Find the number of possible positive real zeros of 2x^4+14x^3-35x^2
1 answer:
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Answer:
2.2 - 0.4
Step-by-step explanation:
1. Approach
To divide by imaginary number, one must take the fraction and multiply the complex conjugate of the denominator. A complex conjugate is a complex number with its imaginary unit multiplied by (-1). Once one multiplies both the numerator and denominator by the complex conjugate, then the denominator should be a real number (this is because the complex numbers act like binomials when multiplied, and hence the difference of square property works). Now all one has to do is divide every term in the numerator by the real number in the denominator.
2. complex conjugate
As mentioned above, to solve this problem, one has to multiply the numerator and denominator by the complex conjugate of the denominator. That is the complex number in the denominator with its imaginary until multiplied by (-1).
Complex number in the denominator;
(-8 - 6i)
complex conjugate;
(-8 + 6i)
3. Multiplying
Now, one has to multiply the problem's numerator and denominator by the complex conjugate of the denominator. Since a number over itself in fraction format is the same as multiplying by (1), one is allowed to do this;
Multiply
Distribute
4. Simplifying
Now all that is left is to simplify and divide to find the quotient.
=
=
Remember the rotations of ,
Simplify further
Divide
2.2 - 0.4
Answer:
a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).
Step-by-step explanation:
a) Let is find first the velocity vector by differentiation:
Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:
Then,
Hence, the particle has a constant speed of 4.
b) The acceleration vector is obtained by deriving the velocity vector.
Velocity and acceleration are orthogonal to each other only if . Then,
Which demonstrates the orthogonality between velocity and acceleration vectors.
c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is:
And cosine decrease and sine increase inasmuch as t becomes bigger.
d) Let evaluate the vector in .
False, the particle begin at the point (0,1).
I would set this up as a ratio:
From here on, you solve for x. To do so, you can cross multiply:
So, Lisa can run 9.2 miles in 69 minutes.
From here on, you solve for x. To do so, you can cross multiply:
So, Lisa can run 9.2 miles in 69 minutes.