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3 years ago

GEOMETRY HELP ASAP!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

vovangra [49]3 years ago

6 0

Area of equilateral triangle = a^2/4 * √3 so side of triangle = a

but if area of equilateral triangle = area of square multiplied by √3 then area of square = a^2 / 4 so side of square = a/2

the ratio length of side triangle to length side of square = a: a/2 that means the side of triangle is doubled the side of square

answer
a) 2:1

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The two dot plots below show the number of the miles run by 14 students at the beginning and end of the school year. complete th

Sliva [168]

Answer:

Start of the year: 77 End of the year: 87

Step-by-step explanation:

1 dot equals the number represented below, so I multiplied up to the answers for both! (Hope you pass ur test :D)

4 0

3 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

The teacher recommends that students read for 20 minutes each

OleMash [197]

They wollll complete 3

7 0

3 years ago

Pls help

AnnZ [28]

Perimeter of figure = 3 sides of rectangle + perimeter of semi-circle.

3 sides of rectangle = 15 + 12 + 15 = 42

Perimeter of semi-circle = πr = 3.14 * 6 = 18.84

In short, Your Answer would be: 42 + 18.84 = 60.84 m

Hope this helps!

5 0

2 years ago

Read 2 more answers

Serenity picked 75% of the apples of a tree in her backyard. If she picked 30 apples, how many apples were on the tree to begin

Stells [14]

Given:

Serenity picked 75% of the apples of a tree in her backyard.

She picked 30 apples.

To find:

The number of apples on the tree in the beginning.

Solution:

Let x be the number of apples on the tree in the beginning.