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2 years ago

{Negative} -2 1/5 as a decimal

Mathematics

1 answer:

hammer [34]2 years ago

3 0

Answer:

-2.2

Step-by-step explanation:

1/5 = 0.2

0.2 + -2 = -2.2

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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

2 years ago

ALGEBRA HELP!! Write an exponential function represented by the table.

marysya [2.9K]

Answer:

y=-50*0.2^x

Step-by-step explanation:

the formula for an exponential function is:

y=a*b^x

what do we multiply -50 by to get -10?

-50x=-10

x=-10/-50

x=1/5

x=2/10

x=0.2

This initial value here is -50, it is the first in the table

y=-50*0.2^x

7 0

2 years ago

You have a garden in your backyard that measures 15 meters by 20 meters. You want to place stepping stones around the perimeter

Anettt [7]

Answer:

0.5 m

Step-by-step explanation:

Given that the dimensions of the garden are 15 meters by 20 meters.

The area of the new garden (original garden + stone placed around the perimeter) is 336m².

Let d be the width of the border having stepping stones as shown in the figure. The shaded region in the figure is the area having stepping stones.

The area including the shaded region $= (15+2d)(20+2d) m^2$

$\Rightarrow 336 = (15+2d)(20+2d) \\\\\Rightarrow 336 = 300+ 70 d +4d^2 \\\\\Rightarrow 4d^2 +70d+300-336=0 \\\\\Rightarrow 4d^2 +70d-36=0 \\\\\Rightarrow 2d^2 +35d-18=0 \\\\\Rightarrow 2d^2 +36d-d-18=0 \\\\\Rightarrow (2d-1)(d+18)=0 \\\\\Rightarrow (2d-1)=0, \; or \; (d+18) \\\\\Rightarrow d= 0.5\;or -18 \\\\$