Answer:
see explanation
Step-by-step explanation:
(a)
The angles are vertical and congruent, that is
x - 10 = 125 ( add 10 to both sides )
x = 135
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(b)
Supplementary angles sum to 180°
The angles are in the ratio 2 : 3 = 2x : 3x ( x is a multiplier ), then
2x + 3x = 180
5x = 180 ( divide both sides by 5 )
x = 36
thus
2x = 2 × 36 = 72
3x = 3 × 36 = 108
Then the 2 angles are 72° and 108°
Answer:
Data: (Cylinder)
h (height) = 8 cm
r (radius) = 5 cm
Adopting:
V (volume) = ?
Solving:(Cylinder volume)
Note: Now, let's find the volume of a hemisphere.
Data: (hemisphere volume)
V (volume) = ?
r (radius) = 5 cm
Adopting:
If: We know that the volume of a sphere is , but we have a hemisphere, so the formula will be half the volume of the hemisphere
Formula: (Volume of the hemisphere)
Solving:
Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)
Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 628 cm³ + 261.6 cm³
Step-by-step explanation:
Imagine that the variable c represents something tangible, like an orange. So what this equation is asking is subtract 1 orange from 12 oranges. So you are left with 11 oranges.
Another way to think about this problem is if you rewrite the equation slightly to:
12c - c =
12c - 1c =
11c
a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
Then the sum itself is telescoping:
b. The proof is trivial:
so the formula found in (a) is correct.
Answer:
assuming the shape is a square
1. 90 degrees
2. 45 degrees
3. 45 degrees
4. 90 degrees
Step-by-step explanation:
maths and angles
