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2 years ago

7

What is the value of x in the equation 1/5x-2/3y=30 when y=15

2 answers:

zmey [24]2 years ago

7 0

1/5x-2/3y=30 when y=15

1/5x-10=30
1/5x=40
x=200

Lemur [1.5K]2 years ago

4 0

X would equal 200......

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A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to

s2008m [1.1K]

Answer:

Part 1 : $A=250 e^{-0.008223t}$

Part 2 : Half life is 84 minutes ( approx )

Step-by-step explanation:

Part 1 : Suppose the function that shows the amount( in grams ) of the substance after t minutes,

$A=A_0 e^{kt}$

If t = 0 min, A = 250 grams,

$250=A_0 e^{0}$

$\implies A_0 = 250$

If t = 250, A = 32 grams,

$32 = A_0 e^{250k}$

$32 = 250 e^{250k}$

$0.128 = e^{250k}$

Taking ln both sides,

$\ln(0.128) = 250k$

$\implies k =\frac{\ln(0.128)}{250}=-0.008223$

Hence, the equation that shows this situation,

$A=250 e^{-0.008223t}$

Part 2 : If A = 250/2 = 125,

$125 = 250 e^{-0.008223t}$

$0.5 = e^{-0.008223t}$

Taking ln both sides,

$\ln(0.5) = -0.008223t$

$\implies t =\frac{\ln(0.5)}{-0.008223}\approx 84$

Therefore, the half life of the substance would be 84 minutes.

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$\large\bf{\underline{Given :}}$

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AD is a bisector of ∠‎A

__________________________________________

$\large\bf{\underline{To \:prove :}}$

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$\large\bf{\underline{In \: triangle \: ABD\:and\: triangle\:ADC}}$

${⟹AD = AD\:\:\:\:\:\:\:\:\:\:\:\:\:\:( common)}$

${⟹∠BAD = ∠CAD\:\:\:\:\:\:\:\:\:( given : AD \:is \:bisector \:of \:∠A )}$

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$\large\bf{\underline{Note :}}$ Slide to view full answer.

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