The answer for the question shown above is the las option, which is: <span>D. 2:3 and 4:9.
The explanation is shown below:
1. You have that</span><span> widths of the two similar rectangles are 10 cm and 15 cm. Therefore:
</span> ratio=10:15
ratio=2:3
2- So, the ratio of the perimeter is:
ratio of the perimeter= 2:3
3- The ratio of the areas is:
ratio of the areas=2²:3²
ratio of the areas=4:9
Answer with Step-by-step explanation:
We are given that u and v are functions of x and both are differentiable at x=0
![u(0)=4,u'(0)=7,v(0)=2,v'(0)=1](https://tex.z-dn.net/?f=u%280%29%3D4%2Cu%27%280%29%3D7%2Cv%280%29%3D2%2Cv%27%280%29%3D1)
a.We have to find the values of ![\frac{d(uv)}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28uv%29%7D%7Bdx%7D)
![\frac{d(u\cdot v)}{dx}=u'v+uv'](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28u%5Ccdot%20v%29%7D%7Bdx%7D%3Du%27v%2Buv%27)
Using this formula
Then , we get
![[\frac{d(uv)}{dx}]_{x=0}=u'(0)v(0)+u(0)v'(0)=7(2)+4(1)=14+4=18](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28uv%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3Du%27%280%29v%280%29%2Bu%280%29v%27%280%29%3D7%282%29%2B4%281%29%3D14%2B4%3D18)
![[\frac{d(uv)}{dx}]_{x=0}=18](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28uv%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D18)
b.![\frac{d(u/v)}{dx}=\frac{u'v-uv'}{v^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28u%2Fv%29%7D%7Bdx%7D%3D%5Cfrac%7Bu%27v-uv%27%7D%7Bv%5E2%7D)
![[\frac{d(u/v)}{dx}]_{x=0}=\frac{u'(0)v(0)-u(0)v'(0)}{v^2(0)}=\frac{7(2)-4(1)}{2^2}=\frac{14-4}{4}=\frac{10}{4}=\frac{5}{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28u%2Fv%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D%5Cfrac%7Bu%27%280%29v%280%29-u%280%29v%27%280%29%7D%7Bv%5E2%280%29%7D%3D%5Cfrac%7B7%282%29-4%281%29%7D%7B2%5E2%7D%3D%5Cfrac%7B14-4%7D%7B4%7D%3D%5Cfrac%7B10%7D%7B4%7D%3D%5Cfrac%7B5%7D%7B2%7D)
![[\frac{d(u/v)}{dx}]_{x=0}=\frac{5}{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28u%2Fv%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D%5Cfrac%7B5%7D%7B2%7D)
c.
![[\frac{d(v/u)}{dx}]_{x=0}=\frac{v'(0)u(0)-v(0)u'(0)}{u^2(0)}=\frac{1(4)-7(2)}{4^2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28v%2Fu%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D%5Cfrac%7Bv%27%280%29u%280%29-v%280%29u%27%280%29%7D%7Bu%5E2%280%29%7D%3D%5Cfrac%7B1%284%29-7%282%29%7D%7B4%5E2%7D)
![[\frac{d(v/u)}{dx}]_{x=0}=\frac{-10}{16}=\frac{-5}{8}](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28v%2Fu%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D%5Cfrac%7B-10%7D%7B16%7D%3D%5Cfrac%7B-5%7D%7B8%7D)
d.![\frac{d(-6v-9u)}{dx}=-6v'-9u'](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28-6v-9u%29%7D%7Bdx%7D%3D-6v%27-9u%27)
![[\frac{d(-6v-9u)}{dx}]_{x=0}=-6v'(0)-9u'(0)=-6(1)-9(7)=-6-63=-69](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28-6v-9u%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D-6v%27%280%29-9u%27%280%29%3D-6%281%29-9%287%29%3D-6-63%3D-69)
![[\frac{d(-6v-9u)}{dx}]_{x=0}=-69](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bd%28-6v-9u%29%7D%7Bdx%7D%5D_%7Bx%3D0%7D%3D-69)
Standard form is ax + by = c. Begin our transformation by multiplying both sides by 2 to get rid of the fraction. Notice that ax + by = c does not allow for fractions. Doing that multiplication gives us 2y=-x + 3. Now move the x over by the y by addition. x + 2y = 3. And there you go!
The contestants total number of points is 20.
30 + 15 = 45
45 - 25 = 20 total points
Answer:
3(2^3+({4}/{2}^3-(6-3)^2)=21