Answer:
- 17. A. 180 in²
- 18. B. 234 in²
Step-by-step explanation:
#17
<u>Total surface area is:</u>
- A = 8(3*2 + 6*2) + 2(3*6) = 180 in²
Correct option is A
#18
<u>Total surface area is:</u>
- A = 2(9*9) + 4(2*9) = 234 in²
Correct option is B
Answer:
The answer in the attached figure
Step-by-step explanation:
Let
x------> the abscissa
y-----> the ordinate
we know that
-----> given problem
The domain is ![[-1, 0, 1]](https://tex.z-dn.net/?f=%5B-1%2C%200%2C%201%5D)
so
For ![x=-1](https://tex.z-dn.net/?f=x%3D-1)
![y=2(-1)=-2](https://tex.z-dn.net/?f=y%3D2%28-1%29%3D-2)
The point is ![(-1,-2)](https://tex.z-dn.net/?f=%28-1%2C-2%29)
For ![x=0](https://tex.z-dn.net/?f=x%3D0)
![y=2(0)=0](https://tex.z-dn.net/?f=y%3D2%280%29%3D0)
The point is ![(0,0)](https://tex.z-dn.net/?f=%280%2C0%29)
For ![x=1](https://tex.z-dn.net/?f=x%3D1)
![y=2(1)=2](https://tex.z-dn.net/?f=y%3D2%281%29%3D2)
The point is ![(1,2)](https://tex.z-dn.net/?f=%281%2C2%29)
The answer in the attached figure
You just need to have the variable by itself, so move the -6.72 to the other side (that will make it +6.72)
So you should have this equation now: y = 253+6.72
Then just add them and you have this: y = 259.72
And that is your answer!
Hope I helped! <3
Answer:
cosФ =
, sinФ =
, tanФ = -8, secФ =
, cscФ =
, cotФ = ![-\frac{1}{8}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B8%7D)
Step-by-step explanation:
If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:
- cosФ =
![\frac{x}{r}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Br%7D)
- sinФ =
![\frac{y}{r}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Br%7D)
- tanФ =
![\frac{y}{x}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bx%7D)
- secФ =
![\frac{r}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bx%7D)
- cscФ =
![\frac{r}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7By%7D)
- cotФ =
![\frac{x}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7By%7D)
- Where r =
(the length of the terminal side from the origin to point (x, y)
- You should find the quadrant of (x, y) to adjust the sign of each function
∵ Point (1, -8) lies on the terminal side of angle Ф in standard position
∵ x is positive and y is negative
→ That means the point lies on the 4th quadrant
∴ Angle Ф is on the 4th quadrant
∵ In the 4th quadrant cosФ and secФ only have positive values
∴ sinФ, secФ, tanФ, and cotФ have negative values
→ let us find r
∵ r = ![\sqrt{x^{2}+y^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%20%7D)
∵ x = 1 and y = -8
∴ r = ![\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%5Csqrt%7B%281%29%5E%7B2%7D%2B%28-8%29%5E%7B2%7D%7D%3D%5Csqrt%7B1%2B64%7D%3D%5Csqrt%7B65%7D)
→ Use the rules above to find the six trigonometric functions of Ф
∵ cosФ = ![\frac{x}{r}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Br%7D)
∴ cosФ =
∵ sinФ = ![\frac{y}{r}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Br%7D)
∴ sinФ = ![-\frac{8}{\sqrt{65}}](https://tex.z-dn.net/?f=-%5Cfrac%7B8%7D%7B%5Csqrt%7B65%7D%7D)
∵ tanФ = ![\frac{y}{x}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bx%7D)
∴ tanФ =
= -8
∵ secФ = ![\frac{r}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bx%7D)
∴ secФ =
= ![\sqrt{65}](https://tex.z-dn.net/?f=%5Csqrt%7B65%7D)
∵ cscФ = ![\frac{r}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7By%7D)
∴ cscФ = ![-\frac{\sqrt{65}}{8}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%7B65%7D%7D%7B8%7D)
∵ cotФ = ![\frac{x}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7By%7D)
∴ cotФ =
Answer:
The standard equation of the parabola is:
![y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
![y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2](https://tex.z-dn.net/?f=y-y_%7Bvertex%7D%3Da%5C%2C%28x-x_%7Bvertex%7D%29%5E2%5C%5Cy-6%3Da%5C%2C%28x-4%29%5E2)
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
![y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}](https://tex.z-dn.net/?f=y-6%3Da%5C%2C%28x-4%29%5E2%5C%5C0-6%3Da%5C%2C%282-4%29%5E2%5C%5C-6%3Da%5C%2C4%5C%5Ca%3D-%5Cfrac%7B6%7D%7B4%7D%20%3D-%5Cfrac%7B3%7D%7B2%7D)
Then the equation of the parabola becomes:
![y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%5C%2C%28x-4%29%5E2%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%28x%5E2-8x%2B16%29%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-24%5C%5Cy%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)