Answer:
Sven used Sugar.
Step-by-step explanation:
The question gives the amount of each ingredient left after making the cake.
= 0.25 - Flour
= 0.33 - Butter
= 0.50 - Sugar
= 0.625 - Eggs
It says that Anna used most of her ingredients, this means she has used the ingredients which has the least amount left. The lowest out of the fractions above is . So Anna used Flour.
Also Olaf used the least of his, meaning he has most of his ingredient left. Highest value in the list is . So Olaf used Eggs.
Kristoff used more than Sven, means that Kristoff has less of his ingredient left compared to Sven. So lower value out of the values left goes to Kristoff, that is . So Kristoff used Butter.
So we are left with Sugar and Sven.
So Sven used Sugar.
Let x be the smaller number.
So the bigger number is x+19 (Their difference is 19)
Their sum: 53
Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:
Since the distance to the top of the tree is 11 ft more than two times the height, then:
Use the Pythagorean Theorem to relate the length of the sides of the right triangle:
Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:
Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.
Therefore, the height of the tree is 39 ft.
It would be less then because, first we need to convert yards into feet which the formula for doing that is 3 feet per yard so if you have 36 yards you would take 36*3=108 then you would add 2 feet because there are 2 extra feet to add on to the end of this question. Like so 108+2=110 then we see which one is bigger 114<110 does not work out and 114=110 is no true but 114>110 is correct and works out to be true therefore your answer is 114 and 2 inches is bigger then 26 yards and 2 feet.
Enjoy!=)
I'm partial to solving with generating functions. Let
Multiply both sides of the recurrence by 
and sum over all 
.
Shift the indices and factor out powers of 
as needed so that each series starts at the same index and power of .
Now we can write each series in terms of the generating function 
. Pull out the first few terms so that each series starts at the same index 
.
Solve for :
Splitting into partial fractions gives
which we can write as geometric series,
which tells us
# # #
Just to illustrate another method you could consider, you can write the second recurrence in matrix form as
By substitution, you can show that
or
Then solving the recurrence is a matter of diagonalizing the coefficient matrix, raising to the power of 
, then multiplying by the column vector containing the initial values. The solution itself would be the entry in the first row of the resulting matrix.
