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3 years ago

Brainliest + 20 Points!

Mathematics

1 answer:

aliina [53]3 years ago

7 0

Answer:

The perimeter of one face of the smaller cube compared to the perimeter of one face of the larger cube is $\frac{2}{5}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

and

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the smaller cube

y ----> the perimeter of the larger cube

$z=\frac{x}{y}$

in this problem we have

$z=\frac{2}{5}$ ----> scale factor

substitute

$\frac{x}{y}=\frac{2}{5}$

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Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be

Travka [436]

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C' (C' = kC)

taking exponents of both sides, we have

$L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}$

When t = 0, A(0) = 0 (since the forest floor is initially clear)

$A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L$

$A = \frac{L}{k} - \frac{L}{k} e^{kt}$

So, D = R - A =

$D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}$

when t = 0(at initial time), the initial value of D =

$D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}$

4 0

3 years ago

If the pattern in the table continues, when will sales for pants equal sales for shirts?

Anika [276]

It won't. Both are increasing by 1.5 every year. If you graph that, the lines will be parallel. Parallel lines have no intercept.

5 0

4 years ago

"The sum of seven-eighths of a<br> number and 20 is 34 at minimum."

Gennadij [26K]

Answer:

Anything greater than or equal to 17.

Step-by-step explanation:

7/8 of 17 is 14.875

6 0

3 years ago

Felipe has 28 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them.

Debora [2.8K]

Ok let’s say he folds N=14 so F would be the other q4

8 0

3 years ago

Help with #9 please?

nekit [7.7K]

We're given a parabola

$y=x^2-4$

and a line

$y = 2x+b$

The zeros of the parabola are

$0=x^2-4$

$4=x^2$

$x=\pm 2$

We see that (-2,0) is on the line as well:

$y = 2x+b$

$0 = 2(-2)+b$

$b=4$

Choice D

4 0

3 years ago