Answer:
eric
Step-by-step explanation:
just took the test
Answer:
15.0
Step-by-step explanation:
Let's start by looking at triangle ORQ. Since RQ is tangent to the circle, we know that angle ∠ORQ is 90°. Then, since OR is equivalent to the radius of 5, RQ is 5√3, and side OQ is clearly larger than RQ, we can identify this as a 90-60-30 degree triangle. This makes side OQ have a length of 10, and angle ∠QOR, opposite of the second largest side, has the second largest angle of 60°, leaving ∠OQR with an angle of 30°.
The formula for the chord length is 2r*sin(c/2), with c being the angle between the two points on the circle (in this case, ∠QOR=∠NOR).. Our radius is 5, so the length of chord NR is 2*5*sin(60/2)=5, making our answer 5(ON)+5(OR)+5(RN)
Answer:
The answer is below
Step-by-step explanation:
The system of equations:
8x-9y+13z=11
-8x-5y+5z=15
3x+4y-8z=-10
The equations can be represented in matrix form as:
AX = B
X = A⁻¹B
Therefore:
![\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] ^{-1}\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-9%2613%5C%5C-8%26-5%265%5C%5C3%264%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C15%5C%5C-10%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-9%2613%5C%5C-8%26-5%265%5C%5C3%264%26-8%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C15%5C%5C-10%5Cend%7Barray%7D%5Cright%5D%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{19} &-\frac{1}{19}&\frac{1}{19}\\-\frac{49}{380}&-\frac{103}{380}&-\frac{36}{95} \\-\frac{17}{380}&-\frac{69}{380}&-\frac{28}{95} \end{array}\right] \left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}-0.74\\-1.69\\0.13\end{array}\right] \\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B19%7D%20%26-%5Cfrac%7B1%7D%7B19%7D%26%5Cfrac%7B1%7D%7B19%7D%5C%5C-%5Cfrac%7B49%7D%7B380%7D%26-%5Cfrac%7B103%7D%7B380%7D%26-%5Cfrac%7B36%7D%7B95%7D%20%5C%5C-%5Cfrac%7B17%7D%7B380%7D%26-%5Cfrac%7B69%7D%7B380%7D%26-%5Cfrac%7B28%7D%7B95%7D%20%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C15%5C%5C-10%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-0.74%5C%5C-1.69%5C%5C0.13%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
