2616.95 rounded to the nearest tenth

The measure of the diagonal KI is approximately 6.465 centimeters.

The diagonals of the quadrilateral RISK are represented by line segments RS and KI, both measured in centimeters. There are two triangles forming the quadrilateral: [tex]\triangle RIS[/tex], [tex]\triangle RKS[/tex]

By Law of Sine and Law of Cosine we determine the measures of all internal angles:

Triangle RIS

[tex]RS^{2} = RI^{2}+IS^{2}-2\cdot RI\cdot IS \cdot \cos I[/tex] (1)

[tex]\frac{RS}{\sin I} = \frac{RI}{\sin S'} = \frac{IS}{\sin R'}[/tex] (2)

Triangle RKS

[tex]RS^{2} = RK^{2} + KS^{2}-2\cdot RK\cdot KS\cdot \cos K[/tex] (3)

[tex]\frac{RS}{\sin K} = \frac{RK}{\sin S''} = \frac{KS}{\sin R''}[/tex] (4)

[tex]S = S' + S''[/tex] (5)

[tex]R = R' + R''[/tex] (6)

By (1) and (3) we find the values of angles I and K:

[tex]I = \cos^{-1}\left(\frac{RI^{2}+IS^{2}-RS^{2}}{2\cdot RI\cdot IS} \right)[/tex]

[tex]I \approx 90.261^{\circ}[/tex]

[tex]K = \cos^{-1}\left(\frac{RK^{2}+KS^{2}-RS^{2}}{2\cdot RK\cdot KS} \right)[/tex]

[tex]K\approx 94.903^{\circ}[/tex]

By (2) and (4) we find the remaining angles for each triangle:

[tex]S' = \sin^{-1}\left[\left(\frac{RI}{RS} \right)\cdot \sin I\right][/tex]

[tex]S' \approx 38.682^{\circ}[/tex]

[tex]R' = \sin^{-1}\left[\left(\frac{IS}{RS} \right)\cdot \sin I\right][/tex]

[tex]R' \approx 51.057^{\circ}[/tex]

[tex]S'' = \sin^{-1}\left[\left(\frac{RK}{RS} \right)\cdot \sin K\right][/tex]

[tex]S'' \approx 28.969^{\circ}[/tex]

[tex]R'' = \sin^{-1}\left[\left(\frac{KS}{RS} \right)\cdot \sin K\right][/tex]

[tex]R'' \approx 56.128^{\circ}[/tex]

Then, we have the values of angles R and S by (5) and (6):

[tex]S \approx 67.651^{\circ}[/tex], [tex]R \approx 107.185^{\circ}[/tex]

The measure of the diagonal KI is found by the Law of Cosine:

[tex]KI = \sqrt{IS^{2}+SK^{2}-2\cdot IS\cdot SK\cdot \cos S}[/tex]

[tex]KI \approx 6.465\,cm[/tex]

The measure of the diagonal KI is approximately 6.465 centimeters.

To learn more on quadrilaterals, we kindly invite to check this verified question: https://brainly.com/question/6321910

Answer:

11y = -32  

Step-by-step explanation:

Answer:

h = 60˚

Step-by-step explanation:

Look at where it shows the 120˚, and its verticle angle. Verticle angles are congruent, or the same meaning it's also 120˚.

Then go to its corresponding angle, which is next to the h. Corresponding angles are also congruent, or the same. I'll call this angle m to save time and hopefully confusion.

Now, h and m are supplementary angles, meaning they add up to 180˚.

180˚ - 120˚, or 60˚ is your answer.

h = 60˚

The solution is, the value of h is, h = 60˚

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure, we get,

Look at where it shows the 120˚, and its vertical angle.

Vertical angles are congruent, or the same meaning it's also 120˚.

now, we have,

Then go to its corresponding angle, which is next to the h. Corresponding angles are also congruent, or the same.

We call this angle m to save time and hopefully confusion.

Now, h and m are supplementary angles,

meaning they add up to 180˚.

so, we have,

180˚ - 120˚,

or 60˚ is your answer.

i.e.

h = 60˚

Hence, The solution is, the value of h is, h = 60˚

To learn more on angle click:

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#SPJ7

Answer:

y = -29/19  and x = -44/19

Step-by-step explanation:

3x + 2y = -10    multiply by -2  ⇔    -6x -  4y = 20

2x - 5y = 3       multiply by 3   ⇔      6x - 15y = 9    

Add the two equation                             -19y = 29

                                                                       y =  -29/19

Use equation one and solve for x

3x + 2(-29/19) = -10

3x - 58/19 = -10

3x = -10 + 58/19

3x = -190/19 + 58/19

3x = (-190 + 58)/19

  3x = -132/19

    x =  - 132/ 19 ÷3                           [tex]\frac{-132}{19} (\frac{1}{3} ) = \frac{-44}{19}[/tex]

    x =  -44/19

Answer:

je suis désolé je ne vois pas bien

Step-by-step explanation:

et aussi je ne comprend pas l'anglais

Answer:

all real numbers i think

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

the probability on getting blue on spinner is 1/2

1/2 x 1/2 =1/4

Answer: Check explanation.

Step-by-step explanation: I think its 0. Not sure. Hope this helped!

Answer:

11 weeks

Step-by-step explanation:

If we multiply 50 by 11 we get 550 with a remainder of 100, if we're to take out another 50 for another week we would have 50 dollars remanding but the question says that we need to have at least 75 remaining so this will not be possible. Therefor 11 weeks is our answer.

I hope this helps have a great day :)

Answer:

All I know is that it is the   Last  Option

Step-by-step explanation:

I did most of this mentally but I can kinda help you out :D

original R: (-5,-5)     New R: (-11,-11)

To go back to original R: (-11+6, -11+6)

original U: (-5, 1)        new U: (1,7)

HOPE THIS HELPEDDDD :333

Answer:

72

Step-by-step explanation:

6(4(6)-3)-9(6)

6×(24−3)−54

I think the answer is 72, sorry if it is wrong

Answer:

I think it's 72

Step-by-step explanation:

4.6=24

24-3=21

21.6=126

9.6=54

126-54= 72

Answer:

83.1219512195

Step-by-step explanation:

Hope this helps!

Answer: d.

15/24 is not an equivalent fraction of 3/5.

Answer:

DCBA

Step-by-step explanation:

461.176470588

Explanation:

2×56=112

112×420=47040

---------------------------------

3×34=102

---------------------------------

47040÷102=461.176470588

Answer:

8x+5y=184

Hope This Helps!!!

Answer:

yeyeyeeyeyeeyeey

Step-by-step explanation:

Answer:

This is what it would look like! Hope this helps!

Answer:

she earned $324 in September

Answer:

she earned 240 dollars

Step-by-step explanation:

can you please mark me as brainlyist

Graphs are used to represent functions, and vice versa

The value of y for q = 360 degrees is 0

The sine equation is given as:

[tex]y = \sin(q)[/tex]

When q= 360 degrees, the sine equation becomes

[tex]y = \sin(360)[/tex]

At q= 360, the graph crosses the x-axis.

i.e. the value of the graph is 0.

So, the sine equation becomes

[tex]y = 0[/tex]

Hence, the value of y for q = 360 degrees is 0

Read more about sine equations at:

https://brainly.com/question/3522842

Answer:

$16.80

Step-by-step explanation:

30% of 24 and the answer is subtracted from $24

Answer:

x = 5/3 or 1.67 and y= 2.5 or 5/2

Step-by-step explanation:

Firstly to find the x intercept make y= 0 meaning put zero at where ever you find y to help eliminate the y

so

3x + 2y =5

3× + 2 (0)=5

3×=5

×=5/3 or 1.67

Secondly for the y intercept make x = 0 meaning put zero at where ever you find x to help eliminate the x leaving you with y

3x + 2y =5

3 (0) + 2y = 5

2y=5

y= 5/2 or 2.5

Answer:

20 cm

Step-by-step explanation:

Use the formula

A=4πr^2

Solving for radius

[tex]r = 1/2 \sqrt{A/\pi } = 1/2 \sqrt{4800/\pi }[/tex] ≈ 19.5441

We are given –

[tex] \sf \begin{cases} \sf A_{\circ} = 4\: 800\: cm^2 \\ \sf \pi = 3 \\ \sf r = \:?\: cm\end{cases}[/tex]

Just use the formulas for the sphere's area to determine the radius.

[tex]\qquad[/tex] [tex]\red{\twoheadrightarrow\bf A_{\bigcirc} = 4 \pi \cdot r^2} [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 4\:800 = 4 \cdot 3 \cdot r^2 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 4\:800 = 12 \cdot r^2 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r^2 = \dfrac{4\:800}{12} [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r^2 = 400 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf r = \sqrt{400} [/tex]

[tex]\qquad[/tex] [tex]\red{\twoheadrightarrow\bf r = 20\: cm} [/tex]

Henceforth, the radius of the sphere measures [tex] \bf = 20\: cm [/tex].