Answer:
radius = 4 cm
Step-by-step explanation:
To find the length of the radius, we will follow the step below;
First, write down the formula for finding the volume of a cylinder
v=πr²h
where v is the volume of a cylinder
r is the radius and
h is the height of the cylinder
from the question given,
v=125.6 and h = 10 cm
we can now proceed to insert the values into the formula and solve for r
note that π is a constant which is equal to 3.14
v=πr²h
125.6 =3.14×r×10
125.6 =31.4 r
Divide both-side of the equation by 31.4
125.6/31.4 =31.4 r/31.4
4 = r
r =4 cm
The length of the radius = 4 cm
Answer:
x = 4
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = 
, then using the upper 45°
sin45° = 
= 
= ( cross- multiply )
x = 4
The coordinates would be (6,-1) I think
Answer:
Elga is 32 years old.
Step-by-step explanation:
Let Alvin's age = A
Let Elga's age = E
Alvin is 10 years younger than Elga, so A = E - 10
The sum of their ages is 54, so A + E = 54
Replace the A in the second equation with E - 10, then solve for E.
A + E = 54 becomes (E - 10) + E = 54
Combine like terms
2E - 10 = 54
Add 10 to both sides
2E = 64
Divide both sides by 2
E = 32
Answer:
There are many examples for the first request, but none for the second.
Step-by-step explanation:
a) There is a theorem which states that the sum of two convergent sequences is convergent, so any pair of convergent sequences (xn), (yn) will work (xn=1/n, yn=2/n, xn+yn=3/n. All of these converge to zero)
If you meant (xn) and (yn) to be both divergent, we can still find an example. Take (xn)=(n²) and (yn)=(1/n - n²). Then (xn) diverges to +∞ (n² is not bounded above and it is increasing), (yn) diverges to -∞ (1/n -n² is not bounded below, and this sequence is decreasing), but (xn+yn)=(1/n) converges to zero.
b) This is impossible. Suppose that (xn) converges and (xn+ýn) converges. Then (-xn) converges (scalar multiples of a convvergent sequence are convergent). Now, since sums of convergent sequences are convergent, (xn+yn+(-xn))=(yn) is a convergent sequence. Therefore, (yn) is not divergent and the example does not exist.
