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3 years ago

5 Points

Mathematics

1 answer:

deff fn [24]3 years ago

7 0

Answer:

D. A rectangle and an isosceles triangle

Step-by-step explanation:

In the figure attached, the sign is shown. There we can see an arrow, which can be decomposed into a rectangle (on the left of the figure) and an isosceles triangle (on the right of the figure)

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A total of 504tickets were sold for the school play. They were either adult tickets or student tickets. There were 54more studen

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Answer:

225 adult tickets

Step-by-step explanation:

S: no. of students

A: no. of adults

S = A + 54

S + A = 504

A + A + 54 = 504

2A = 450

A = 225

S = 225 + 54

S = 279

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3 years ago

Let II be the tangent plane to the graph of f(x, y) = 8 – 2x^2 – 3y^2 at the point (1, 2,-6). Let S, x² + y^2 + z = 4 be another

stealth61 [152]

Let $F(x,y,z)=f(x,y)-z$ . The tangent plane to $f(x,y)$ at (1, 2, -6) has equation

$\nabla F(1,2,-6)\cdot(x-1,y-2,z+6)=0$

We have

$\nabla F(x,y,z)=(-4x,-6y,-1)\implies\nabla F(1,2,-6)=(-4,-12,-1)$

Then the tangent plane has equation

$(-4,-12,-1)\cdot(x-1,y-2,z+6)=0\implies -4(x-1)-12(y-2)-(z+6)=0\implies 4x+12y+z=22$

Let $g(x,y)=4-x^2-y^2$ , and $G(x,y,z)=g(x,y)-z$ . The tangent plane to $S$ at a point $(a,b,c)$ is

$\nabla G(a,b,c)\cdot(x-a,y-b,z-c)=0$

We have

$\nabla G(x,y,z)=(-2x,-2y,-1)\implies \nabla G(a,b,c)=(-2a,-2b,-1)$

so that this plane has equation

$(-2a,-2b,-1)\cdot(x-a,y-b,z-c)=0\implies2ax+2by+z=2a^2+2b^2+c$

In order for this plane to be parallel to the previous plane, we need to have

$\begin{cases}2a=4\\2b=12\end{cases}\implies a=2,b=6\implies g(a,b)=c=-36$

so the point we're looking for is (2, 6, -36).

6 0

3 years ago