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125 children tickets were sold
<u>Solution</u>:
Given that
Price of 1 ticket sold to children = $5
Price of 1 ticket sold to adult = $12
Total number of ticket sold = 400
Amount generated by selling 400 tickets = $3925.
Need to calculate number of ticket sold to children’s
Let’s assume number of tickets sold to childrens = x
So number of tickets sold to adults = 400 – x
Amount generated from x ticket sold to children
Amount generated from (400 – x) tickets sold to adults
<em>Total amount generated from 400 tickets = Amount generated from children’s tickets + Amount generated from adults ticket </em>
= 5x + (4800 – 12x) = 4800 -7x
As given that amount generated = 3965
=> 3965 = 4800 – 7x
Solving above expression to get value of x, we get
7x = 4800 - 3965
=> 7x = 875
=> x = 125.
Hence number of children tickets sold = 125.
Answer:
Take as the projection of u onto v and
as the vector such that b+w =u
Step-by-step explanation:
The formula of projection of a vector u onto a vector v is given by
, where
is the dot product between vectors.
First, let b ve the projection of u onto v. Then
We want a vector w, that is orthogonal to b and that b+w = u. From this equation we have that w = u-b = (-6,8)-\frac{-17}{25}(7,1)= \frac{1}{25}(-31,217)[/tex]
By construction, we have that w+b=u. We need to check that they are orthogonal. To do so, the dot product between w and b must be zero. Recall that if we have vectors a,b that are orthogonal then for every non-zero escalar r,k the vector ra and kb are also orthogonal. Then, we can check if w and b are orthogonal by checking if the vectors (7,1) and (-31, 217) are orthogonal.
We have that . Then this vectors are orthogonal, and thus, w and b are orthogonal.