Solve. 5=15x−3 Enter your answer in the box.
2 answers:
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1. a. Pretty much, you just have to rearrange it so that the highest power is in the front. So, here's your answer:
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.
2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞
3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):
If you multiply it out, you get (also your answer):
4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.
Hope this helps!
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.
2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞
3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):
If you multiply it out, you get (also your answer):
4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.
Hope this helps!
Answer:
a)
b)
c)
d)
e)
And we take the absolute value on the middle integral because the distance can't be negative.
f)
g) The particle is speeding up
And would be slowing down from
Step-by-step explanation:
For this case we have the following function given:
Part a: Find the velocity at time t.
For this case we just need to take the derivate of the position function respect to t like this:
Part b: What is the velocity after 3 s?
For this case we just need to replace t=3 s into the velocity equation and we got:
Part c: When is the particle at rest?
The particle would be at rest when the velocity would be 0 so we need to solve the following equation:
We can divide both sides of the equation by 3 and we got:
And if we factorize we need to find two numbers that added gives -6 and multiplied 5, so we got:
And for this case we got
Part d: When is the particle moving in the positive direction? (Enter your answer in interval notation.)
For this case the particle is moving in the positive direction when the velocity is higher than 0:
So then the intervals positive are
Part e: Find the total distance traveled during the first 6 s.
We can calculate the total distance with the following integral:
And if we replace we got:
And we take the absolute value on the middle integral because the distance can't be negative.
Part f: Find the acceleration at time t.
For this case we ust need to take the derivate of the velocity respect to the time like this:
Part g and h
The particle is speeding up
And would be slowing down from