4. Match these equation balancing steps with the description of what was done in each step.
Step 1:
12x−6 =10 6x−3 =5
Step 2:
6x−3 =5 6x =8
Step 3:
6x =8 x =43
Descriptions to match with each step:
A: Add 3 to both sides
B: Multiply both sides by 16
C: Divide both sides by 2

The given curve crosses the x-axis whenever x is a multiple of π, and it lies above the x-axis between consecutive even and odd multiples of π. So the regions with area S₀, S₁, S₂, ... are the sets

[tex]R_0 = \left\{(x, y) : 0 \le x \le \pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

[tex]R_1 = \left\{(x, y) : 2\pi \le x \le 3\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

[tex]R_2 = \left\{(x, y) : 4\pi \le x \le 5\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

and so on, with

[tex]R_k = \left\{(x, y) : 2k\pi \le x \le (2k+1)\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

for natural number k.

The areas themselves are then given by the integral

[tex]S_k = \displaystyle \int_{2k\pi}^{(2k+1)\pi} \int_0^{e^{-x}\sin(x)} dy \, dx = \int_{2k\pi}^{(2k+1)\pi} e^{-x}\sin(x) \, dx[/tex]

Integrate by parts twice. Take

[tex]u = e^{-x} \implies du = -e^{-x} \, dx[/tex]

[tex]dv = \sin(x) \, dx \implies v = -\cos(x)[/tex]

so that

[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -e^{-x}\cos(x) - \int e^{-x}\cos(x) \, dx[/tex]

then

[tex]u = e^{-x} \implies du = -e^{-x} \, dx[/tex]

[tex]dv = \cos(x) \, dx \implies v = \sin(x)[/tex]

so that

[tex]\displaystyle \int e^{-x}\cos(x) \, dx = e^{-x}\sin(x) + \int e^{-x}\sin(x) \, dx[/tex]

Overall, we find

[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -e^{-x}\cos(x) - e^{-x}\sin(x) - \int e^{-x}\sin(x) \, dx[/tex]

or

[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -\frac12 e^{-x} (\cos(x)+\sin(x)) + C[/tex]

Using the antiderivative and the fundamental theorem of calculus, we compute the k-th area to be

[tex]\displaystyle S_k = -\frac12 e^{-(2k+1)\pi} (\cos((2k+1)\pi)+\sin((2k+1)\pi)) + \frac12 e^{-2k\pi} (\cos(2k\pi)+\sin(2k\pi))[/tex]

[tex]\displaystyle S_k = \frac12 e^{-2k\pi} \cos(2k\pi) \left(e^{-\pi} + 1\right)[/tex]

[tex]\displaystyle S_k = \frac{e^{-\pi}+1}2 e^{-2k\pi}[/tex]

Since [tex]\left|e^{-2\pi}\right|<1[/tex], the sum we want is a convergent geometric sum. As n goes to ∞, we have

[tex]\displaystyle \lim_{n\to\infty} \sum_{k=0}^n S_k = \frac{e^{-\pi}+1}2 \cdot \frac1{1 - e^{-2\pi}} = \boxed{\frac{e^\pi+1}{4\sinh(\pi)}}[/tex]

Answer:

i dont know just need points

Step-by-step explanation:

[tex]\\ \sf\Rrightarrow (10101)_2[/tex]

[tex]\\ \sf\Rrightarrow 1\times 2^0+0\times 2^1+1\times 2^2+0\times 2^3+1\times 2^4[/tex]

[tex]\\ \sf\Rrightarrow 1+4+16[/tex]

[tex]\\ \sf\Rrightarrow (21)_{10}[/tex]

Done!

Answer:

y=2 and x=1

Step-by-step explanation:

2y=7y-14+4

2y-7y=-14+4

-5y=-10/-5

y=2

4x=6-4+2x

4x-2x=6-4

2x=2/2

x=1

Answer:

  3 3/4 hours

Step-by-step explanation:

If Henry can fill 2 shelves in the time it takes Jacob to fill one, working together they can fill 3 shelves in 3/4 hour, an average rate of 1/4 hour per shelf. It will take them 15 times 1/4 hour to fill 15 shelves.

Henry and Jacob working together can fill 15 shelves in 3 3/4 hours.

Answer:

22x+15=20x

Step-by-step explanation:

Jemma requires 22 dollars per hour, plus a 15 dollar original fee. Debra requires a 20 dollar fee per hour.

Answer:22x+15=20x

Step-by-step explanation:

Answer:

Total Circumference = 514, 170 miles

Total Mass = 2, 467, 000, 000, 000 metric tons

Step-by-step explanation:

hope this helps

Answer:

378,675 km (Saturn) + 449,197 km (Jupiter) = 827, 872 km (514,416 mi)

5.683 × 10^26 kg (Saturn) + 1.898 × 10^ kg (Jupiter) =568300000000000000000000018.98 kg (5.683 × 10^26)

Answer:

164 round = 160

your answer now can you please help me

Step-by-step explanation:

Answer: 135 points

Step-by-step explanation: 220 + -85 would be the equation

Answer: =20 feet

= 35 feet

Explanation :

let width = a

length = a+15

Now,

2(2w+15)=110

2w=55-15

w=40/2

w=20

Answer:

2√6

Step-by-step explanation:

1. First, let's solve for the base of the triangle with the help of the Pythagorean Theorem (a^2 + b^2 = c^2).

2. Now, let's find the factors of 24 and see which one is a perfect square:

Therefore, the answer is 2√6.

Answer:

[tex]b=2\sqrt{6}[/tex]

Step-by-step explanation:

The triangle shown is a right triangle.

Because this triangle is a right triangle, we can use they Pythagorean theorem to find the missing side length.

Pythagorean theorem : [tex]a^2+b^2=c^2[/tex]

where a and b = length of legs and c = hypotenuse ( longest side )

we have the hypotenuse ( 7 ) and a leg (5) and need to find the other leg.

So we know that a = 5 and c = 7 and we need to find b

Using the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

a = 5 and c = 7

[tex](5)^2+b^2=(7)^2[/tex]

simplify exponents 5² = 25 and 7² = 49

[tex]25+b^2=49[/tex]

subtract 25 from both sides

[tex]b^2=24[/tex]

take the square root of both sides

[tex]b=\sqrt{24}[/tex]

simplify radical

[tex]b=2\sqrt{6}[/tex]

And we are done!

A counterargument simply means the acknowledgement of the standpoints that go against one's argument and then re-affirming the argument.

A persuasive speech means a form if speech where the goal of the speaker is to convince the audience to accept hai or her point of view.

A counterargument shows that a individual is capable of understanding the multiple sides that are in an argument. A rebuttal simply means a form of evidence that's presented in order to nullify the other evidences that are provided by another party.

Learn more about counterargument on:

https://brainly.com/question/1198856

Answer:

Step-by-step explanation:

New equation equals   - 5y = - 35

Step 2. y = 7

Step 3. 5x - 4( 7 ) = - 23

Step 4. ( 1 , 7 )

Answer:

3. Option No. 2:  

6x + 2y = 22

3x + 3y = 18

4. Option No. 2:

$2.50

Step by step explanation:

4. 6x + 2y = 22  

 (3x + 3y = 18) * 2

- Negate

6x + 2y = 22

6x + 6y = 36

2y - 6y = 22 - 36

-4y = -14

y = -14/-4

y = 3.5

An order of onion rings = $3.50

- Substitute to find for x

6x + 2(3.5) = 22

6x + 7 = 22

6x = 22 - 7

6x = 15

x = 15/6

x = 2.5

An order of French fries = $2.50

Answer:

6 hours

Step-by-step explanation:

lmk if you want an explanation

Answer:

Bottle B has a larger volume of lotion therefore the correct answer

Step-by-step explanation:

1×2×6=12/3=4 Bottle A

1.5×3×4=18/3=6 Bottle B

Answer:

Bottle B contains 6 in3 of lotion, and Bottle A contains 4 in3. Bottle B contains more.

Step-by-step explanation:

pf

Answer:

12

Step-by-step explanation:

Volume= pi x radius squared x height

substitiute values

540π= π x r^2 x 15

divide 540π by π and 15

so thats 36= radius squared

so the radius is 6 as 6 squared is 36

so the diameter is radius x2

so the answer is 12

3

Pentagon PQRST is 1/2 the size of ABCDE therefore, x = 3

Answer: there is no x so i can't answer it

Step-by-step explanation:

Answer:

£39.20

Step-by-step explanation:

2+1+5=8

£78.40/8 = 9.8

9.8*5= 49

49-9.8= 39.2

Answer:

A(1) = 5

A(4) = 5.5

A(10) = 6.5

Step-by-step explanation:

An nth term formula works, whether for a arithmetic or geometric sequence, can be used to find any term in a sequence;

Simply substitute the number that corresponds with the position of the term you want to find and the formula will give the value of that term;

So:

A(1) = 5 + ⅙((1) - 1) = 5

A(4) = 5 + ⅙((4) - 1) = 5.5

A(10) = 5 + ⅙((10) - 1) = 6.5

Answer:

35

Step-by-step explanation:

5x (5+3)=40-5=35

Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation: 108/3 is 36, 36/3 is 12, and 12/3 is 4. :)

Answer:

y=65x+30

Step-by-step explanation:

Using y=mx+b, we see that they need 65 dollars per hour, and since x represents the # of hours, we put 65 there as our "slope." Then 30 is the starting amount, or our y-intercept

Wednesday reported -20 compared to the other days recording -5, 15, and 20 degrees. In this case, Wednesday had the coldest temperature.

Answer: Wednesday

Step-by-step explanation: Think of it like this; all temperatures are cold for us human beings. The question is being asked which days did Elizabeth record the lowest (coldest) temperature.

You can put this figures into a number line. Any number going to the right of a number line is an increase. So Monday and Tuesday can be eliminated. Any number going the left of a number line is decreasing. - 5 is very cold but -20 is colder than -5. Therefore, the lowest (coldest) temperature is -20 which was Wednesday,

Hope this explanation helps.

Answer:

20 sides ( Icosagon )

3240 is the interior angles sum

Step-by-step explanation:

360 ÷ 18 = 20

180 - 18 = 162

162*20 = 3240 is the interior angles sum

Answer:

0.053 kg

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Step-by-step explanation:

Annie = x

Brianna = y

Carly = z

Now,

x + y + z = 105 ...(1)

Carly has sold ten more than three times Brianna's sales.

z = 10 + 3y ...(2)

Brianna sold five more than Annie.

y = 5 + x ...(3)

Now,

z = 10 + 3y

z = 10 + 3(5 + x)

z = 10 + 15 + 3x

z = 25 + 3x

Now,

x + y + z = 105

x + (5 + x) + 25 + 3x = 105

5x + 30 = 105

5x = 105 - 30

5x = 75

5x/5 = 75/5

x = 15

So,

y = 5 + x

y = 5 + 15

y = 20

Now,

z = 25 + 3x

z = 25 + 3(15)

z = 25 + 45

z = 70

Thus,

Annie Sold 15 boxes

Brianna Sold 20 boxes

Carly Sold 70 boxes

Answer: [tex]y=\frac{-3}{4}x-3[/tex]

Ok done. Thank to me :>