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2 years ago

10

Which factor did the railroad contribute to by encouraging population growth in West Texas from 1870 to 1890?

1 answer:

wariber [46]2 years ago

7 0

Answer:

A

Step-by-step explanation:i took the test

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i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

3 years ago

Describe the steps that transform the graph of the function y=x^2 to y=2(x+3)^2. Which attributes are not affected by the transf

dolphi86 [110]

Step-by-step explanation:

y=2(x+3)² y=x²

x²=2(x²+9+6x)

x²=2x²+18+12x

0=x²+18+12x

x²+18+12x=0

7 0

3 years ago

Read 2 more answers

Mike plans to paint a wall in his living room blue.that wall measures 10 feet tall and 8 feet wide.what is the area of the wall

Lorico [155]

Answer:

Step-by-step explanation:

L x W

10 x 8

<h3>80ft squared </h3><h3 /><h3 /><h3 />

5 0

3 years ago

X + y = 0<br> x - y = 4 <br> Then what does x =

mylen [45]

X - (-x) = 4
2x = 4

x=2

8 0

3 years ago

The circular opening of a vase has an inside diameter of 13.5 cm.

Sunny_sXe [5.5K]

Answer:

$Area = 143cm^2$

Step-by-step explanation:

Given

Shape: Opening of a circular vase

$Diameter =13.5cm$

$\pi = 3.14$

Required

Determine the area

This opening implies a circle; hence the area will be calculated using area of a circle.

$Area = \pi r^2$

Solve for radius (r)

$r = \frac{d}{2}$

$r = \frac{13.5\ cm}{2}$

$r = 6.75\ cm$

Substitute 6.75 for r in $Area = \pi r^2$

$Area = 3.14 * 6.75^2$

$Area = 143.06625$

$Area = 143cm^2$ --- Approximated

4 0

3 years ago