Answer:
My sister will swing the total distance = 40 feet
Step-by-step explanation:
On the first swing my sister travels a distance of 8 feet.
In every successive swing she travels 80% of the distance of the previous distance.
So the sequence formed by the distance traveled in every swing will be a geometric sequence.
First term of the sequence 'a' = 8 feet
common ratio 'r' = 0.80
Since this sequence is an infinite geometric sequence,
Sum of this sequence = 
[Since r < 1]
= 
= 
= 40 feet
Therefore, my sister will cover the total distance = 40 feet
Unfortunately, I don’t knooow :(
Answer:
5088
Step-by-step explanation:
212*24=5088
So 3 and 1/4 is equal to 4/4+4/4+4/4+1/4=13/4
so she put in 3 and 1/9 or 9/9+9/9+9/9+1/9 or 28/9
28/9+x=13/4
13/4-28/9=x
so we convert so that the bottom numbers are the same
a short cut is 3 and 1/4+x=3 and 1/9
3 1/9+x=3 1/4
subtract 3 from both sides
1/9+x=1/4
subtract 1/4 from both sides
x=1/4-1/9
convert bottom number to same thing
1/9=4/36
1/4=9/36
x=9/36-4/36
x=5/36
5/36 cups
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
