2 years ago

7.) A window washing company has a contract to wash 3,082 windows on a 23

Mathematics

1 answer:

SOVA2 [1]2 years ago

5 0

134 windows on each floor

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Mr. Chang’s class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang

DedPeter [7]

Okay, so we know a number of students and the amount of girls as a bracket. So what we have to do now is multiply them with each other.
28 *4/7 = 16
So there are 16 girls in Mr. Chang´s class.
You can also determine the boys by - the students with the girls:
28-16=12 boys

Have a nice day :D

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3 years ago

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to meet increased demand, world food production must rise 50% by 2030. write this percentage as a fraction in simplest form.

Leya [2.2K]

It would be 1/2 because that is the fraction of 50<span>%

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3 years ago

The figure shows the construction steps to duplicate an angle. The steps are in an incorrect order. What is the correct order of

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The correct order of the steps to duplicate an angle is A. ADFECB

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3 years ago

On the last three chemistryexams a student scored 87, 88, and 89. What score must the student earn on the next exam to have an

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Answer:96%

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3 years ago

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)

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3 years ago