

We know that they charge 100 initially and then an addition 50 for each person.

We add 100 to 50 but we do not know the amount of people, which leaves it unknown (p)

The total cost (t) is also unknown which stays unknown until we calculate the amount of people.

The Given Polynomial has three different parameters scattered, first we have to rearrange and then solve for the missing numbers the answer is gotten as 2x^2+7x+4

Given Data

2x−6+4x^2+5x−2x^2+10

We begin by collecting like terms

4x^2-2x^2+2x+5x-6+10

Carrying out addition and subtraction operation on like terms

2x^2+7x+4

The Simplified polynomial is

2x^2+7x+4

Learn more about polynomial here:

https://brainly.com/question/2833285

Answer:

16+ 2x

Step-by-step explanation:

2(10) +2(x-4)

20 + 2x -8

16+ 2x

Answer:

[tex]x = \frac{4}{3}- 1[/tex]

x=4/3 , -1

Answer:

it's a it's the first one

Step-by-step explanation:

because if the trick would use less oil then that would make it look like the truck is less expensive but it's not

Answer:

Its C: 12 units × 8 units are the dimensions of the rectangle

Step-by-step explanation:

Answer:

[tex]\tt x=21[/tex]

Step-by-step explanation:

[tex]\tt 45+63+4x-12=180[/tex]

[tex]\tt \cfrac{4x}{4} =\cfrac{180-96}{4}[/tex]

[tex]\tt x=21[/tex]

~

Answer:

x-intercept is 5

y-intercept is -6

Step-by-step explanation:

To find x-intercept put y=0

since 6x-5y=30 then 6x=30

x=30/6 = 5

To find y-intercept put x=0

since 6x-5y=30 then -5y=30

y=30/-5 = -6

Answer:

[tex]46\frac{1}{8}[/tex]

Step-by-step explanation:

Formulate

[tex]1845\div40[/tex]

Calculate

[tex]\frac{1845}{40}[/tex]

Cross out the common factor

[tex]\frac{369}{8}[/tex]

Write [tex]\frac{369}{8}[/tex] as a mixed fraction

[tex]46\frac{1}{8}[/tex]

I hope this helps you

:)

Answer:

It grew by 500% meaning it grew on average 83.333% per week

Step-by-step explanation:

To find the percent growth you divide the end weight by the starting weight:

[tex]7.5/1.5=5[/tex]

However, that is the percentage in decimal form. To convert that number to a percentage move the decimal place to the right 2 places. This results in 500%

To get the average weekly growth weight, simply divide the 500% by the amount of weeks (6). This then gives the 83.333% per week.

Note: I didn't know which answer you were looking for. That is why there are 2.

Answer:

the answer send me a 100dollar gift card

Answer:

(3/2, -1/2)

Step-by-step explanation:

add the 2 inequalities together.

you get 2X<3 so x<3/2. plug X back in and solve for y and you get y= -1/2

Answer:

x = 7

Step-by-step explanation:

8 = x + 1

prove that the value of x is 7

proven

Answer:

3/5 miles

Step-by-step explanation:

Average Distance = Total Distances / Total Number of Runners

Average Distance = [0.3+0.4+0.5+0.6+(4*0.7)+0.8] / 9 = 3/5

Answer:

[tex] - 4 \: \: \: \: \: 2 \ \\ - 3 \: \: \: 0[/tex]

Answer:

10 = 3 hours

one hour = 3.33 dollars

Step-by-step explanation:

Answer:

for the values 45, 81

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factors of 81 are: 1, 3, 9, 27, 81

Then the greatest common factor is 9.

Answer:

Step-by-step explanation:

Factor of 45: → 1, 3, 5, 9, 15, 45

Factor of 81: →  1, 3, 9, 27,81

Therefore, GCF of 45 and 81 is 9

~