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2 years ago

8

How many kernels of corn will be in the bag on the 26 days

1 answer:

Fantom [35]2 years ago

8 0

Notice that each day the number of kernels doubles, then we can model that behavior with the following equation:

$N=2^{n-1}.$

Where N is the number of kernels on the nth day.

Evaluating the above function at n=26 we get:

$N=2^{26-1}=2^{25}=33554432.$

Answer: 33554432.

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

4 years ago

Solve the equation for x.<br> – 1/2x – 3 = 4

Nana76 [90]

Answer:

x = -4

Step-by-step explanation:

Multiply both sides by 2. Move constant to the right-hand side and change the sign. Add the numbers. And change the signs on both sides of the equation.

5 0

3 years ago

Read 2 more answers

If log2 5 = k, determine an expression for log32 5 in terms of k.

lukranit [14]

Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

$2^5$

Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

6 0

3 years ago

Homework Due Tomorrow please help me it would be great

olga nikolaevna [1]

Answer:

c

Step-by-step explanation:

work out the average for the data below

6 0

2 years ago

The school that Mary goes to is selling tickets to a spring musical. On the first day of ticket sales

andrezito [222]

Answer:

The cost of one adult ticket is $13, and the price of one student ticket is $4.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the cost of an adult ticket

y is the cost of a student ticket.

6 adult tickets and 1 student ticket for a total of $82

This means that

$6x + y = 82$

$y = 82 - 6x$

The school took in $51 on the second day by selling 3 adult tickets and 3 student tickets.

This means that

$3x + 3y = 51$

Simplifying by 3

$x + y = 17$

Since $y = 82 - 6x$

$x + 82 - 6x = 17$

$-5x = -65$

$5x = 65$

$x = \frac{65}{5} = 13$

$y = 82 - 6x = 82 - 6*13 = 82-78 = 4$

The cost of one adult ticket is $13, and the price of one student ticket is $4.

4 0

3 years ago