All categories

1 year ago

What compass heading represents 20° north of east?

Mathematics

1 answer:

sleet_krkn [62]1 year ago

6 0

Answer:

45°

Step-by-step explanation:

Northeast (NE), 45°, halfway between north and east, is the opposite of southwest. Southeast (SE), 135°, halfway between south and east, is the opposite of northwest. Southwest (SW), 225°, halfway between south and west, is the opposite of northeast.

You might be interested in

Joseph ordered 17 yards of lumber to build a tree house. how many inches of lumber did he order?

masya89 [10]

Answer:

612 inches.

Step-by-step explanation:

1 yard = 36 inches.

17 * 36 =

8 0

2 years ago

Read 2 more answers

T F IfA and B are similar matrices, then AT=BT

muminat

Answer:

Step-by-step explanation:

We know that for two similar matrices $A$ and $B$ exists an invertible matrix $P$ for which

$[tex]B = P^{-1} AP$ [/tex]

∴ $B^{T} = (P^{-1})^{T} A^{T} P^{T} \\$

Also $P^{-1}P = I\\$

and $(P^{-1})^{T} = (P^{T})^{-1}$

∴ $(P^{-1})^{T}P^{T} = I$

so, $B^{T} = (P^{-1})^{T} A^{T} P^{T} = (P^{T})^{-1}A^{T} P^{T}\\B^{T} = A^{T} I\\B^{T} = A^{T}$

7 0

2 years ago

5x(2x-y) -3y(2+3x) expand and simplify

OleMash [197]

Answer:

10x² - 14xy -6y

Step-by-step explanation:

5x(2x-y)-3y(2+3x)

10x²-5xy-6y-9xy

10x² - 14xy - 6y

5 0

2 years ago

What is 48 square feet in square meters

Marina86 [1]

Answer: 4.45935

Step-by-step explanation: 1 Square foot (sqft) is equal to 0.09290304 square meter (sqm). For example, to convert 100 square feet to square meters, multiply 100 by 0.09290304, that makes 9.290304 sqm is 100 sqft. Hope this helps.

6 0

2 years ago

What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?

scoray [572]

Answer:

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to c} x = c$

Special Limit Rule [L’Hopital’s Rule]:
$\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$

Differentiation

Derivatives
Derivative Notation

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

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify given limit.

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}$

Step 2: Find Limit

Let's start out by directly evaluating the limit:

[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}$

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

[Limit] Apply Limit Rule [L' Hopital's Rule]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}$
[Limit] Differentiate [Derivative Rules and Properties]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}$
[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}$