Answer:


Step-by-step explanation:
step 1
Find the equation of the solid line
From the graph take the points (0,3) and (4,11)
Find the slope

The equation of the solid line in slope intercept form is equal to

we have

----> the y-intercept is the point (0,3)
substitute

therefore
The inequality is

step 2
Find the equation of the dashed line
The slope is given

From the graph take the y-intercept (0,-5)
The equation of the solid line in slope intercept form is equal to
we have

substitute

therefore
The inequality is

because the shaded region is below the dashed line
therefore
The system of inequalities is


Answer:
constant of variation = 3
Step-by-step explanation:
we know that b varies jointly with c and d
so:
b∝c∝d
and b varies inversely with e, so
b∝
and i will call the constant of variation k, this way we can make an equation for b in the following form:

this satisfy that b varies jointly with c and d (if b increases, c and d also increase) and inversely with e (if b increases, e decreases)
we know that when b is 18, c is 4, d is 9, and e is 6:

substituting this in our equation for b:

and we solve operations and clear for the constant of variation k:

the constant of variation is 3.
Answer:
Component form : (-7 , 2)
Step-by-step explanation:
P(4 , 5) = P'(4 +x , 5+y) = P'(-3 , 7)
4 + x = -3
x = -3 - 4
x = -7
5 + y = 7
y = 7 - 5
y = 2
Vector form : -7i + 2j
Component form : (-7 , 2)
Answer:
10
Step-by-step explanation:
Answer:
1) 
2) 
Step-by-step explanation:
Assuming that our function is
for the first case and
for the second case.
Part 1
We can rewrite the expression like this:

And we can reorder the terms like this:

Now if we apply integral in both sides we got:

And after do the integrals we got:

Now we can use the initial condition 

And the final solution would be:

Part 2
We can rewrite the expression like this:

And we can reorder the terms like this:

Now if we apply integral in both sides we got:

And after do the integrals we got:

Now we can use the initial condition 

And the final solution would be:
