Answer:
4√3
Step-by-step explanation:
The distance formula applies. It tells you ...
distance = √((x2 -x1)² +(y2 -y1)²)
Filling in the given values, you have ...
distance = √((-√32 -(-4√2))² +(2√3 -(-√12))²)
= √((-4√2+4√2)² +(2√3 +2√3)²)
= √(0 + (4√3)²)
distance = 4√3
___
We make use of the fact that ...
The value of y in the code segment is 444
<h3>How to determine the value of y?</h3>
The code segment is given as:
y = int(3 * '4')
Evaluate the expression in the bracket
y =int('444')
Remove the bracket
y = 444
Hence, the value of y in the code segment is 444
Read more about code segments at:
brainly.com/question/26683418
#SPJ1
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...
.
.
.
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
The first carpenter is 0.4464 of the way is ahead of the second carpenter
<u>Solution:</u>
Given, Two carpenters are building a fence
After 5 minutes, one carpenter is finished 4/7 of the way
Second carpenter finished 1/8 of the way
Now, let us find the work done by each carpenter
Then, extra work done by first carpenter over second carpenter = work done by first carpenter – work done by second carpenter
= 0.5714 – 0.125 = 0.4464
Hence, the 1st carpenter is 0.4464 of the way is ahead of the 2nd carpenter
12n+32=10n+20
-10n -10n
2n+32=20
-32 -32
2n= -12
2 2
N = -6
