How do you find the lateral area of a pentagonal prism?

Mathematics

1 answer:

Sloan [31]3 years ago

3 0

AL=5ah!!!!!!!!!! Hope it helps

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Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 8exyz, (0, 0, 8

Dima020 [189]

Let $f(x,y,z)=x+y+z-8e^{xyz}$ . The tangent plane to the surface at (0, 0, 8) is

$\nabla f(0,0,8)\cdot(x,y,z-8)=0$

The gradient is

$\nabla f(x,y,z)=\left(1-8yze^{xyz},1-8xze^{xyz},1-8xye^{xyz}\right)$

so the tangent plane's equation is

$(1,1,1)\cdot(x,y,z-8)=0\implies x+y+(z-8)=0\implies x+y+z=8$

The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by $t$ , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation

$(1,1,1)t+(0,0,8)=(t,t,t+8)$

or $x(t)=t$ , $y(t)=t$ , and $z(t)=t+8$ .

(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)

4 0

3 years ago

You are 5 feet tall and cast a 10-foot shadow. a flagpole nearby casts a shadow that is 28 feet. which equation can you use to s

VashaNatasha [74]

As the ratio of your shadow to your height is 2:1 assuming the flagpole would form a similar triangle the shadow is twice the height of the pole meaning the pole is 14 feet tall

3 0

4 years ago

Read 2 more answers

What is the area of a circle with a radius of 21 feet?

lidiya [134]

Answer:

Area is about 1520.53

Step-by-step explanation:

$A=\pi r^{2}$