T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6 5. Using k as the constant of variation, which

Question

T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6

5. Using k as the constant of variation, which of the following is the equation of variation?
A. T=
\frac{kp {}^{2} }{z}
z
kp
2

​

B. T=
kpz {}^{2}kpz
2

C. T=
\frac{kz}{p {}^{2} }
p
2

kz
​

D. T=
\frac{pz {}^{2} }{k}
k
pz
2

​

6. Which of the following is the value of the variation constant:
A. 6
B. 8
C. 10
D. 12

7. Which of the following is twice the value of T when P=9 and Z=6?
A. 108
B. 216
C. 54
D. 36
​

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Ngọc Hoa 5 years 2021-07-27T11:07:42+00:00 1 Answers 292 views -1

Answers ( )

  1. Nick
    0
    2021-07-27T11:09:37+00:00
    Reply

    Answer:

    A. T= \frac{KP^2}{Z}

    D. K = 8

    B. 216

    Step-by-step explanation:

    Q. T varies directly as the square of P and inversely as Z and T=12 when P=3 and Z=6

    Solution:

    According to the given information:

    T varies directly as the square of P.

    T\alpha P^2..... (1)

    T varies inversely as Z.

    T\alpha \frac{1}{Z} ..... (2)

    Combining equations (1) & (2)

    T\alpha \frac{P^2}{Z}

    T= \frac{KP^2}{Z}

    (Where K is proportionality constant)

    (This is the equation of variation)

    Plug T=12, P=3 and Z=6 in the above equation of variation, we find:

    12= \frac{K(3)^2}{6}

    12= \frac{K\times 9}{6}

    K= \frac{12\times 6}{9}

    K= \frac{72}{9}

    K= 8

    So, the value of the variation constant = 8

    Next, plug P=9, Z=6 and K = 8 in the above equation of variation, we find:

    T= \frac{8(9)^2}{6}

    T= \frac{8\times 81}{6}

    T= \frac{648}{6}

    T= 108

    2T= 2\times 108

    2T= 216

    So, 216 is twice the value of T.

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