Tinutulungan ka ng Imhr.ca na makahanap ng maaasahang mga sagot sa lahat ng iyong mga katanungan mula sa mga eksperto. Tuklasin ang detalyadong mga sagot sa iyong mga tanong mula sa isang malawak na network ng mga eksperto sa aming komprehensibong Q&A platform. Nagbibigay ang aming platform ng seamless na karanasan para sa paghahanap ng mapagkakatiwalaang sagot mula sa isang network ng mga bihasang propesyonal.
Sagot :
Answer:
1)
- A. [tex]r=\frac{4}{3}[/tex]
- B. [tex]s=36[/tex]
- C. [tex]u=4[/tex]
2) [tex]x=108\\[/tex]
3) [tex]w=\frac{1600}{3}[/tex]
Step-by-step explanation:
Variation, in mathematics, is the relationship between two or more variables. One is constant and the other one is changing. The process of changing variables is called variation.
Two Types of Variation
1. Varies Directly
2. Varies Inversely
Varies directly is the relationship between two variables when both of them go in the same direction. For example, one variable is increasing, the other one should also be increasing.
Varies inversely or indirectly is the relationship between two variables when they don't tend in the same direction. For example, one variable goes increasing and the other one goes decreasing.
Definition 1: We say that [tex]y[/tex] varies directly with [tex]x[/tex], then there exist a [tex]k[/tex] such that [tex]y=kx[/tex].
Definition 2: We say that [tex]y[/tex] varies inversely with [tex]x[/tex], then there exists a [tex]k[/tex] such that [tex]y=\frac{k}{x}[/tex].
For number 1, since [tex]r[/tex] varies directly as [tex]s[/tex] and inversely as the square of [tex]u[/tex], then the mathematical representation is [tex]r=\frac{ks}{u^2}[/tex]. Substitute the values of [tex]u=2[/tex], [tex]r=2[/tex], and [tex]s=18[/tex] into the model and solve for [tex]k[/tex].
[tex]\begin{aligned}r&=\frac{ks}{u^2}\\2&=\frac{k(18)}{2^2}\\2&=\frac{18k}{4}\\4\left(2\right)&=4\left(\frac{18k}{4}\right)\\8&=18k\\\frac{8}{18}&=\frac{18k}{18}\\\frac{8}{18}&=k\\\frac{4}{9}&=k\end{aligned}[/tex]
- A. Find [tex]r[/tex], when [tex]u=3[/tex] and [tex]s=27[/tex].
[tex]\begin{aligned}r&=\frac{ks}{u^2}\\r&=\frac{\frac{4}{9}(27)}{3^2}\\r&=\frac{4(3)}{9}\\r&=\frac{12}{9}\\r&=\frac{4}{3}\end{aligned}[/tex]
- B. Find [tex]s[/tex], when [tex]u=2[/tex] and [tex]r=4[/tex].
[tex]\begin{aligned}r&=\frac{ks}{u^2}\\4&=\frac{\frac{4}{9}s}{2^2}\\4&=\frac{\frac{4}{9}s}{4}\\4(4)&=4\left(\frac{\frac{4}{9}s}{4}\right)\\16&=\frac{4}{9}s\\\frac{9}{4}(16)&=\frac{9}{4}\left(\frac{4}{9}s\right)\\9(4)&=s\\36&=s\end{aligned}[/tex]
- C. Find [tex]u[/tex], when [tex]r=1[/tex] and [tex]s=36\\[/tex].
[tex]\begin{aligned}r&=\frac{ks}{u^2}\\1&=\frac{\frac{4}{9}(36)}{u^2}\\1&=\frac{4(4)}{u^2}\\1&=\frac{16}{u^2}\\u^2(1)&=u^2\left(\frac{16}{u^2}\right)\\u^2&=16\\\sqrt{u^2}&=\sqrt{16}\\u&=4\end{aligned}[/tex]
For number 2, since [tex]x[/tex] varies directly as [tex]y^2[/tex] and inversely as [tex]z[/tex], then the mathematical representation is [tex]x=\frac{ky^2}{z}[/tex]. Substitute the values of [tex]x=12[/tex], [tex]y=3[/tex], and [tex]z=6[/tex] into the model and solve for [tex]k[/tex].
[tex]\begin{aligned}x&=\frac{ky^2}{z}\\12&=\frac{k(3^2)}{6}\\12&=\frac{9k}{6}\\12(6)&=6\left(\frac{9k}{6}\right)\\72&=9k\\\frac{72}{9}&=\frac{9k}{9}\\8&=k\end{aligned}[/tex]
- Find [tex]x[/tex], when [tex]y=9[/tex] and [tex]z=6[/tex].
[tex]\begin{aligned}x&=\frac{ky^2}{z}\\x&=\frac{8(9^2)}{6}\\x&=\frac{648}{6}\\x&=108\end{aligned}[/tex]
For number 3, since [tex]w[/tex] varies directly as [tex]x[/tex] and [tex]y[/tex], and varies inversely as [tex]v^2[/tex] then the mathematical representation is [tex]w=\frac{kxy}{v^2}[/tex]. Substitute the values of [tex]x=4[/tex], [tex]w=1200[/tex], [tex]y=9[/tex], and [tex]v=6[/tex] into the model and solve for [tex]k[/tex].
[tex]\begin{aligned}w&=\frac{kxy}{v^2}\\1200&=\frac{k(4)(9)}{6^2}\\1200&=\frac{36k}{36}\\1200&=k\end{aligned}[/tex]
- Find [tex]w[/tex], when [tex]x=3[/tex], [tex]y=12[/tex], and [tex]v=9[/tex].
[tex]\begin{aligned}w&=\frac{kxy}{v^2}\\w&=\frac{1200(3)(12)}{9^2}\\w&=\frac{43,200}{81}\\w&=\frac{1600}{3}\end{aligned}[/tex]
#BetterWithBrainly
To learn more about variations, please click the following links:
https://brainly.ph/question/2476944
https://brainly.ph/question/845317
https://brainly.ph/question/1922362
Umaasa kami na nakatulong ang impormasyong ito. Huwag mag-atubiling bumalik anumang oras para sa higit pang mga sagot sa iyong mga tanong at alalahanin. Pinahahalagahan namin ang iyong pagbisita. Lagi kaming narito upang mag-alok ng tumpak at maaasahang mga sagot. Bumalik anumang oras. Ang Imhr.ca ay nandito upang magbigay ng tamang sagot sa iyong mga katanungan. Bumalik muli para sa higit pang impormasyon.
