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2 years ago

DRAW TWO LINES THAT BOTH REPRESENT PROPONTINAL RELATIONSHIPS BUT HAVE DIFFRENT SLOPES LABEL ONE LINE A AND OTHER B

Mathematics

2 answers:

Sophie [7]2 years ago

4 0

Answer:

may i see the question

Olin [163]2 years ago

3 0

Answer:

gjtudt57uydt57uy

Step-by-step explanation:

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Which facts could be applied to simplify this expression? Check all that apply.

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Answer:

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2 years ago

17. Add - 16 + (-27)

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2 years ago

What is the measurement for <8? A:108 B:98 C:252 D: 37.4

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2 years ago

The graph of a linear equation passes through three of these points: (0, 5), (2, 2), (3, 1), and (4, -1). The point that the gra

dlinn [17]

Label the given points as follows:
A (0, 5)
B (2, 2)
C (3, 1)
D (4, -1)

The straight line has a constant slope. Therefore it should have the same value when any two of the four points are used to calculate the slope.

Try A and B:
Slope = (2 - 5)/(2 - 0) = -3/2

Try A and C:
Slope = (1 - 5)/(3 - 0) = -4/3

Try A and D.
Slope = (-1 - 5)/(4 - 0) = -3/2

Try B and D.
Slope = (-1 - 2)/(4 - 2) = -3/2

Clearly, C does not lie on the straight line.

Answer: The point that the graph does not pass through is (3,1).

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2 years ago

The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars on advertising is

sattari [20]

Answer:

The company should spend $40 to yield a maximum profit.

The point of diminishing returns is (40, 3600).

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinate Planes

Coordinates (x, y) → (s, P)

Functions

Function Notation

Terms/Coefficients

Factoring/Expanding

Quadratics

Algebra II

Coordinate Planes

Maximums/Minimums

Calculus

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

1st Derivative Test - tells us where on the function f(x) does it have a relative maximum or minimum

Critical Numbers

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle P = \frac{-1}{10}s^3 + 6s^2 + 400$

Step 2: Differentiate

[Function] Derivative Property [Addition/Subtraction]: $\displaystyle P' = \frac{dP}{ds} \bigg[ \frac{-1}{10}s^3 \bigg] + \frac{dP}{ds} [ 6s^2 ] + \frac{dP}{ds} [ 400 ]$
[Derivative] Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle P' = \frac{-1}{10} \frac{dP}{ds} \bigg[ s^3 \bigg] + 6 \frac{dP}{ds} [ s^2 ] + \frac{dP}{ds} [ 400 ]$
[Derivative] Basic Power Rule: $\displaystyle P' = \frac{-1}{10}(3s^2) + 6(2s)$
[Derivative] Simplify: $\displaystyle P' = -\frac{3s^2}{10} + 12s$

Step 3: 1st Derivative Test

[Derivative] Set up: $\displaystyle 0 = -\frac{3s^2}{10} + 12s$
[Derivative] Factor: $\displaystyle 0 = \frac{-3s(s - 40)}{10}$
[Multiplication Property of Equality] Isolate s terms: $\displaystyle 0 = -3s(s - 40)$
[Solve] Find quadratic roots: $\displaystyle s = 0, 40$

∴ s = 0, 40 are our critical numbers.

Step 4: Find Profit

[Function] Substitute in s = 0: $\displaystyle P(0) = \frac{-1}{10}(0)^3 + 6(0)^2 + 400$
[Order of Operations] Evaluate: $\displaystyle P(0) = 400$
[Function] Substitute in s = 40: $\displaystyle P(40) = \frac{-1}{10}(40)^3 + 6(40)^2 + 400$
[Order of Operations] Evaluate: $\displaystyle P(40) = 3600$

We see that we will have a bigger profit when we spend s = $40.

∴ The maximum profit is $3600.

∴ The point of diminishing returns is ($40, $3600).

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation (Applications)

5 0

2 years ago