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4 years ago

PLEASE HELP ASAP!! WILL MARK BRAINLIEST

Mathematics

2 answers:

KATRIN_1 [288]4 years ago

8 0

The slope is mx+b so find two points in the graph and use y-rise/x-run

kirill115 [55]4 years ago

6 0

The slope is mx+b so find two points in the graph and use y-

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Let R = [ 0 , 1 ] × [ 0 , 1 ] R=[0,1]×[0,1]. Find the volume of the region above R R and below the plane which passes through th

Bond [772]

The three vectors $\langle0,0,1\rangle$ , $\langle1,0,8\rangle$ , and $\langle0,1,9\rangle$ each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

$\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle$

$\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle$

Then the cross product of these two results is normal to the plane:

$\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle$

Let $(x,y,z)$ be a point on the plane. Then the vector connecting $(x,y,z)$ to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that

$\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0$

which reduces to the equation of the plane,

$-7x-8y+z-1=0\implies z=7x+8y+1$

Let $z=f(x,y)$ . Then the volume of the region above $R$ and below the plane is

$\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}$

6 0

3 years ago

Which of the following is the solution set of 18 - 3n + 2 = n + 20 - 4n?

exis [7]

The solution set of the equation is all reals ⇒ 3rd answer

Step-by-step explanation:

The solution set of an function is the set of all vales make the equation true. The equation has:

Solution if the left hand side is equal to the right hand side
No solution if the left hand side doesn't equal the right hand side

∵ The equation is 18 - 3n + 2 = n + 20 - 4n

- Add the like terms in each side

∴ (18 + 2) - 3n = (n - 4n) + 20

∴ 20 - 3n = -3n + 20

- Add 3n to both sides

∴ 20 = 20

In the equation of one variable, when we solve it if the variable is disappeared from the two sides, and the two sides of the equations are equal, then the variable can be any real numbers, if the two sides are not equal, then the variable couldn't be any value

∵ The the variable n is disappeared

∵ The left hand side = the right hand side

∴ n can be any real number

∴ The solution set of the equation is all real numbers

The solution set of the equation is all reals

Learn more:

You can learn more about the equations in brainly.com/question/11229113

#Learnwithbrainly

8 0

3 years ago

Read 2 more answers

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