1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrei [34K]
4 years ago
8

A shooting star forms a right triangle with the Earth and the Sun, as shown below:

Mathematics
1 answer:
frez [133]4 years ago
3 0

The positions of the sun, earth and shooting star form a right angled triangle, where distance between earth and sun is 'y', and the angle 'x°' is given

Now, in a right angled triangle using trigonometry, we can determine a side of the triangle is one of the sides and one of the angles is known

Here, if we use cos x = \frac{Base}{Hypotenuse} we can determine the distance between the shooting star and the sun. This can be done because we know that the base is 'y', the angle is x° and the hypotenuse represents the distance between the sun and the shooting star

Note: cos values for each x are definite.

You might be interested in
Please help!
BaLLatris [955]

a) The polynomial in expanded form is f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18.

b) The slant asymptote is represented by the linear function is y = -x + 1.

c) There is a discontinuity at x = 2  with a slant asymptote.

a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form x-r_{i}, where r_{i} is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial f(x) has the following form:

f(x) = (x-6)\cdot (x+1)\cdot (x+3)

And the expanded form is obtained by some algebraic handling:

f(x) = (x-6)\cdot (x^{2}+4\cdot x +3)

f(x) = x\cdot (x^{2}+4\cdot x + 3)-6\cdot (x^{2}+4\cdot x +3)

f(x) = x^{3}+4\cdot x^{2}+3\cdot x -6\cdot x^{2}-24\cdot x -18

f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18 (1)

The polynomial in expanded form is f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18.

b) In this question we divide the polynomial found in a) (in factor form) by the polynomial x^{2}-x -2 (also in factor form). That is:

g(x) = \frac{(x-6)\cdot (x+1)\cdot (x+3)}{(x-2)\cdot (x+1)}

g(x) = \frac{(x-6)\cdot (x+3)}{x-2} (2)

The slant asymptote is defined by linear function, whose slope (m) and intercept (b) are determined by the following expressions:

m =  \lim_{x \to \pm \infty} \frac{g(x)}{x} (3)

b =  \lim_{x \to \pm \infty} [g(x)-x] (4)

If g(x) = \frac{(x-6)\cdot (x+3)}{x-2}, then the equation of the slant asymptote is:

m =  \lim_{x \to 2} \frac{(x-6)\cdot (x+3)}{x\cdot (x-2)}

m =  \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x^{2}-2\cdot x} \right)

m =  1

b =  \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x-2}-x \right)

b =  \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x - 18-x^{2}+2\cdot x}{x-2}\right)

b =  \lim_{n \to \infty} \left(\frac{-x-18}{x-2} \right)

b = -1

The slant asymptote is represented by the linear function is y = -x + 1.

c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at x = 2  with a slant asymptote.

We kindly invite to check this question on asymptotes: brainly.com/question/4084552

8 0
2 years ago
Mr. Rivera can grade 18 math teat in 15minutes. What is the teachers unit rate?
Andru [333]

In this question, you're trying to find the unit rate in which the teacher can grade tests.

A unit rate is another word for "rate of change".

This means that we have to find how many tests the teacher could grade in 1 minute.

To find the unit rate, divide 18 by 15

18 ÷ 15 = 1.2

This means that Mr. Rivera can grade 1.2 tests in 1 minute.

Answer:

1.2 tests

6 0
3 years ago
Zoe and Hannah share tips in the ratio 3:7. Last week Zoe recieved £24. How much did Hannah recieve last week?
Mrrafil [7]
Zoe to Hannah is 3 to 7.
We want to know x.
24 to x
three goes into 24 eight times so multiply 7 by eight
x=56
5 0
3 years ago
Read 2 more answers
Gina has an meeting in 45 min. She is driving at a rate of 30 mi/h. If she is 24 mi away, will she arrive on time? If not, how e
dsp73
Gina will be late because she's still missing 1.5 miles
7 0
3 years ago
Help someoneee!!!! <br> ill give a brainliest
Serjik [45]

Answer:

-13.5

Step-by-step explanation:

-4/3w=18

You would need to get the w by itself on one side so the easiest way to do so would be to divide both sides my -4/3.

This would give you an answer of w= -27/2 or w= -13.5

8 0
3 years ago
Other questions:
  • Select the correct answer
    7·1 answer
  • CAN SOMEONE HELP ME PLEASE (ASAP)
    10·1 answer
  • Sarah has 80 books in her collection if 60% of the books or fiction how many of the books or nonfiction
    10·1 answer
  • Determine the end behavior of each rational function below. <br> f(x) = 7x5 − 3x + 1 / 4x3 + 2
    10·1 answer
  • I’ll mark brainlest! pls help :(
    9·1 answer
  • Fiona has $18 to spend. She spent $4.25, including tax, to buy a notebook. She needs to save $9.75, but she wants to buy a snack
    12·1 answer
  • Please help! Question Below!!
    11·1 answer
  • Explain:<br><br><br><br><br><br><br><br><br><br> 10 to the 3rd power
    7·2 answers
  • Find the unit rate.<br> 2378 miles in 6 hours
    13·2 answers
  • <img src="https://tex.z-dn.net/?f=3x%2B42%3D75" id="TexFormula1" title="3x+42=75" alt="3x+42=75" align="absmiddle" class="latex-
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!