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3 years ago

Steve bought 2 plain and 1/4 of a pepperoni pizza. In all how much pizza did he buy?

Mathematics

1 answer:

sineoko [7]3 years ago

7 0

In all he brought

Plain pizza + pepperoni pizza

= 2 + ¼
= 2¼

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Which term describes the variable y in the expression yn?<br> A.Product B.Factor C.Base D.Exponent

grigory [225]

If the expression is: yⁿ
then y is the Base.

If the expression is: yn
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3 years ago

the half-life of chromium-51 is 38 days. If the sample contained 510 grams. How much would remain after 1 year?

madam [21]

Answer:

About 0.6548 grams will be remaining.

Step-by-step explanation:

We can write an exponential function to model the situation. The standard exponential function is:

$f(t)=a(r)^t$

The original sample contained 510 grams. So, a = 510.

Each half-life, the amount decreases by half. So, r = 1/2.

For t, since one half-life occurs every 38 days, we can substitute t/38 for t, where t is the time in days.

Therefore, our function is:

$\displaystyle f(t)=510\Big(\frac{1}{2}\Big)^{t/38}$

One year has 365 days.

Therefore, the amount remaining after one year will be:

$\displaystyle f(365)=510\Big(\frac{1}{2}\Big)^{365/38}\approx0.6548$

About 0.6548 grams will be remaining.

Alternatively, we can use the standard exponential growth/decay function modeled by:

$f(t)=Ce^{kt}$

The starting sample is 510. So, C = 510.

After one half-life (38 days), the remaining amount will be 255. Therefore:

$255=510e^{38k}$

Solving for k:

$\displaystyle \frac{1}{2}=e^{38k}\Rightarrow k=\frac{1}{38}\ln\Big(\frac{1}{2}\Big)$

Thus, our function is:

$f(t)=510e^{t\ln(.5)/38}$

Then after one year or 365 days, the amount remaining will be about:

$f(365)=510e^{365\ln(.5)/38}\approx 0.6548$

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<h2><u>We can solve it using trigonometric values.</u></h2>

<h3>So , <u> </u><u>sin</u><u> </u><u>θ</u><u> </u> = ( Perpendicular / Hypotenuese )</h3>

<h2><u>Given</u><u> </u></h2>

Perpendicular = x

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${ \sf{sin \: \: 45 {}^{ \degree} = \dfrac{1}{ \sqrt{2} } = \dfrac{x}{ 30} }}$

${ \sf{x = \dfrac{30}{ \sqrt{2} } }}$

<h2>∴ x ( Perpendicular)= 15√2 <u>Ans</u><u>.</u></h2>

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3 years ago

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bonufazy [111]

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