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3 years ago

A petri dish of bacteria grow continuously at a rate of 200% each day. If the petri dish began

Mathematics

1 answer:

Molodets [167]3 years ago

4 0

Answer: 2430 bacteria.

Step-by-step explanation:

When we have a quantity A, and we have an increase of the X%, the new quantity can be written as:

A + (X%/100%)*A

In this case, we have A = 10 bacteria.

And X% = 200%.

Then if we start with 10 bacteria.

After one day, we will have:

10 bacteria + (200%/100%)*10 bacteria

= 10 bacteria + 2*10 bacteria = 3*10 bacteria.

After another day, we will have:

3*10 bacteria + (200%/100%)*(3*10 bacteria)

3*10 bacteria + 2*(3*10 bacteria)

3*(3*10 bacteria)

10 bacteria*(3)^2

We already can see the pattern here.

After t days, we will have:

10 bacteria*(3)^t.

This is the equation f(t) we wanted:

f(t) =10 bacteria*(3)^t

after 5 days, we will have:

f(5) = 10 bacteria*(3)^5 = 2430 bacteria.

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Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integ

liq [111]

Answer:

1/2

Step-by-step explanation:

The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

$\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy$

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.

Mx(x,y) = d/dx 8x²y = 16xy
Ly(x,y) = d/dy 7y²x = 14xy

Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy$

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2$

We conclude that the line integral is 1/2

4 0

3 years ago

Find A and C for both questions

Andre45 [30]

Link is scam dont put it in

3 0

3 years ago

My homework lesson 2 order of operations

djyliett [7]

Not sure what your question is but if you are learning the order of operations you can use the phrase "Please Excuse My Dear Aunt Sally"....

Parentheses
Exponents
Multiplication from left to right
Division from left to right
Addition from left to right
Subtraction from left to right

Hope this help :)

3 0

3 years ago

Which account has the lowest minimum balance requirement? Bank Account Terms and Conditions Bank A has a $500 minimum balance, b

Genrish500 [490]

Answer:

The correct option is Account D

Step-by-step explanation:

Bank requires that $500 minimum balance,this is the highest minimum balance out of all the four banks.

Bank B's minimum required balance is $250 which is the third highest minimum balance.

Bank C requires account holder to have as minimum balance $300 which is second highest minimum balance.

Bank D only requires $100 that is the minimum among all the four banks

6 0

3 years ago

What are the coordinates of the midpoint for segment AB if A is (14 , -2) and B is (7 , -8)

Alenkasestr [34]

Answer:

Step-by-step explanation:

(14 + 7)/2 = 21/2= 10.5

(-2 + (-8))/2= -10/2= -5

Midpoint(10.5, -5)

5 0

3 years ago