How to express 24.357 in unit form
1 answer:
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Answer:
There is a total of 66 different fruit salads.
Step-by-step explanation:
One fruit salad differs from the other only in the amount of pieces of certain fruit put in it. In order to easier denote fruit pieces we introduce these notations:
A-how many apples are put into the salad;
B-how many bananas are put into the salad;
C-how many cranberries are put into the salad.
Since she can freely choose the number of pieces of each fruit, we have these conditions for the variables A, B and C:
-
(she cannot choose a negative number of pieces)
(because she can get the total of 10 pieces of fruit)
Another condition for forming the salad is that the salad must consist of exactly 10 pieces of fruit, hence we have this equation to solve:
but we must obtain the non-negative integer solutions of this equation.
That is equivalent to calculating the number of r-combinations of the multi-set S with objects of k different types with infinite repetition numbers.
The formula for obtaining the number of such r-combinations is:
We have that and that
and we can observe the repetition number as infinite since she can create a fruit salad with only one piece of fruit and the repetition number in such cases is the maximum 10. Finally, we have that the total number of fruit salads equals:
.
1. The area of the rhombus can be found by the formula
where
are rhombus's diagonals.
Note that then
2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs
The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem
3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.
Use twice the Pythagorean theorem to find this height:
where x is projection of leg 12 cm and h is height.
Subtract the first equation from the second:
Then
Answer: