Answered

Makakuha ng mga solusyon sa iyong mga katanungan sa Imhr.ca, ang mabilis at tumpak na Q&A platform. Kumuha ng detalyado at eksaktong sagot sa iyong mga tanong mula sa isang komunidad ng mga eksperto sa aming komprehensibong Q&A platform. Sumali sa aming Q&A platform upang kumonekta sa mga eksperto na dedikado sa pagbibigay ng eksaktong sagot sa iyong mga tanong sa iba't ibang larangan.

find the equation and solve for the constant of the variation k.
1. A varies directly as T and S = 12 when T-8
2. E is inversely proportional to the square of F and E = 4 when F-5
3. varies jointly as Q and R, and P=12 when Q-8 and R-3
4. Z varies directly as X and inversely as Y and Z=10 when X-5 and Y=12

this is for my ate, I am answering her modules but I don't know how to answer these, she is sick and her module is due very soon. please help me, I even watched yt videos to answer this. please explain if you can, I really need it.​

Sagot :

ARMYL

Find the equation and solve for the constant of the variation k.

[tex] \\ [/tex]

1. A varies directly as T and A= 12 when T=8

[tex] \\ [/tex]

Equation:

[tex]A = kT \\ [/tex]

-Evaluate the values

[tex]12 = k(8) \\ [/tex]

-Divide both sides to 8, then cancel both 8 from the right side

[tex] \frac{12}{8} = \frac{k(8)}{8} \\ \frac{12}{8} = \frac{k( \cancel8)}{ \cancel8} \\ [/tex]

-Divide 12 by 8

[tex] \green{ \boxed{ \boxed{ \: \: k = \frac{3}{2 \: \: }}}} \\ \\ [/tex]

2. E is inversely proportional to the square of F and E = 4 when F=5

[tex] \\ [/tex]

Equation:

[tex] E = \frac{k}{ {F}^{2} } \\ [/tex]

-Evaluate the given values

[tex]4 = \frac{k}{ {5}^{2} } \\ [/tex]

-Square 5

[tex]4 = \frac{ k}{25} \\ [/tex]

-Multiply 25 to both sides, then cancel both 25 from the right side

[tex](25)(4) = \frac{k}{25} (25) \\ (25)(4) = \frac{k}{( \cancel{25)}} ( \cancel{25}) \\ [/tex]

-Multiply 25 by 4

[tex] \green{ \boxed{ \boxed{ \: \: k = 100 \: \: }}} \\ \\ [/tex]

3. P varies jointly as Q and R, and P=12 when Q=8 and R= 3

Equation:

[tex]P = kQ R \\ [/tex]

-Evaluate the values

[tex]12 = k(8)(3) \\ [/tex]

-Multiply 8 by 3

[tex]12 = k(24) \\ [/tex]

-Divide 24 by both sides, then cancel both 24 from the right side

[tex] \frac{12}{24} = \frac{k(24)}{24} \\ \frac{12}{24} = \frac{k( \cancel{24})}{ \cancel{24}} \\ [/tex]

-Divide 12 by 24

[tex] \green{ \boxed{ \boxed{ \: \: k = \frac{1}{2 } \: \: }}} \: \: \\ \\ [/tex]

4. Z varies directly as X and inversely as Y and Z=10 when X=5 and Y=12

[tex] \\ [/tex]

Equation:

[tex]Z = \frac{kX }{ Y} \\ [/tex]

-Evaluate the values

[tex]10 = \frac{k (5)}{12} \\ [/tex]

-Multiply 12 by both sides, then cancel both 12 from the right side.

[tex](12)(10) = \frac{k(5)}{12} (12) \\ (12)(10) = \frac{k(5)}{ \cancel{12}} ( \cancel{12}) \\ [/tex]

-Multiply 12 by 10

[tex]120 = k(5) \\ [/tex]

-Divide 5 by bith sides, then cancel both 5 from the right side.

[tex] \frac{120}{5} = \frac{k(5)}{5} \\ \frac{120}{5} = \frac{k( \cancel{5})} {\cancel{5}} \\ [/tex]

-Divide 120 by 5

[tex] \green{ \boxed{ \boxed{ \: \: k = 24 \: \: }}} \\ \\ \\ [/tex]

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. Nagagalak kaming sagutin ang iyong mga tanong. Bumalik sa Imhr.ca para sa higit pang mga sagot.