Answer:
Problem 20)
Problem 21)
A)
The velocity function is:
The acceleration function is:
B)
Step-by-step explanation:
Problem 20)
We want to differentiate the equation:
We can take the natural log of both sides. This yields:
Since ln(aᵇ) = bln(a):
Take the derivative of both sides with respect to <em>x: </em>
<em /><em />
Implicitly differentiate the left and use the product rule on the right. Therefore:
Simplify:
Simplify and multiply both sides by <em>y: </em>
<em /><em />
Since <em>y</em> = (cos x)ˣ:
Problem 21)
We are given the position function of a particle:
A)
Recall that the velocity function is the derivative of the position function. Hence:
Differentiate:
The acceleration function is the derivative of the velocity function. Hence:
Differentiate:
B)
The position at <em>t</em> = 0 will be:
The velocity at <em>t</em> = 0 will be:
And the acceleration at <em>t</em> = 0 will be:
Answer:
1.50x+10=34
Step-by-step explanation:
Answer:
Step-by-step explanation:
You first equate it to zero to get:
Then solve using square root method
Or
Now work it backwards
Hence the factored form is:
Answer:
21:126
6:36
1:6
Step-by-step explanation:
Hi,
Concept: This is work & time related problem which can be solved in their inverse proportions.
Let Lisa can do a work in x hours.
Lisa's one hour work = 1 / x
According to the problem, Justin can do the same work in 2x hours.
Justin's one hour work = 1 / (2x)
Now, we shall find both 1 hour work just by adding their 1 hour's work.
Both 1 hour's work = (1 /x) + [1 / (2x)] = 3 / (2x)
Full works time = (2x /3) hours.
Again, according to the problem,
2x / 3 = 8
or, x= 12 hours.
Hence Justin will take 2x = 24 hours to complete work as alone.