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
Answer: The total number of pizzas that can be made from the given choices is 24.
Step-by-step explanation: Given that a pizza parlor offers 3 sizes of pizzas, 2 types of crust, and one of 4 different toppings.
We are to find the number of different pizzas that can be made from the given choices.
We have the <em><u>COUNTING PRINCIPLE :</u></em>
If we have m ways of doing one task and n ways of doing the second task, then the number of ways in which we can do both the tasks together is m×n.
Therefore, the number of different pizzas that can be made from the given choices is
Thus, the total number of pizzas that can be made from the given choices is 24.
Ok this is a very question that can solved very easily. So we know that there three numbers, and they are consecutive, this means that they are all one bigger than the number before so for example 1,2, and 3 or 20, 21, and 22. These numbers are called consecutive. Now let's just pretend that the answer to this question is the variable "x". Now x is the smallest number in all the three numbers.
Using our knowledge of consecutive numbers we can say that the next to numbers will be one more than the number before so:
(x+1) and (x+2)
So we have our three numbers: x , x+1 , and x+2. Now let's set these numbers equal to 177.
177 = x + x + 1 + x + 2 → Combine like terms.
177 = 3x + 3 → Subtract 3 from both sides.
174 = 3x → Divide both sides by 3
58 = x
So that means that our first and smallest number is going to be 58 our second number will be +1 so 59 and our third number will be +2 so 60.
So the three numbers will be 58, 59, and 60.
Hope this helped.
You can buy 7 flats of flowers. this is because 10.99 is close to 11.00, and 7 x 11 is 77. and you cant do 77 + 11 to get less then 80.
the answer: 7 flats of flowers
hope it helps :)
4x - 3y = -2
3y = 4x + 2
y = 4/3 x + 2/3
Answer: y = 4/3 x + 2/3
