Y varies inversely with x
means that y=k/x
with x=0.7 and y=80
we have 80=k/0.7
k=0.7x80=56
so the equation is
y=56/x
Answer: 5870 rounded to the nearest thousand is 6000
Step-by-step explanation:
Remember, when we round we have to be careful with the place value they are asking you to round to. Here, they want you to round to the thousands place. So, you have to look at the hundreds.
5870. 800 is the hundreds, and it is greater than “5”. So, you round to the next thousands. It happens to be 6000.
<em>Hence, 5870 rounded is 6000.</em>
Question:
Find the point (,) on the curve
that is closest to the point (3,0).
[To do this, first find the distance function between (,) and (3,0) and minimize it.]
Answer:

Step-by-step explanation:
can be represented as: 
Substitute
for 

So, next:
Calculate the distance between
and 
Distance is calculated as:

So:


Evaluate all exponents

Rewrite as:


Differentiate using chain rule:
Let


So:



Chain Rule:




Substitute: 

Next, is to minimize (by equating d' to 0)

Cross Multiply

Solve for x


Substitute
in 

Split

Rationalize



Hence:

Answer:
Both functions have one x-intercept each.
Step-by-step explanation:
The first function is

This is a parabola with vertices at the origin and has one x-intercept at t=0.
The transformed function is

The function g(t) is obtained by shifting the graph of f(t) to the left by 3 units.
This graph also has one x-intercept at x=-3.
Therefore both functions has the same number of x-intercepts
The answer is either b or c