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
Romashka [77]
2 years ago
8

I need help on number 5

Mathematics
1 answer:
nikdorinn [45]2 years ago
3 0
A fraction is undefined if its denominator is zero, because then it's saying
"Division by zero !" which is a definite no-no.

Can the denominator of the fraction in #5 ever be zero ?

The denominator is a quadratic polynomial.  Do you know
how to solve (a quadratic polynomial) = 0  ?

This problem is even easier than that, because it gives you some choices.
So you don't even have to solve the quadratic equation.  All you have to do
is check out the choices.
Do you see choice of 'x' values that make the denominator zero ?

Big sloppy hint:  Look at choice-E very very carefully.

Is that enough help ?
You might be interested in
Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!
astra-53 [7]
(a) By DeMoivre's theorem, we have

(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta

On the LHS, expanding yields

\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta

Matching up real and imaginary parts, we have for (i) and (ii),


\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta
\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta

(b) By the definition of the tangent function,

\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}
=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}

=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}
=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}


(c) Setting \theta=\dfrac\pi5, we have t=\tan\dfrac\pi5 and \tan5\left(\dfrac\pi5\right)=\tan\pi=0. So

0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}

At the given value of t, the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.


0=t^5-10t^3+5t\implies0=t^4-10t^2+5

Remember, this is saying that

0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5

If we replace \tan^2\dfrac\pi5 with a variable x, then the above means \tan^2\dfrac\pi5 is a root to the quadratic equation,

x^2-10x+5=0

Also, if \theta=\dfrac{2\pi}5, then t=\tan\dfrac{2\pi}5 and \tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0. So by a similar argument as above, we deduce that \tan^2\dfrac{2\pi}5 is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5

But \tanx>0 for all 0, as is the case for x=\dfrac\pi5 and x=\dfrac{2\pi}5, so we choose the positive root.
3 0
3 years ago
1. P, Q and R are three buildings. A car began its journey at P, drove to Q, then to R and returned to P. The bearing of Q from
juin [17]

Statement Problem: P, Q and R are three buildings. A car began its journey at P, drove to Q, then to R and returned to P. The bearing of Q from P is 058° and R is due east of Q. PQ = 114 km and QR = 70 km. ( Draw a clearly labelled diagram to represent the above information.

Solution:

8 0
1 year ago
What inequality does the graph represent?
slega [8]
The shaded region is above the line so it would be y> so then the equation is y=4x+2 since the graph has a y intercept of 2 and a slope of four

tl;dr the answer is B


8 0
3 years ago
Read 2 more answers
Does anybody know how to do this?
Degger [83]
List the degrees from least to greatest ie, 11,7,7,6,4,3 then the first is ur degree. So the answer is D. 11
7 0
2 years ago
What is the axis of symmetry gor Graph A​
Lady_Fox [76]

Answer:

X=-2

Step-by-step explanation:

The axis of symmetry for any parabola is the x value of the vertex. Dividing the parabola along the vertex will always yield two symmetric halves.

7 0
3 years ago
Other questions:
  • If the federal reserve decreases
    6·1 answer
  • PLEASE HELP! What is the equation of the given quadratic function? (I'll put a picture of the graph)
    10·1 answer
  • What is 4067x5672 please only amrsaraege and someone else answer it
    14·2 answers
  • I need the answer to K/8-12=-8
    5·1 answer
  • Please help me on this question please
    10·1 answer
  • Target sells AAA batteries for $1.10 and AA batteries for $0.50. They sold 350 total batteries earning a total of $560. How many
    13·1 answer
  • Which options could be the next step in simplifying this expression?   (18 + 23) + 7   Choose exactly two answers that are corre
    13·1 answer
  • chris worked 3 1/2 hours at his uncles farm. He was paid 8$ for every 1/4 hour he worked. How much money did chris make
    11·1 answer
  • The neighborhood movie theatre is running several specials this summer. You get a free soda with every fifth ticket you buy. You
    13·1 answer
  • If you are just building your payment history, how many points from a perfect score will you possibly miss?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!