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andriy [413]
3 years ago
10

The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 66​% of the​ carbon-1

4 expected in living​ matter, when did the tree​ die?
Mathematics
1 answer:
Likurg_2 [28]3 years ago
5 0
The tree died 3696 years ago because 66x5600=369600/10=3696.
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Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators
Nata [24]

Answer:

The solution is y=-\frac{12}{12x-30x^2+1}.

Step-by-step explanation:

A first order differential equation y'=f(x,y) is called a separable equation if the function f(x,y) can be factored into the product of two functions of x and y:

f(x,y)=p(x)h(y)

where p(x) and h(y) are continuous functions.

We have the following differential equation

y'=(1-5x)y^2, \quad y(0)=-12

In the given case p(x)=1-5x and h(y)=y^2.

We divide the equation by h(y) and move dx to the right side:

\frac{1}{y^2}dy\:=(1-5x)dx

Next, integrate both sides:

\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C

Now, we solve for y

-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}

We use the initial condition y(0)=-12 to find the value of C.

-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}

Therefore,

y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}

4 0
3 years ago
NOT A SCAM..... PLEASE HELP MEMEEEEEEEEEEEEEE
umka21 [38]

Answer:

(3, 0).

Step-by-step explanation:

dentifying the vertices of the feasible region. Graphing is often a good way to do it, or you can solve the equations pairwise to identify the x- and y-values that are at the limits of the region.

In the attached graph, the solution spaces of the last two constraints are shown in red and blue, and their overlap is shown in purple. Hence the vertices of the feasible region are the vertices of the purple area: (0, 0), (0, 1), (1.5, 1.5), and (3, 0).

The signs of the variables in the contraint function (+ for x, - for y) tell you that to maximize C, you want to make y as small as possible, while making x as large as possible at the same time.

Hence, The Answer is ( 3, 0)

3 0
3 years ago
Read 2 more answers
The function h(x) is given below:
g100num [7]

Step-by-step explanation:

The domain and range of a function and its inverse are inverted i.e. The domain of the function will become range of its inverse and the range of the function will become the domain of its inverse.

When representing the function in ordered pairs, the first values in the pair represents the domain and second values represent the range of the function.

h(x) = {3,5),(5,-7)(6,-9)(10,-12)(12,16)}

Domain of h(x) is: {3, 5, 6, 10, 12}

Range of h(x) is: (5, -7, -9, -12, 16}

So,

Domain of h^{-1}(x) = Range of h(x) = (5, -7, -9, -12, 16}

Range of h^{-1}(x) = Domain of h(x) = {3, 5, 6, 10, 12}

Therefore, h^{-1}(x) will be represented as:

{(5,3), (-7,5), (-9, 6), (-12, 10), (16,12)}

It seems like you have made some error while writing the original function because of which we are not getting an exact match in the answer. However by looking at the answers, option B is the nearest most and seems the correct answer.

6 0
3 years ago
the price of a small pizza increased from $5 to $8. what is the percent of increase in the cost of the pizza? round to the neare
Ne4ueva [31]
60%

Working

£5:100%
£1:20%
£8:160%

So percentage increase is 60%
6 0
3 years ago
What is 2y/√4y^3 written in simplest form? assume all variables are positive.
diamong [38]

Answer:

√y/y  c.

Step-by-step explanation:

2y/√4y^3

=  2y / 2 y^3/2

= 1  / √y

= √y/y

3 0
3 years ago
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