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zzz [600]
3 years ago
11

The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park

, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?
Mathematics
1 answer:
elena55 [62]3 years ago
7 0
This is harder than it looks I cant figure it out
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PLZ help me I have no idea lol
Artemon [7]

Answer:

48 divided by 16

Step-by-step explanation:

16 oz=1 lb

Divided by 16 because there are 16 oz per pound

5 0
3 years ago
Use lagrange multipliers to find the point on the plane x â 2y + 3z = 6 that is closest to the point (0, 2, 4).
Arisa [49]
The distance between a point (x,y,z) on the given plane and the point (0, 2, 4) is

\sqrt{f(x,y,z)}=\sqrt{x^2+(y-2)^2+(z-4)^2}

but since \sqrt{f(x,y,z)} and f(x,y,z) share critical points, we can instead consider the problem of optimizing f(x,y,z) subject to x-2y+3z=6.

The Lagrangian is

L(x,y,z,\lambda)=x^2+(y-2)^2+(z-4)^2+\lambda(x-2y+3z-6)

with partial derivatives (set equal to 0)

L_x=2x+\lambda=0\implies x=-\dfrac\lambda2
L_y=2(y-2)-2\lambda=0\implies y=2+\lambda
L_z=2(z-4)+3\lambda=0\implies z=4-\dfrac{3\lambda}2
L_\lambda=x-2y+3z-6=0\implies x-2y+3z=6

Solve for \lambda:

x-2y+3z=-\dfrac\lambda2-2(2+\lambda)+3\left(4-\dfrac{3\lambda}2\right)=6
\implies2=7\lambda\implies\lambda=\dfrac27

which gives the critical point

x=-\dfrac17,y=\dfrac{16}7,z=\dfrac{25}7

We can confirm that this is a minimum by checking the Hessian matrix of f(x,y,z):

\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}

\mathbf H is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.

At this point, we get a distance from (0, 2, 4) of

\sqrt{f\left(-\dfrac17,\dfrac{16}7,\dfrac{25}7\right)}=\sqrt{\dfrac27}
8 0
3 years ago
I NEED HELP ASAP PLEASE
Naddika [18.5K]
I think you would put 570 in the blank since 19 x 3 = 57
7 0
3 years ago
Whats an equation that uses all numbers 1-10
svet-max [94.6K]

Answer:

linear equations

Step-by-step explanation:

linear inequalities

7 0
3 years ago
Read 2 more answers
What is the opposite of the opposite of 8 1/4
Alenkasestr [34]
8 1/4
33/4
the opposite is 4/33
8 0
3 years ago
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