The correct answer for this question is letter "a.rectangle, square, quadrilateral, parallelogram, and rhombus" <span>Judging by appearance, at first, we can say that the figure is a square and at the same time a quadrilateral. Then square is a rectangle. And it connects with the parallelogram and rhombus.</span>
The area of the cylinder is a function of its height (h) and radius, (
)
The exact value of h is: ![\mathbf{7\sqrt 2- 4\sqrt 3}](https://tex.z-dn.net/?f=%5Cmathbf%7B7%5Csqrt%202-%204%5Csqrt%203%7D)
The given parameters are:
![\mathbf{Area =56\pi\sqrt 6}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D56%5Cpi%5Csqrt%206%7D)
![\mathbf{r=4\sqrt 3}](https://tex.z-dn.net/?f=%5Cmathbf%7Br%3D4%5Csqrt%203%7D)
The surface area of a cylinder is calculated as:
![\mathbf{Area = 2\pi rh + 2\pi r^2}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%202%5Cpi%20rh%20%2B%202%5Cpi%20r%5E2%7D)
Substitute values for Area
![\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}](https://tex.z-dn.net/?f=%5Cmathbf%7B56%5Cpi%5Csqrt%206%3D%202%5Cpi%20rh%20%2B%202%5Cpi%20r%5E2%7D)
Divide through by pi
![\mathbf{56\sqrt 6= 2 rh + 2r^2}](https://tex.z-dn.net/?f=%5Cmathbf%7B56%5Csqrt%206%3D%202%20rh%20%2B%202r%5E2%7D)
Substitute value for r
![\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}](https://tex.z-dn.net/?f=%5Cmathbf%7B56%5Csqrt%206%3D%202%20%284%5Csqrt%203%29h%20%2B%202%284%5Csqrt%203%29%5E2%7D)
![\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}](https://tex.z-dn.net/?f=%5Cmathbf%7B56%5Csqrt%206%3D%208h%5Csqrt%203%20%2B%202%5Ctimes%2048%7D)
![\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}](https://tex.z-dn.net/?f=%5Cmathbf%7B56%5Csqrt%206%3D%208h%5Csqrt%203%20%2B%2096%7D)
Collect like terms
![\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}](https://tex.z-dn.net/?f=%5Cmathbf%7B8h%5Csqrt%203%20%3D%2056%5Csqrt%206-%2096%7D)
Make h the subject
![\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bh%20%3D%20%5Cfrac%7B56%5Csqrt%206%7D%7B8%5Csqrt%203%7D-%20%5Cfrac%7B96%7D%7B8%5Csqrt%203%7D%7D)
![\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bh%20%3D%207%5Csqrt%202-%20%5Cfrac%7B12%7D%7B%5Csqrt%203%7D%7D)
Rationalize
![\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bh%20%3D%207%5Csqrt%202-%20%5Cfrac%7B12%5Csqrt%203%7D%7B3%7D%7D)
![\mathbf{h = 7\sqrt 2- 4\sqrt 3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bh%20%3D%207%5Csqrt%202-%204%5Csqrt%203%7D)
Hence, the exact value of h is: ![\mathbf{7\sqrt 2- 4\sqrt 3}](https://tex.z-dn.net/?f=%5Cmathbf%7B7%5Csqrt%202-%204%5Csqrt%203%7D)
Read more about surface areas t:
brainly.com/question/25131428
Answer:
Step-by-step explanation:
Let
x-----> the number
we know that
![p\%=\frac{p}{100}](https://tex.z-dn.net/?f=p%5C%25%3D%5Cfrac%7Bp%7D%7B100%7D)
so
![\frac{p}{100}*x=a](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7B100%7D%2Ax%3Da)
solve for x
-----> expression that represent the number
Answer:
Step-by-step explanation:
LOL The graph doesn’t match the y intercept :)
Anyway
If we have point (0,-3) we have a quadratic of
y=ax^2+bx-3 we are given points (-1,0) and (2,0) so
a-b-3=0 and 4a+2b-3=0
4a+2b-3+2(a-b-3)=0
4a+2b-3+2a-2b-6=0
6a-9=0
6a=9
a=1.5, since a-b=3
1.5-b=3
b=-1.5
y=1.5x^2-1.5x-3
According to Vieta's Formulas, if
![x_1,x_2](https://tex.z-dn.net/?f=x_1%2Cx_2)
are solutions of a given quadratic equation:
Then:![a(x-x_1)(x-x_2)](https://tex.z-dn.net/?f=a%28x-x_1%29%28x-x_2%29)
is the completely factored form of
![ax^2+bx+c](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc)
.
If choose
![x=d^2](https://tex.z-dn.net/?f=x%3Dd%5E2)
, then:
![\displaystyle x^2-8x+16=0\\\\x_{1,2}= \frac{8\pm \sqrt{64-64} }{2}=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2-8x%2B16%3D0%5C%5C%5C%5Cx_%7B1%2C2%7D%3D%20%5Cfrac%7B8%5Cpm%20%20%5Csqrt%7B64-64%7D%20%7D%7B2%7D%3D4%20)
So, according to Vieta's formula, we can get:
![x^2-8x+16=(x-4)(x-4)= (x-4)^2](https://tex.z-dn.net/?f=x%5E2-8x%2B16%3D%28x-4%29%28x-4%29%3D%20%28x-4%29%5E2)
But
![x=d^2](https://tex.z-dn.net/?f=x%3Dd%5E2)
: