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Mandarinka [93]

2 years ago

10

A camper ties a rope from a tree to the ground to help build a shelter. The rope is 8 feet long, and it is tied 6 feet up the tr

ee. How far from the tree is the rope anchored to the ground? Use the Pythagorean theorem to the find the answer. WILL GIVE BRAINLIEST

1 answer:

Alexandra [31]2 years ago

7 0

C=8
B=6
A=?
C^2=b^2+a^2
8^2=6^2+a^2
It is the square root of 28

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Can some one check this please!4 1/3 + 3 1/2= 7 5/6

babunello [35]

yes it is correct

13/3+7/2=47/6

(26+21)/6=47/6

47/6=47/6

7 0

2 years ago

I NEED THIS ASAP, PLEASE HELP!!!

WINSTONCH [101]

Answer: 22.5 ; 5 ; 14

Step-by-step explanation:

Given the dataset:

{20,22,23,24,26,26,28,29,30}

The lower quartile (Q1) = 1/4(n + 1)th term

Where n = number of observations, n = 9

Q1 = 1/4 (9 + 1)th term

Q1 = 1/4(10) = 2.5

We average the 2nd and 3rd term:

(22 + 23) / 2

45 / 2 = 22.5

B) The interquartile range(IQR) of the dataset :

{62,63,64,65,67,68,68,68,69,74}

IQR = Q3 - Q1

The lower quartile (Q1) = 1/4(n + 1)th term

Where n = number of observations, n = 10

Q1 = 1/4 (10 + 1)th term

Q1 = 1/4(11) = 2.75 term

We take the average of the 2nd and 3rd term:

(63 + 64) / 2

45 / 2 = 63.5

The upper quartile (Q3) = 3/4(n + 1)th term

Where n = number of observations, n = 10

Q3 = 3/4 (10 + 1)th term

Q3 = 3/4(11) = 8.25 term

We take the average of the 8th and 9th term:

(68 + 69) / 2

137 / 2 = 68.5

IQR = Q3 - Q1

IQR = 68.5 - 63.5

IQR = 5

C) give the dataset :

{7,8,8,9,10,12,13,15,16}

The upper quartile (Q3) = 3/4(n + 1)th term

Where n = number of observations, n = 9

Q3 = 3/4 (9 + 1)th term

Q3 = 3/4(10) = 7.5 term

We take the average of the 7th and 8th term:

(13 + 15) / 2

28 / 2 = 14

7 0

3 years ago

The answers ? Plssss I’ll mark u brianliest

frez [133]

Answer:

4. C

5. B

Step-by-step explanation:

4. Circumference = diameter * pi

pi is approximately 3.14

Diameter = 2*radius

Diameter = 2*8 = 16

Circumference = 3.14 (16), so the answer is C.

5. The question asking asking for the surface of the toy box.

Surface area of a cube = 6*the area of one face of the cube = 6 (edge * edge)

Substitute the edge with 2

Surface area of the toy box = 6(2*2) = 6(4) = 24

Surface area is 24 feet squared, so the answer is B

Hope this helps :)

Have an awesome day!!

4 0

2 years ago

A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th

jeyben [28]

Consider a circle with radius $r$ centered at some point $(R+r,0)$ on the $x$ -axis. This circle has equation

$(x-(R+r))^2+y^2=r^2$

Revolve the region bounded by this circle across the $y$ -axis to get a torus. Using the shell method, the volume of the resulting torus is

$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

where $2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}$ .

So the volume is

$\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx$

Substitute

$x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt$

and the integral becomes

$\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt$

Notice that $\sin t\cos^2t$ is an odd function, so the integral over $\left[-\frac\pi2,\frac\pi2\right]$ is 0. This leaves us with

$\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt$

Write

$\cos^2t=\dfrac{1+\cos(2t)}2$

so the volume is

$\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}$

6 0

3 years ago

6x2 - 5x - 4 is equivalent to:

Sophie [7]

Answer:

<em>(</em><em>2</em><em>x</em><em> </em><em>+</em><em> </em><em>1</em><em>)</em><em> </em><em> </em><em>(</em><em>3</em><em>x</em><em> </em><em>-</em><em> </em><em>4</em><em>)</em>

Step-by-step explanation:

Solution:

6x² - 5x - 4
6x²- (8 - 3)x - 4
6x²- 8x + 3x - 4
2x (3x - 4) +1 (3x - 4)
(2x + 1) (3x - 4)

4 0

2 years ago