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2 years ago

13

Element X decays radioactively with a half life of 15 minutes. If there are 340 grams of Element X, how long, to the nearest ten

th of a minute, would it take the element to decay to 6 grams?

1 answer:

NikAS [45]2 years ago

6 0

Answer: 57 min

i used a calculator.

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Solve the equation 2cosA = 3tanA

zavuch27 [327]

$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)
\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\
-----------------------------\\\\

2cos(A)=3tan(A)\implies 2cos(A)=3\cfrac{sin(A)}{cos(A)}
\\\\\\
2cos^2(A)=3sin(A)\implies 2[1-sin^2(A)]=3sin(A)
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2-2sin^2(A)=3sin(A)\implies 2sin^2(A)+3sin(A)-2$

$\bf \\\\\\
0=[2sin(A)-1][sin(A)+2]\implies 
\begin{cases}
0=2sin(A)-1\\
1=2sin(A)\\
\frac{1}{2}=sin(A)\\\\
sin^{-1}\left( \frac{1}{2} \right)=\measuredangle A\\\\
\frac{\pi }{6},\frac{5\pi }{6}\\
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0=sin(A)+2\\
-2=sin(A)
\end{cases}$

now, as far as the second case....well, sine of anything is within the range of -1 or 1, so -1 < sin(A) < 1

now, we have -2 = sin(A), which simply is out of range for a valid sine, so there's no angle with such sine

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3 years ago

What id 2756 divided by 53

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8x^2 - 2x = 1 quadratic simplification

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Answer:

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Step-by-step explanation:

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3 years ago

In the xy-plane, if line k has negative slope and passes through the point (−5,r), is the x-intercept of line k positive?

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4 years ago

Julie and Eric row their boat (at a constant speed) 18 miles downstream for 3 hours helped by the current. Rowing at the same ra

Nastasia [14]

Answer

Find out the the rate of the boat in still water.

To proof

let us assume that the speed of the boat in the still water = u

let us assume that the speed of the current = v

Formula

$speed = \frac{Distance}{time}$

As given

18 miles downstream for 3 hours

Now for the downstream

$u + v = \frac{18}{3}$

u + v = 6

now for the upstream

As given

the trip back against the current takes 6 hours

$u - v = \frac{18}{6}$

u-v = 3

Than the two equation becomes

u + v = 6 and u - v = 3

add both the above equation

we get

2u = 9

u = 4.5miles per hour

put this in the u - v = 3

4.5 -v = 3

v =1.5 miles per hour

The rate of the boat in the still water is 4.5miles per hour .

Hence proved

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