A rectangular plot of ground is 10 meters longer than it is wide. its area is 10,000 square meters

Mathematics

1 answer:

yarga [219]4 years ago

6 0

Keep in mind x >0 since x is a measurement of length.

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ANEK [815]

A. x = 7, y = 4, z = 3

How?

Just plug in the numbers.

7 + 4 + 3 = 14

11 + 3 = 14

14 = 14

Next.

4 + 3 = 7

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A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowing in at 4

kicyunya [14]

Answer:

dx/dt = 4c - 4x/15

Step-by-step explanation:

a. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution

Let c be the concentration of the incoming brine in grams per liter. Since it flows in at a rate of 4 liters per minute, the mass flow in is thus 4m.

Let x be the mass of salt present at time, t. The concentration of salt present at time, t is thus mass of salt/volume of tank = x/15. Since the well mixed solution is drained at 4 liters per minute, the mass flow out is thus 4x/15.

The net rate of change of amount of salt dx/dt = mass flow in - mass flow out

dx/dt = 4c - 4x/15

3 0

4 years ago

What is the derivative of 5x^4+4?

Andru [333]

Answer:

$\displaystyle \frac{dy}{dx} = 20x^3$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = 5x^4 + 4$

Step 2: Differentiate

Derivative Property [Addition/Subtraction]: $\displaystyle y' = \frac{d}{dx}[5x^4] + \frac{d}{dx}[4]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle y' = 5\frac{d}{dx}[x^4] + \frac{d}{dx}[4]$
Basic Power Rule: $\displaystyle y' = 20x^3$