Answer:
![8x^3y+x^2+5y^2x-14z-2](https://tex.z-dn.net/?f=8x%5E3y%2Bx%5E2%2B5y%5E2x-14z-2)
Step-by-step explanation:
For a polynomial to be written in standard form, we arrange the terms of x from greatest degree to least.
The greatest power of x in this expression is x³. This term comes first. The next greatest is x²; this is second. Next we have the term with x¹, then the one with the variable z, and lastly the constant term.
Consider ∆JWZ and ∆JKZ
WZ~KJ (given)
<u>/</u><u> </u><u>WZJ</u>~<u>/</u><u> </u>KJZ (given)
JZ~JZ (common)
Therefore,
∆JWZ~∆JKZ by SAS congruence rule.
JW~ZK by CPCT.
Answer:
y = -7
Step-by-step explanation:
It has a slope of zero (it is just a straight,infinite line)
And it passes through the point (5,-7) because it is continuous and infinite
Answer:
-0.032
Step-by-step explanation:
The given equation is
![{x}^{3} + 5x + y = {y}^{3}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B3%7D%20%20%2B%205x%20%2B%20y%20%3D%20%20%7By%7D%5E%7B3%7D)
We differentiate implicitly to get:
![3{x}^{2} + 5 + \frac{dy}{dx} = 3 {y}^{2} \frac{dy}{dx}](https://tex.z-dn.net/?f=3%7Bx%7D%5E%7B2%7D%20%20%2B%205%20%2B%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%203%20%7By%7D%5E%7B2%7D%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
![\frac{dy}{dx} - 3 {y}^{2} \frac{dy}{dx} = - ( 3{x}^{2} + 5)](https://tex.z-dn.net/?f=%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20-%20%203%20%7By%7D%5E%7B2%7D%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20-%20%28%203%7Bx%7D%5E%7B2%7D%20%20%2B%205%29)
![(1 - 3 {y}^{2} )\frac{dy}{dx} = - ( 3{x}^{2} + 5)](https://tex.z-dn.net/?f=%281%20%20-%20%203%20%7By%7D%5E%7B2%7D%20%29%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20-%20%28%203%7Bx%7D%5E%7B2%7D%20%20%2B%205%29)
![\frac{dy}{dx} = \frac{ - ( 3{x}^{2} + 5)}{1 - 3 {y}^{2} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%5Cfrac%7B%20-%20%28%203%7Bx%7D%5E%7B2%7D%20%20%2B%205%29%7D%7B1%20%20-%20%203%20%7By%7D%5E%7B2%7D%20%7D%20)
![\frac{dy}{dx} = \frac{ 3{x}^{2} + 5}{ 3 {y}^{2} - 1 }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%5Cfrac%7B%20%203%7Bx%7D%5E%7B2%7D%20%20%2B%205%7D%7B%203%20%7By%7D%5E%7B2%7D%20-%201%20%7D%20)
We differentiate again using the quotient rule:
![\frac{d^{2} y}{d {x}^{2} } = \frac{ 6 {x} (3 {y}^{2} - 1) - (3 {x}^{2} + 5)(6y \frac{dy}{dx}) }{ (3 {y}^{2} - 1)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E%7B2%7D%20y%7D%7Bd%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%3D%20%5Cfrac%7B%206%20%7Bx%7D%20%283%20%7By%7D%5E%7B2%7D%20-%201%29%20-%20%283%20%7Bx%7D%5E%7B2%7D%20%20%2B%205%29%286y%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%20%20%7D%7B%20%283%20%7By%7D%5E%7B2%7D%20-%201%29%5E%7B2%7D%20%20%7D%20)
At (1,2), x=1, and y=2
![\frac{d^{2} y}{d {x}^{2} } = \frac{ 6 { \times 1} (3 { \times 2}^{2} - 1) - (3 { \times 1}^{2} + 5)(6 \times 2 \times \frac{8}{11} ) }{ (3 { \times 2}^{2} - 1)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E%7B2%7D%20y%7D%7Bd%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%3D%20%5Cfrac%7B%206%20%7B%20%5Ctimes%201%7D%20%283%20%7B%20%5Ctimes%202%7D%5E%7B2%7D%20-%201%29%20-%20%283%20%7B%20%5Ctimes%201%7D%5E%7B2%7D%20%20%2B%205%29%286%20%5Ctimes%202%20%5Ctimes%20%20%5Cfrac%7B8%7D%7B11%7D%20%29%20%20%7D%7B%20%283%20%7B%20%5Ctimes%202%7D%5E%7B2%7D%20-%201%29%5E%7B2%7D%20%20%7D%20)
![\frac{d^{2} y}{d {x}^{2} } = - 0.032](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E%7B2%7D%20y%7D%7Bd%20%7Bx%7D%5E%7B2%7D%20%7D%20%20%20%3D%20%20-%200.032)