Find the square root of 2937.44 by the arithmetic method

We are given with a sequence, which is a GP (Geometric Progression), as the ratio [tex]{\bf{a_{n+1}:a_{n}}}[/tex] is 1/3 for every [tex]{\bf{n\in \mathbb{N}}}[/tex], so 1/3 is the comman ratio r, and we needa find sum till 6 terms, so n = 6, and first term is 6, so putting all the values we will be having ;

[tex]{:\implies \quad \sf S_{6}=\dfrac{6\bigg\{1-{\bigg(\dfrac13\bigg)}^{6}\bigg\}}{1-\dfrac13}}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{6\bigg(1-\dfrac{1}{3^{6}}\bigg)}{\dfrac{3-1}{3}}}[/tex]

[tex]{:\implies \quad \sf S_{6}=6\bigg(\dfrac{3^{6}-1}{3^{6}}\bigg)\div \dfrac23}[/tex]

[tex]{:\implies \quad \sf S_{6}=6\bigg(\dfrac{3^{6}-1}{3^{6}}\bigg)\times \dfrac32}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{3^{6}-1}{3^{4}}}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{3^6}{3^4}-\dfrac{1}{3^4}}[/tex]

[tex]{:\implies \quad \sf S_{6}=3^{2}-\dfrac{1}{81}}[/tex]

[tex]{:\implies \quad \sf S_{6}\approx 9-0.012\approx 8.988\approx \boxed{\bf{8.99}}}[/tex]

Step-by-step explanation:

SinP = sin30° = 1/2

sinQ = sin60° = root3/2

cosR = cos90° = 0

cosQ = cos60° = 1/2

sinR = sin90° = 1

Answer:

9

Step-by-step explanation:

700,000

90,000

6,000

100

40

2

Answer:

9

Step-by-step explanation:

796,142

100000  10000    1000  100  10   1

Answer:

49/3 or 16.33...

Step-by-step explanation:

15 + 4/3.

15/1 + 4/3

45/3 + 4/3.

ANSWER: 49/3

Answer:

I dont see any triangle but the sum of the interior angles of every triangle is 180

Step-by-step explanation:

<+<+<=180˚

Answer:

Step-by-step explanation:

In order to determine the correct answer, we need to confirm it first by making the solution below:Costs: $89.95 = New Lamp $239.99 = Comforter 6 3/5% = Sales Tax (convert this to decimal and we get 6.6%)  $351.72 = Total amount the Chang's paidLet's get the total costs first which is $329.946.6% of 329.94 is $21.78The total cost with the tax would be $351.72.Therefore, the Chang's paid the correct amount. The correct answer would be option D. The Chang's family paid the correct amount for their purchases.

Answer:

3780/90

what number close to 37 is divisible by 9 ? 36 !!

3600/90=40 or 3690/90=41

3780/90=42

this an underestimate because the compatible numbers 3600 and 3690 are less than 3780

yall be safe

Our estimate is 38. This estimate is an overestimate because we rounded up both numbers, so we expect the actual quotient to be slightly smaller than our estimate.

Compatible numbers are numbers that are simple to mentally work with and can be used to estimate or simplify a more complex calculation.

When performing addition, subtraction, multiplication, or division, for example, it is often helpful to choose numbers that are easy to manipulate in your head or by hand, such as multiples of 10, 100, or 1000.

To estimate the quotient of 3,780 divided by 90 using compatible numbers, we can round 3,780 to 3,800 (which is divisible by 100) and round 90 to 100. Then, we have:

3,800 ÷ 100 = 38

Thus, the estimate is 38. This estimate is an overestimation because we rounded both numbers, so we anticipate that the actual quotient will be slightly lower than our estimate.

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Answer:

1a. 210 m^2  1b. 14 ft^2  1c. 199.5 in^2

2a. 270 cm^2  2b. 162 m^2  2c. 272 cm^2

3a. 348 ft^2  3b. 230 in^2  3c. 312.5

Step-by-step explanation:

The area of a triangle can be calculated with one equation...

A = 1/2bh

b stands for base, h stands for height

1a. A = 1/2(21)(20)

    One half divides 20 easily..

A = 21(10)

A = 210

1b. A = 1/2(7)(4)

    One half divides 4 easily..

A = 2(7)

A = 14

1c. A = 1/2(19)(21)

A = 1/2(399)

A = 199.5

2a. A = 1/2(36)(15)

    One half divides 36 easily..

A = 18(15)

A = 270

2b. A = 1/2(18)(18)

   One half divides 9 easily..

A = 9(18)

A = 162

2c. A = 1/2(32)(17)

  One half divides 32 easily..

A = 16(17)

A = 272

3a. A = 1/2(29)(24)

  One half divides 24 easily..

A = 12(29)

A = 348

3b. A = 1/2(23)(20)

  One half divides 20 easily..

A = 10(23)

A = 230

3c. A = 1/2(25)(25)

A = 1/2(625)

A = 312.5

Finding area of triangle --> [tex]\frac{1}{2}*b*h[/tex]

     Question 1:

         a.   [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*20*21 = 210 m^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*4*7 = 14 ft^2[/tex]

         c. [tex]Area = \frac{1}{2}*b*h= \frac{1}{2} *21*19=199.5in^2[/tex]

     Question 2:

         a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *36*15 = 270cm^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *18*18 = 162m^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *17*32 = 272cm^2[/tex]

     Question 3:

         a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *24*29 = 348ft^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *20*23 = 230in^2[/tex]

         c. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *25*25 = 312.5cm^2[/tex]

Finding Area of Parallelogram --> b * h

     Question 1

         a. [tex]Area = b * h = 24 * 26 = 624cm^2[/tex]

         b. [tex]Area = b * h = 15 * 30 = 450in^2[/tex]

         c. [tex]Area = b * h = 21 * 31 = 651 mm^2[/tex]

      Question 2

         a. [tex]Area = b * h = 18 * 17 = 306 in^2[/tex]

         b. [tex]Area = b * h = 10.5 * 15 = 157.5m^2[/tex]

         c. [tex]Area = b * h = 12.5*11=137.5cm^2[/tex]

      Question 3:

          a. [tex]Area = b * h = 5.7*11.5=65.55in^2[/tex]

          b. [tex]Area = b * h = 8 * 12.5 = 100ft^2[/tex]

          c. [tex]Area = b * h = 1.7 * 3.6 = 6.12m^2[/tex]

Hope that helps!

Answer:

-1.8 kJ

Step-by-step explanation:

Given

Solving

Answer:

2250 J

Step-by-step explanation:

Work done is given by the formula :

work done = force × distance

Substituting values given gives us:

Work done = 45 × 40

Work done = 2250 J

Answer:

x = 5

x = -15

Explanation:

Let the number be "x"

===================

Answer:

x= 5 or -15

Step-by-step explanation:

let the number be x

(x+5)^2=100

x^2+10x+25=100

x^2+10x-75=9

look for factors of 75 that when you gives you 10 and when you multiply gives you -75

those factors are 15 and -5

replace 10x with 15x and -5x

x^2+15x-5x-75=0

then group them, and factorize

x(x+15)-5(x+15)=0

x-5=0 or x+15=0

x= 5 or x= -15

For questions 4 – 6, name all of the radii of the circle shown in the figure.

For questions 7 – 10, find the measure of the radius of the circle. 7. 8.

Answer:

center(-2,5) r=6

Answer:

-8.5

Step-by-step explanation:

this is because the more negative a number is, the less value it is, hence -8.5 is greater than -15.

Answer:

0.3

Step-by-step explanation:

Start at the beginning, follow the branch to A and then the branch to D (see attached annotated diagram).

When calculating the probability of an event AND another event, multiply the probabilities.

P(A and D) = 0.5 x 0.6 = 0.3

Answer:

1, 5

Step-by-step explanation:

I may be a little wrong but;

Multiply it by 3 and 4-

-12x+9y=-51

12x-16y=44

-7y=-7

y=1

x=5

Answer:

3(x-6)=3x-18

Step-by-step explanation:

Δ perimeter of swimming area:

Δ area of roped off section:

Answer:

No

Step-by-step explanation:

6 time 180 is only 108

108<120

There is not enough chalk.

Answer:

Jason can afford 5 more additional lines, making 9 lines total because

175-120=55

55/10=5.5 so He can not afford more than 5 more additional lines.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.

Answer:

The answer is 37.

Step-by-step explanation:

First of all we use Pemdas. Add the parantheses first. So its 7-18(-5/3) then you multiple the -18 to 5/3 Because after Parantheses its Exponents multiplication. So it becomes 30. Then you add 7 to get 37. I hope this is helpful.

I bet the sum you're referring to is supposed to be

[tex]\displaystyle \sum_{r=0}^{20} r^2 \times {}^{20}C_r[/tex]

or equivalently,

[tex]\displaystyle \sum_{r=0}^{20} r^2 \binom{20}r[/tex]

where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.

Recall the binomial series,

[tex](1+x)^\alpha = \displaystyle \sum_{r=0}^\infty \binom\alpha r x^r[/tex]

which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)

Differentiating both sides with respect to x gives

[tex]\alpha (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^{r-1}[/tex]

Multiply both sides by some arbitrary x in |x| < 1 :

[tex]\alpha x (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^r[/tex]

Repeat:

[tex]\alpha (1+x)^{\alpha-1} + \alpha(\alpha-1) x(1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^{r-1}[/tex]

[tex]\alpha x (1+x)^{\alpha-1} + \alpha(\alpha-1) x^2 (1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^r[/tex]

Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to

[tex]20 \times 2^{19} + 20\times19\times 2^{18} = (20 + 10\times19)\times2^{19} = \boxed{210\times2^{19}}[/tex]

Answer:

x = -12

Step-by-step explanation:

⇒ -5x = 60

Isolate the variable "x" by dividing by -5 on each side.

⇒ -5x/-5 = 60/-5

⇒ x = -12

The solution is x = -12

[tex]\boxed{ \sf \bold{x = -12}}[/tex]

Explanation:

[tex]\dashrightarrow \ \ \sf -5x = 60[/tex]

divide both sides by -5

[tex]\dashrightarrow \ \ \sf \dfrac{-5x}{-5} = \dfrac{60}{-5}[/tex]

simplify

[tex]\dashrightarrow \ \ \sf x = -12[/tex]

Answer:

Step-by-step explanation:

Although Alex and Lauren will both step into position 4,6, they will not do it at the same time, so they will not meet.

Lauren:

Alex:

Both will step in the position 4,6, However, Lauren will be in this positon in the second 4, while Alek will do it on the second 3.

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In order to solve this equation, we need to take the square root of both sides (in order to get rid of the square and isolate x, because we are asked to determine the value(s) of x)

x²=36

√x²=√36

x=6

Is this the only solution?

A negative times a negative is a positive...

-6 is another solution of this equation! :)

Hence, the answers are:-

[tex]\boxed{\boxed{\bold{x=6; ~x=-6}}}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Hello! My name's Cupcake, And I will be helping you today! :D

In order to solve this equation, we need to take the square root of both sides.

Why? Because we need to isolate x. Our goal is:- To find the value of x.

So in order to get rid of the square and find the value of x, we take the square root of both sides:-

x^2=36

x=6, x=-6 (solutions)

Hope it helps!

Any queries - comment !

Answer:

109.2 degrees

Step-by-step explanation:

Use the cos law to find angle F

3.1^2 = 2^2 + 1.8^2 - 2 (2)(1.8) cos F

shows cos f = -.329

arc cos( - .329) = angle F =109.2 degrees

ANSWER = 0.48

HOPE IT HELPS :)

Answer: 0.48

Step-by-step explanation:

6 x 8 = 48

we add those decimals back in which would be 0.48

Answer:

________________________________________________________

Multiply all numbers by the multiplier, the smaller number, and then use any extra digits you carry, bringing you to the ten thousands place.

________________________________________________________

Ask me in the comments box, I can help.