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3 years ago

Which statement is true? A 0.265 <0.3 B 0.265 >0.3 C 0.265 =0.3

Mathematics

1 answer:

mestny [16]3 years ago

5 0

Answer:

Step-by-step explanation:

265 < 300, so 0.265 < 0.3

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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

I need help with this!

Viefleur [7K]

Answer:

the answer is option E.

Step-by-step explanation:

it is in the form f/g (x).

we know f and g from the equation;

we can rewrite it as, (√(9-x^2)/(3x-1))

if you notice you cannot put any number less than -3 or greater than 3 in the numeror because if you do you get a negative root which is false. for instance if you put 4 or -4 in the numerator you get 9 - (4 or -4 square ) which is 9- 16 which is a negative number and you cannot take root of a negative number.

on the numerator if you put 1/3 as the value for x you will get zero in the denominator. and any number divided by zero is undefined so that cannot be.

this means that option E is the right one that satisfies the condition. it means the domain is [-3, 1/3) U (1/3, 3] .

4 0

3 years ago

The price of a candy bar is $1.53. If this is three cents more than triple the price ten years ago, how much did the candy bar c

Tamiku [17]

Answer:

$0.51

Step-by-step explanation:

Hello! Using what we know, the price of the candy bar at the moment is $1.53, triple the price from 10 years ago. So, triple cents would technically be $0.03. We divide $1.53 and $0.03 and get 51! But, it would not make sense for the price ten years ago to be 51 then go to 1.53, so we make 51 a decimal, 0.51. We can check to see if this correct, by doing 0.51 times 3, because the price is tripling, and we get $1.53! Have an awesome day! :)

6 0

3 years ago

Write the equation.Please help

Scorpion4ik [409]

Answer: y=3x

Step-by-step explanation:

We want an equation of the form y=mx+b where m is the slope and b is the y-intercept (the value of y when x is 0).

The slope: From the point (0,0), the braph goes to point (2,6). Slope is the rise (y) over the run(x): (6/2) or 3. The slope, m, is 3. b, the y-intercept, is 0. y is 0 when x is 0.

y=3x

7 0

3 years ago

PLSSSSS HELPPP ASAP WILL GIVE BRAINLEAST 10 POINTS!!

Feliz [49]

I think it’s C. If you turn them both the same way, they look to be around the same size.

7 0

3 years ago