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Ratling [72]
2 years ago
8

Simplify 21^6y^5/14x^2y^9

Mathematics
1 answer:
nevsk [136]2 years ago
6 0

1 2 2 5 2 3 0 3 ^1 4 ^2/2

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A dog is given a dosage of 100 mg of antibiotics. The amount of antibiotics in the dog's bloodstream will decrease by 40% each h
jek_recluse [69]

After each hour 60% ( or 0.60) of the drug will be present.

The equation is A = 100(0.6)^t where t = time in hours. (answer)

5 0
3 years ago
Hal has a square garden in his backyard with an area of 210 square feet. To the nearest half foot, what are the dimensions of th
Zanzabum

I believe the answer is 57sqft

7 0
3 years ago
x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco
igomit [66]

Answer:

x=-cos(t)+2sin(t)

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

Will have a characteristic equation of the form:

a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0

Where solutions r_1,r_2...,r_n are the roots from which the general solution can be found.

For real roots the solution is given by:

y(t)=c_1e^{r_1t} +c_2e^{r_2t}

For real repeated roots the solution is given by:

y(t)=c_1e^{rt} +c_2te^{rt}

For complex roots the solution is given by:

y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)

Where:

r_1_,_2=\lambda \pm \mu i

Let's find the solution for x''+x=0 using the previous information:

The characteristic equation is:

r^{2} +1=0

So, the roots are given by:

r_1_,_2=0\pm \sqrt{-1} =\pm i

Therefore, the solution is:

x(t)=c_1cos(t)+c_2sin(t)

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of x(t) in order to find the constants c_1 and c_2:

x'(t)=-c_1sin(t)+c_2cos(t)

Evaluating the initial conditions:

x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1

And

x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2

Now we have found the value of the constants, the solution of the second-order IVP is:

x=-cos(t)+2sin(t)

3 0
3 years ago
6. Examine the prism shown below.
bulgar [2K]
It may be can be number 1 (a)
8 0
2 years ago
48 notebooks to 14 notebooks
rewona [7]
Set up a x/100 = (14-48)/48 = -34/48 Multiply the cross 48x = -3400 x = 70.8333 so around -70.83% change
3 0
3 years ago
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