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2 years ago

Which composition of transformations will create a pair of similar, nol congruent triangles?

Mathematics

2 answers:

Andrej [43]2 years ago

3 0

Answer:

Rotation then dilation.

Step-by-step explanation:

Dilation changes the size. So the result is a similar not congruent triangle. The other transformations move the figure around on the plane.

Ymorist [56]2 years ago

3 0

The answer is D, hope this 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

2 years ago

PLZ HELP...Enter in standard form the equation of the line passing through the given point and having the given slope.

Alenkinab [10]

Standard form for the equation of the line is

$$y=-\frac{2}{3} x-\frac{25}{3}$

Solution:

Given point is (2, –5).

slope of the line m = $-\frac{2}{3}$

Here, $x_1=2, y_1=-5$

Equation of a line passing through the point:

$y-y_1=m(x-x_1)$

$$y-(-5)=-\frac{2}{3} (x-(-5))$

$$y+5=-\frac{2}{3} (x+5)$

$$y+5=-\frac{2}{3} x-\frac{10}{3}$

Subtract 15 from both sides of the equation.

$$y+5-5=-\frac{2}{3} x-\frac{10}{3}-5$

$$y=-\frac{2}{3} x-\frac{25}{3}$

Standard form for the equation of the line is

$$y=-\frac{2}{3} x-\frac{25}{3}$

7 0

3 years ago

2. Lamar purchases comic books at garage

Otrada [13]

<u>Answer:</u>

Lamar will charge $\$7$ to the comic dealer for a comic book.

<u>Solution:</u>

It is given that lamar purchases a comic book for $\$4$ . He then marks up the price of a comic book by $75\%$ which means he increases the price of the book by $75\%$ and then sells it to the comic dealer.