Jon has 212 meters of wood that he plans to cut into 4 equal pieces to use as part of his new wood floor. What is the length, in meters, of each piece of wood

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Actually Welcome to the concept of Surface areas and volumes.

Here we will find surface areas by adding individual parts.

Surface area ==> Small rectangle + big rectangle + base rectangle + 2* right angled triangles.

so we get as,

area of shape = 721.1 yards.

option D.) is correct.

The volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.

The equation of the circle can be given as,

[tex]x^2+y^2=r^2[/tex]

Here, (r) is the radius of the circle.

Rewrite this equation as,

[tex]y^2=r^2-x^2\\y=\sqrt{r^2-x^2}[/tex]

This will give you the half the length of the side. Thus, the length of the side of the square is,

[tex]s=2y=2\sqrt{r^2-x^2}[/tex]

The area of the square it square of its side. Thus, the area of the square is,

[tex]A(x)=s^2\\A(x)=(2\sqrt{r^2-x^2})^2\\A(x)=4(r^2-x^2})[/tex]

The volume of the solid can be got by integrating the area of the cross-section.

[tex]V=\int\limits {A(x)} \, dx[/tex]

Here, A(x), provides the area of the square at the point x. Thus,

[tex]V=\int\limits {A(x)} \, dx\\V=\int\limits_{-r}^r {4(r^2-x^2)} \, dx\\V=[ {4(r^2x-\dfrac{x^3}{3})}]^r_{-r}\\V= {4(r^2(r)-\dfrac{(r)^3}{3})}- {4(r^2(-r)-\dfrac{(-r)^3}{3})}\\V=4[r^3-\dfrac{r^3}{3}}+ {r^3-\dfrac{r^3}{3}]\\V=\dfrac{16r^3}{3}[/tex]

Thus, the volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.

Learn more about the equation of circle here;

https://brainly.com/question/1506955

Answer:

broken

Step-by-step explanation:

when there isn’t an equals sign the line will always be broken

Step-by-step explanation:

Using the formula:

Sin☆=Perpendicular ÷ Hypotenus

Sin☆ = 35 ÷ 48

Sin☆ = 0.7291666667

☆ = Sin^-1 (0.7291666667)

☆ =46.8165782066

where ☆= Degree.

Hence final answer is 46.816

I hope this is right.....

Answer: A= 42 degrees

Step-by-step explanation:

A= 180-90-48=42 (degrees)

Answer:

A= 42 degrees

a = 27

c= 40.4

Step-by-step explanation:

48 - 90 = 42 (we know the remaining angle area is 90 because its a right triangle and a traingle is 180 degrees)

to find the answer of a we need to use tan(48) and when you convert that to radians you get 1.1106 ish tan is opposite over adjacent and we know the opposite is 30 but we dont know a so we put [tex]\frac{30}{a}[/tex] = 1.1106 and put a on both sides so you divide 30 by 1.1106 and dget 27.0124 and round to the nearest tenth to get 27

to find c you need to find the hypotanuse which is [tex]a^{2}[/tex]+[tex]b^{2} =c^{2}[/tex]

30 squared is 900 add that to 27 squared which is 729 and you get 1629

find the square root of 1629 to get 40.3608 and then round that to the nearest tentth to get 40.4

[tex]~~~~(3x-4)^2 = 22\\\\\implies 3x-4 = \pm\sqrt{22}\\\\\implies 3x = 4 \pm\sqrt{22}\\\\\implies x = \dfrac{4\pm \sqrt{22}}3 \\\\\text{Hence,}~~ x = \dfrac{4+ \sqrt{22}}3~~ \text{and}~~ x = \dfrac{4-\sqrt{22}}3[/tex]

Answer:

[tex] a = ( \frac{ - 6}{2} )[/tex]

Step-by-step explanation:

-2g=?

[tex] - 2( \frac{3 }{ - 1} ) \\ \\ ( \frac{ - 6}{2} )[/tex]

Answer:

y = 4(x+3)^2 - 3

Step-by-step explanation:

Vertex form  y = a(x+3)^2 -3    sub in   2,97   to calculate a

                     97 = a(2+3)^2 - 3

                        a = 4

Answer:

Option D, [tex]2010\ cm^3[/tex]

Step-by-step explanation:

Step 1:  Determine the volume of a single cylinder

[tex]V=\pi r^2h[/tex]

[tex]V=\pi *(4\ cm)^2 * 10\ cm[/tex]

[tex]V = 3.14 * 16\ cm^2 * 10\ cm[/tex]

[tex]V = 502.4\ cm^3[/tex]

Step 2:  Determine the total volume

[tex]502.4\ cm^3 * 4[/tex]

[tex]2,009.6\ cm^3[/tex]

Answer: Option D, [tex]2010\ cm^3[/tex]

Answer:

The last one :)

Step-by-step explanation:

I hoped this helped have a good day! <3

Answer:

  13. x=11; MN=65°; NP=115°; NQP=245°

  15. x=9; AD=108°; BC=23°; DC=139°; DBC=221°

Step-by-step explanation:

The marked arcs are congruent, so we can equate the given expressions for their measures:

  10x -45 = 6x -1

  4x = 44 . . . . . . . . . add 45-6x

  x = 11 . . . . . . . . . . divide by 4

The arc measures are found by using the value of x in the corresponding expression. Arcs around a circle total 360°.

  arc MN = (10(11) -45)° = 65°

  arc NP = 180° -65° = 115°

  arc NQP = 360° -NP = 245°

__

The sum of arcs around a circle is 360°. We can use this fact to write an equation involving the given expressions. Clockwise from A, we have ...

  90 +(2x +5) +(17x -14) +12x = 360

  31x = 279 . . . . . . . subtract 81, collect terms

  x = 9 . . . . . . . . . divide by 31

The arc measures are found by using the value of x in the corresponding expression.

 arc AD = 12(9)° = 108°

  arc BC = (2(9) +5)° = 23°

  arc DC = (17(9) -14)° = 139°

  arc DBC = 360° -DC = 221°

Answer:

1/21 * 7  = 1/3

Step-by-step explanation:

The numbers in 1/3 divided by 7 are labeled below:

To make it a fraction form answer, you keep the numerator and multiply the denominator by the whole number to make a new denominator:

1

-------

3 x 7

 =  

1

-----

21

Thus, the answer to 1/3 divided by 7 in fraction form is:

1/21

To make the answer to 1/3 divided by 7 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

1/21 = 0.04761904761

1/21 * 7 = 0.3333333333.... ( 1/3 )

Answer:Slope=-240.000/2.000=-120.000

Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    120*x+y-(1200)=0

STEP

1

:

Equation of a Straight Line

1.1     Solve   120x+y-1200  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

Answer:

ok

Step-by-step explanation:

Answer:

The correct answer would be C) 30

The equation of c is an illustration of subject of formula

The equation of c in terms of r and t is c = r - 15/t

The equation is given as:

t = 15/(r - c)

Cross multiply

t(r - c) = 15

Divide both sides by t

r - c = 15/t

Subtract r from both sides

-c = -r + 15/t

Multiply both sides by -1

c = r - 15/t

Take LCM

[tex]c = \frac{rt - 15}{t}[/tex]

Hence, the equation of c in terms of r and t is [tex]c = \frac{rt - 15}{t}[/tex]

Read more about subject of formula at:

https://brainly.com/question/10643782

Answer:

Step-by-step explanation:

The experimental probability of choosing Grace is 13.6% (17/125*100)

The theoretical probability of choosing Grace is 16.67% (1/6)

Each probability would change because they depend on the data set so if the data set changes, that means the probability will also change depending on the amount it changes.

Answer:butt no ayes

Step-by-step explanation:10 is a yes is no

Answer:

30

Step-by-step explanation:

500 g = 1/2 kg => 2 weeks he loses 1 kg

105 - 90 = 15 kg

So he needs to take 30 weeks in total. ( 15 * 2)

Let weeks be x

So

Answer:

$336

Step-by-step explanation:

Find the perimeter, 5x2 + 16x2 = 10 + 32 = 42

Fencing material = $8 per 1 meter

42 meters, so 42 * 8 = $336

Answer:

the difference of the numbers are 217 and 55.

Step-by-step explanation:

a+b=272

a/b=3…52

a=3b+52

4b+52=272

4b=220

b=55

a=272-55=217

Answer:

1.97

Step-by-step explanation:

1 whole square is filled so that would equal 1

97 out of 100 squares in the second is filled so it would be = 0.97

combine them:

0.97+1=1.97

Answer:

24

Step-by-step explanation:

area = wl (6×4 = 24)

w width l length

Answer:

QR = 14.00 cm to the neatest hundredth.

Step-by-step explanation:

This is a right triangle with < P = 90.

So QR is the hypotenuse.

< Q is the angle opposite to the line PR.

sin Q = opposite/hypotenuse = PR/QR

sin 40 = 9/QR

QR = 9/sin40

= 14.002 cm.

Answer:

5

Step-by-step explanation:

[tex]\text{Endpoints of diameter,}~~ A(4,6)~ \text{and}~ B(-3,-1)\\\\\text{Diameter,}~AB = \sqrt{(4+3)^2+(6+1)^2}\\\\~~~~~~~~~~~~~~~~~~~=\sqrt{7^2+7^2}\\\\~~~~~~~~~~~~~~~~~~~=7\sqrt2\\\\\text{So , radius}~ = \dfrac{AB}2 = \dfrac{7\sqrt 2}2 =4.9~\text{units.}\\\\\text{Hence the answer is B.}[/tex]

Answer:

a) growth

b) 3%

c) 6 years (since the beginning of the decade)

Step-by-step explanation:

Given:

The population P (in thousands) of Austin, Texas during a recent decade can be approximated by [tex]y=494.29(1.03)^t[/tex] when t is the number of years since the beginning of the decade.

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If [tex]b > 1[/tex] then it is an increasing function

If [tex]0 < b < 1[/tex] then it is a decreasing function

a) The model represents exponential growth as 1.03 > 1

b) The annual percent increase of the population is 3%

1.03 - 1 = 0.03

0.03 x 100 = 3%

c) To estimate when was population about 590,000 set y = 590 and solve for t:

[tex]\implies 590=494.29(1.03)^t[/tex]

[tex]\implies \dfrac{590}{494.29}=(1.03)^t[/tex]

Take natural logs of both sides:

[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t[/tex]

[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)[/tex]

[tex]\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}[/tex]

[tex]\implies t=5.988069001...[/tex]

Therefore the population was about 590,000 6 years since the beginning of the decade.

Answer:

355 miles

Step-by-step explanation:

Figure out how far the car travelled in 1 hour - 3 hours can be divided by 3 for 1 hour, so do the same for the miles - 213 / 3 = 71 miles.

So we know the car travelled 71 miles in 1 hour.

Now just multiply the miles by 5 to figure out the answer - 71 * 5 = 355 miles

:)