All Answers 358232 Answers

(a)

We can transform the original equation to this :

4x^2  + 25y^2   = 100

The center of this ellipse is  at  (0,0)

So..the translated equation is

4x^2 - 16x  + 25y^2 + 150y  =   -c     complete the square on  x and y

4(x^2 -  4x + 4)  + 25 (y^2 + 6y + 9)  =  -c + 16 + 225

4(x - 2)^2  + 25(y +3 )^2  = 241  - c       divide through by 100

(x - 2)^2 / 25 + (y +3 ) / 4  =    [241 - c ] / 100

We want the right side to =  1...so....c  = 141

The center of this ellipse is at  (2 , -3)   so....this is the transaltion  vector

So  a  = 2   b  = -3    and c  = 141

(b)  The center of the translated ellipse is (2, -3)

The minor axis  is parallel to the y axis

The length of this axis  = 4

And the tangent lines tangent to the ellipse and parallel to the x axis  are 2 units above and below the center.....so....their equations are  y = -3 + 2   ⇒  y  = -1  and

y = -3 - 2  ⇒ y = -5

Here's the graph : https://www.desmos.com/calculator/k2p2x4xh7k

thank you

3+0.22 = 3.22

Here is a good page for new people if you wanna read over that!

https://web2.0calc.com/questions/information-for-new-people

Welcome to the site!

$50,000 for each person....so...for two people $100,000  ⇒  "C"

A segment drawn parallel to the base of a triangle splits the sides proportionately

In triangle AXC....since  segment ZY  is parallel to base XC..so...

XZ : ZA  = YC : AY

4 : 8  = YC  : AY

1 : 2  =  YC : AY 

And in triangle ABC.....segment XY  is parallel to base BC...so...

BX :  AX =  YC  : AY

So

BX : AX  = 1 : 2

BX : [  XZ + ZA ]  = 1 : 2

BX /  [ 4 + 8 ]  = 1 : 2

BX / 12  = 1 : 2

So  BX  =  6

Nevermind, I worked it out. For anyone who will need this in the future, make sure you don't forget to divide by six in the SD formula and make sure that in the ME formula, you square root the 325. You should get 17.66 after you round the answer, if you plugged everything in correctly. 

tan  =  opp side /  adjacent side  =  20 / 15  =  4 / 3  ≈   1.33  ⇒ "C"

Sphere volume =  (4/3) pi (5)^3   =  500/3  pi

(1/2) the height of the cylinder is given by  sqrt  [ 5^2 - 3^2 ] = sqrt (16)  = 4

So....the total  height  = 8

Cylinder volume  = pi * (3^2) * ( 8)  =  72 pi

Volume outside the cylinder but inside the sphere  =  pi [ 500 / 3 - 72 ]  =

[ 500 - 216 ] / 3  * pi   =  [284/3] pi

So  W  =   284 / 3

\(f(x) \text{ will be continuous if the each of the individual parts is continuous }\\ \text{and the value of those parts agree at }0 \\ \text{each part is composed of continuous functions so we just have to check values at 0}\\ f(0^-)= a \tan^{-1}(0) + b = b \\ f(0^+) = \lim \limits_{x \to 0}~\dfrac{\ln(1+\sin(x))}{x}\\ \text{Using L'Hopital's rule we take the derivatives of numerator and denominator and look at the ratio} \\ \left .\dfrac{d}{dx} \ln(1+\sin(x)) = \dfrac{\cos(x)}{1+\sin(x)} \right|_{x=0} = 1\\ \dfrac{d}{dx}=1 \text{ and thus the limit is }\\ f(0^+) = \lim \limits_{x \to 0}~\dfrac{\ln(1+\sin(x))}{x} = \dfrac 1 1 = 1 \\ \text{and thus }b=1\)

\(\text{The value of the derivative at 0 must also agree from both sides} \\ \text{I'm going to let you work this bit out}\\ \text{Take the derivatives of both terms of f(x) }\\ \text{one can be immediately evaluated at 0, the other you'll have to take the limit as }x\to 0 \\ \text{set the value }a \text{ such that the two values agree}\)

P  =  2DB

This is the 6 month premium

We need to divide this by 6 to get the monthkly premium

P  = 2 * 1.02 *  500  /  6  =  1000* 1.02 / 6  =  1020 / 6 = $170  ⇒  "A"

Thank you for your help!

Snaps*

4)

4.3 / 9.7 =(3x - 8.6) / 1.4             cross multiply
4.3 x 1.4 =9.7(3x - 8.6)
6.02 =29.1x - 83.42
6.02 + 83.42 =29.1x
89.44 = 29.1x                              divide both sides by 29.1
x =89.44 / 29.1
x =3.0735