Hey so yeah this can be a challenging problem, Vol (V) is much easier to solve than surface area (SA), but I'll show you how it's done, my friend.
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3
So now for the hard part... how to calculate the SA of this prism
IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]
means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??
This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).
Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38
Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
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now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft
NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2
49=16+x^2
x^2= 33
x= square root of 33
Option A
The restaurant Manager can afford at most 10 employees for the day
<em><u>Solution:</u></em>
Given that restaurant manager can spend at most $600 a day for operating costs and payroll
It costs $100 each day to operate the bank and $50 dollars a day for each employee
The given inequality is:
Where , "x" is the number of employees per day
Let us solve the inequality for "x"
Add -100 on both sides of inequality
Divide by 50 on both sides of inequality
Hence the restaurant Manager can afford at most 10 employees for the day
Thus option A is correct
Answer:
30 km
Step-by-step explanation:
1 kilometer = 100 meters.
1 meter = 100 cm
therefore, 1 km = 10,000
and then, 300000 cm is 30 km
a) The fire burnt 840.6 square miles
b) The fire burnt 16.8 tempe
Step-by-step explanation:
1 square mile = 640 acres
a) to find how many square miles did the fire burn:
Total area the fire burn = 538000 acres
1 square miles = 640 acres
Concert the acres into square miles
538000/ 640 = 840.6 square miles
The fire burnt 840.6 square miles
b) 50 square miles= 1 temperatures
The no. Of tempe the fire burn = 840.6/50
= 16.8 tempe
The fire burnt 16.8 tempe
