Answer:
L=7.295
Step-by-step explanation:
I can't type in a square root symbol so here's the sequence:
divide both sides by 2 Pi
square both sides
now you have:
.227973=L/32
multiply both sides by 32
L=7.295
Answer:
the dimensions of the most economical shed are height = 10 ft and side 5 ft
Step-by-step explanation:
Given data
volume = 250 cubic feet
base costs = $4 per square foot
material for the roof costs = $6 per square foot
material for the sides costs = $2.50 per square foot
to find out
the dimensions of the most economical shed
solution
let us consider length of side x and height is h
so we can say x²h = 250
and h = 250 / x²
now cost of material = cost of base + cost top + cost 4 side
cost = x²(4) + x²(6) + 4xh (2.5)
cost = 10 x² + 10xh
put here h = 250 / x²
cost = 10 x² + 10x (250/ x² )
cost = 10 x² + (2500/ x )
differentiate and we get
c' = 20 x - 2500 / x²
put c' = 0 solve x
20 x - 2500 / x² = 0
x = 5
so we say one side is 5 ft base
and height is h = 250 / x²
h = 250 / 5²
height = 10 ft
9514 1404 393
Answer:
consistent, independent
Step-by-step explanation:
Systems of equations are most easily classified these ways if the equations are in the same form. If we solve the second equation for y, we have ...
y = x - 1
The x-coefficients of this and the first equation are different, so the system is <em>consistent</em> and <em>independent</em>.
__
A system is independent if the equations describe different lines.
A system is inconsistent if the equations describe parallel lines.
Here, the different lines are not parallel, so the system is independent and consistent.
I would use a graphing tool like desmos or geogebra, or a texas instruments graphing calculator, there a number of tools out there. The first two options are free online tools. Using technology to graph is much preferred over doing it by hand.
If you must do it by hand, then the idea is to plug in various values of x to get corresponding values of y. For instance, if x = 7, then
y = sqrt(x-3)
y = sqrt(7-3)
y = sqrt(4)
y = 2
So the point (x,y) = (7,2) is on this curve. Repeat for other x values to get more points. Then plot the points all on the same xy grid. Lastly, draw a curve through those points. The more points you have, the more accurate the graph. Use graphing technology to help confirm you have the right graph.
As for the question of one-to-one, you are looking to see if the horizontal line test fails or not. After fully graphing y = sqrt(x-3), try to construct a single horizontal line that will pass through more than one point on the curve. You'll find that such a task is not possible in this case; therefore, this graph passes the horizontal line test and consequently the graph is one-to-one.
An example where a graph is not one-to-one would be a parabola. It is possible to pass a single horizontal line through more than one point on a parabola.
You would add up the ones taking math, science, and both. Then subtract that from 147. Then divide that by 147, then times by 100. This wouldn't work because 95 + 73 = 168.
