How do I find and interpret slope

2 answers:

8 0

If there’s a graph, draw a triangle and do rise/run.
If there are two given points use formula: (y2-y1)/(x2-x1) to find slope

Alex_Xolod [135]3 years ago

4 0

Answer:

The slope is the rise over run. The change in y over the change in x. Pick two points on a line and find the change. It is usually represented by m in the slope intercept form.

$m=\frac{y_2-y_1}{x_2-x_1}$

Pick two points on a line and use the formula m to find the slope, which represents the rate of change.

Step-by-step explanation:

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Can someone simplify these expressions (c)

creativ13 [48]

Answer:

(10x+5)-(-23-2x)=

10x+5+23+2x

=12x+28

2x+5x^2-(3x+7x^2)=

2x+5x^2-3x-7x^2

= -2x^2-1

8 0

3 years ago

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)

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