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3 years ago

For which value of x must the square root 97x be further simplified

Mathematics

1 answer:

lys-0071 [83]3 years ago

6 0

Question:

For which value of x must the expression √97x be further simplified?

A. 5 B. 10 C. 15 D. 20

Answer:

$D.$ $x = 20$

Step-by-step explanation:

Given

$\sqrt{97x$

Required

For what value of x can it be simplified

From the list of options, only (D) is correct

D. 20

Substitute 20 for x in $\sqrt{97x$

$\sqrt{97 x} = \sqrt{97 * 20}$

Express 20 as 4 * 5

$\sqrt{97 x} = \sqrt{97 * 4 * 5}$

Reorder

$\sqrt{97 x} = \sqrt{4 *97 * 5}$

Split

$\sqrt{97 x} = \sqrt{4} *\sqrt{97 * 5}$

$\sqrt{97 x} = 2*\sqrt{97 * 5}$

$\sqrt{97 x} = 2*\sqrt{485}$

$\sqrt{97 x} = 2\sqrt{485}$

With other values of x, the given expression can not be simplified.

Hence:

$x = 20$

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3 years ago

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slavikrds [6]

Answer:

a. $\frac{dT}{dt}=k(T-Tm); T(0)=190$

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c. $k=-0.00259$

d. $t=153.39838\\$ minutos

Step-by-step explanation:

a. Newton's law of cooling states that the speed with which a body is cooled is proportional to the difference between its temperature and that of the medium in which it is found. Then, the initial value problem is given by:

$Tm=68$

$\frac{dT}{dt}=k(T-Tm); T(0)=190$

b. The differential equation obtained is a differential equation of separable variables:

$\frac{dT}{T-Tm}=kdt\\\\\int {\frac{dT}{T-Tm}}=\int{kdt}\\\\Ln|T-Tm|=kt+C\\\\T(t)=C_{0}e^{kt}+Tm=C_{0}e^{kt}+68\\\\T(0)=C_{0}e^{k(0)}+68=190\\\\C_{0}=122$

c. After 33 minutes of serving the coffee has cooled to 180°:

$T(33)=122e^{33k}+68=180\\\\e^{33k}=\frac{112}{122}\\\\33k=Ln(\frac{112}{122})\\\\k=-0.00259$

$150=122e^{-0.00259t}+68\\\\Ln(\frac{150-68}{122})=-0.00259t\\\\t=153.39838\\\\$

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3 years ago