All Answers 358090 Answers

Rearranging the equation, we have:
x^2 - 2xy + y^2 = 17

Factoring the left side of the equation, we get:
(x - y)^2 = 17

To find the lattice points, we need to find integer solutions for (x, y) that satisfy the equation.

2) By the Binomial Theorem, the expansion of (5a/3−2b/3)10 is \begin{align*} &\binom{10}{0} \left( \frac{5a}{3} \right)^{10} \left( -\frac{2b}{3} \right)^{0} + \binom{10}{1} \left( \frac{5a}{3} \right)^{9} \left( -\frac{2b}{3} \right)^{1} + \binom{10}{2} \left( \frac{5a}{3} \right)^{8} \left( -\frac{2b}{3} \right)^{2} + \dots + \binom{10}{10} \left( -\frac{2b}{3} \right)^{10} \ &= \frac{5^{10}a^{10}}{3^{10}} - \frac{2^{10}b^{10}}{3^{10}} + \dots + \frac{2^{10}b^{10}}{3^{10}} \ &= \frac{5^{10}a^{10} - 2^{10}b^{10}}{3^{10}}. \end{align*}The sum of the coefficients is then [\frac{5^{10}a^{10} + 2^{10}b^{10}}{3^{10}} = \frac{1}{3^{10}} (5^{10} + 2^{10}) = \frac{9766649}{59049}.]

If you could envision rotating \(\triangle \text{ABC}\) around \(\overline{\text{AB}}\), then the diagram would look like the following diagram. I realize the diagram is not drawn to scale. As of now, I have not yet worked out how to draw 3-dimensional figures efficiently.

The surface area of right cones are \(\text{SA}_\text{right cone} = \pi r^2 + \pi rL\) where r is the radius of the right cone and the L is the slant height of the right cone. We already know the radius of this cone, but we can find L with the use of Pythagorean's Theorem.

\(L^2 = 1^2 + 3^2 \\ L^2 = 1 + 9 \\ L^2 = 10 \\ L = \sqrt{10} \text{ or } L = -\sqrt{10}\)

Since we are dealing with lengths, reject \(L = -\sqrt{10}\). Now that we have found all the necessary lengths, we can find the surface area of this right cone.

\(\begin{align*} \text{SA}_\text{right cone} &= \pi r^2 + \pi rL \\ &= \pi * 3^2 + \pi * 3 * \sqrt{10} \\ &= 9\pi + 3\sqrt{10}\pi \\ &= (9 + 3\sqrt{10}) \pi \end{align*} \)

The question asks what the surface area is pi times what number? Well, that number would be \(9 + 3\sqrt{10}\).

Lol. Plaintainmountain is raging. But seriously he needs to stop assuming accurate answers are ai. There are more users plaintainmountain goes against. IhaveHairyStuff, tastyabananas2ndDad, SpectraSynth, Ginstioniff, and more.

We have that 2−1≡4(mod7) and 3−1≡5(mod7), so L≡4+5≡1(mod7). Also, 2+3≡5(mod7), so (2+3)−1≡7−5≡2(mod7), so R≡2+5≡7(mod7). Therefore, L−R=6​.

Here is a more detailed explanation of the steps involved:

We find that 2−1≡4(mod7) and 3−1≡5(mod7) using the Euclidean algorithm.

We find that L≡4+5≡1(mod7) by applying the congruence ab≡1(modm) to a=2, b=4, and m=7.

We find that R≡2+5≡7(mod7) by applying the congruence ab≡1(modm) to a=5, b=2, and m=7.

We find that L−R=6​ by subtracting R from L.

( x + y)  =54

(x + y)^2  = 54^2  =  2916

Let P =  ( x ,12)

Using the square of the  distance  formula.... P is 10 units from (2,5)....so....

10^2 = ( 2 - x)^2 + ( 12 - 5)^2

100 = x^2 -4x + 4  + 49      simplify and rearrange as 

x^2  -4x + 4 = 51

(x - 2)^2  = 51     take the  positive  root

x - 2  =  sqrt (51)

x =   2 + sqrt (51)

P = (2 + sqrt (51) , 12)

Distance from  the  origin =    sqrt [  ( 2 + sqrt (51))^2  + 12^2  ] =

n =  sqrt  [  4 + 4sqrt (51) + 51 + 144 ]  =

sqrt [ 199 + 4sqrt (47) ]     ≈ 15.09 

x^2+y^2=14x+48y-8x-26y+16   rearrange as

x^2 -6x + y^2 -22y  = 16   complete the square on x, y

x^2  - 6x + 9  + y^2 -22y + 121  =  16 + 9 + 121

(x - 3)^2  + (y -11)^2 = 146

This is a  circle centered at (3, 11)  with a radius  of sqrt (146)

The minimum value of y =   11 - sqrt (146) ≈   -1.083

Angle XOZ = 360 - 124 -92 =  144°

Angle XYZ is a  circumscribed angle  subtending the same arc as  central  angle XOZ

So...its measure  is 1/2 angle XOZ =  (1/2) * 144 =  72°

% discount =   amt off original  price / original price

Cost per lb.  =   $2 / 4 lbs  =  .50 / lb.  =  50 cents per pound

You should be able to answer now