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4 years ago

54 - 4a^2 + 3b^3 when a = -2 and b = 4.

Mathematics

1 answer:

hoa [83]4 years ago

4 0

54 - 4(-2)^2 + 3(4)^3 = 230 = 2.3*10^2

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96 16 81 = x 11 15 18 = y what is the value of y-2x?

qwelly [4]

Hey, im not really sure but i think it is that 1. x=96 y=11 2. x=16 y=15 3.x=81 y=18
Then you just substitute the numbers into the letters. For example,

11-96(2)= -181

15-16(2)= -17

18-81(2)= -144

3 0

3 years ago

1/ 12 exponent 3 write it as negative exponent

kramer

1728 is the answer. (1/12)^-3

5 0

3 years ago

If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0

4 years ago

Zach's Italian pizza bar bates 2000 pizzas in the first year that are open. In the second year they baked 3,000 pizzas and in th

Vesna [10]

what is the question?

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Two of the vertices of a triangle are located at (6,0) and (5,10) on the coordinate plane. The third vertex is located at (x,20)

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The answer is 1,1 . 3,-3, 5, -3

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3 years ago