since there are 180 degrees in a triangle so :
65+72+y=180 add like terms
137 + y=180 now subtract 137
y= 180-137
y=43 degrees
Answer:
y=9
Step-by-step explanation:
y=mx+c
gradient of a horizontal line is 0
y=0x+9
y=9
It will be A² + B² = C²
So 3²+5² is 34
And the square root of 34 is about 5.83
3² + 5² ≈ 5.83²
Hope that helps :)
Answer:
A
Step-by-step explanation:
A series is said to be convergent if |r| < 1. Where r is the common ratio of the series.
If |r| ≥ 1 then the geometric series diverges.
12/5 + 48/25 + 192/125 + ....
r = 192/125 ÷ 48/25 = 4/5
r = 48/25 ÷ 12/5 = 4/5
In the series, r is less than 1. So the series is convergent.
Answer:
Step-by-step explanation:
Let the side of the square base be x
h be the height of the box
Volume V = x²h
13500 = x²h
h = 13500/x² ..... 1
Surface area = x² + 2xh + 2xh
Surface area S = x² + 4xh ...... 2
Substitute 1 into 2;
From 2; S = x² + 4xh
S = x² + 4x(13500/x²)
S = x² + 54000/x
To minimize the amount of material used; dS/dx = 0
dS/dx = 2x - 54000/x²
0 = 2x - 54000/x²
0 = 2x³ - 54000
2x³ = 54000
x³ = 27000
x = ∛27000
x = 30cm
Since V = x²h
13500 = 30²h
h = 13500/900
h = 15cm
Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm
