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3 years ago

Given that tan(x)= -4/7, and 270 degrees< x< 360 degrees, what is the exact value of sec(x)

Mathematics

1 answer:

Maurinko [17]3 years ago

4 0

Answer:

sec(x) = 1.15

Step-by-step explanation:

We can figure out what x is by using the arctan(x) function:

$x = arctan(-\frac{4}{7}) = -29.74$

So, now let's figure out the cos(x) as sec(x) is equal to the reciprocal of cos(x):

$cos(-29.74) = 0.87$

Let's take the reciprocal:

$sec(x) = \frac{1}{cos(-29.74)} = 1.15$

And that's your answer.

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Which could be the name of a line? A.R B. D C. m D. Rs

MrMuchimi

Hi there!

The answer is C. m
The name of a line is always a lower-case letter (e.g. m, k or any other letter from the alphabet).

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4 years ago

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Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.

skelet666 [1.2K]

Answer:

$y=\dfrac {60} {x}$ or $xy=60$ (depending on your teacher's format preference)

Step-by-step explanation:

<h3><u>Proportionality background</u></h3>

Proportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Direct
Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

$y=kx$ y is directly proportional to x
$y=kx^2$ y is directly proportional to x squared
$y=kx^3$ y is directly proportional to x cubed
$y=k\sqrt{x}}$ y is directly proportional to the square root of x
$y=\dfrac {k} {x}$ y is inversely proportional to x
$y=\dfrac {k} {x^2}$ y is inversely proportional to x squared

From these examples, we see that two things:

things that are <u>directly proportional</u> -- the thing is <u>multipli</u>ed to the constant of proportionality "k"
things that are <u>inversely proportional</u> -- the thing is <u>divide</u>d from the constant of proportionality "k".

<h3><u>Looking at our question</u></h3>

In our question, y is inversely proportional to x, so the equation we're looking at is the following $y=\dfrac {k} {x}$ .

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it: "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

<h3><u>Solving for k, and finding the general equation</u></h3>

General Inverse variation equation...

$y=\dfrac {k} {x}$

Substituting known values...

$(12)=\dfrac {k} {(5)}$

Multiplying both sides by 5...

$(12)*5= \left ( \dfrac {k} {5} \right ) *5$

Simplifying/arithmetic...

$60=k$

So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is $y=\dfrac {60} {x}$ .

The way your question is phrased, they may prefer the form: $xy=60$

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2 years ago

Lin ran 29 meters in 10 seconds. she ran at a constant speed. At this rate, how far can she run in 1 minute

scoundrel [369]

Answer:

2.9 per second

Step-by-step explanation:

3 0

3 years ago

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Mr suresh had 7/9 kg of sugar. He used 1/3 of it. How much sugar did he use?

BabaBlast [244]

1/3 * 7/9 kg = (1 * 7)/(3 * 9) kg = 7/27 kg

He used 7/27 kg of sugar.

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3 years ago

Can someone help me please

Ulleksa [173]

In geometry, there is a theorem that states: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs

Therefore, this problem has two secants, so m∠x= 1/2(141-25)

m∠x=1/2(116)

m∠x=58

Hope this helped :)

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3 years ago

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