What would the equation be of the relationship??

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

2 years ago

Help please asap and or ill eat your mom

tresset_1 [31]

The answer is F

I hope I helped. Brainliest would be appreciated.

5 0

2 years ago

Yesterday the student councils bank account balance was -$54.31. Today the balance is $65.10. What is the change in dollars in t

uysha [10]

-$69.68 is your answer if I hope that this is correct.

3 0

2 years ago

15 POINTS: The ratio of the same side interior angles of two parallel lines is 33:3. Find the measures of all eight angles forme

larisa [96]

Answer:

$15^\circ,165^\circ,15^\circ,165^\circ\\15^\circ,165^\circ,15^\circ,165^\circ$

Step-by-step explanation:

The ratio of the same side interior angles of two parallel lines is 33:3

If two parallel lines are cut by a transversal

Sum of the same side interior angles = 180 degrees.

Therefore, the two same-side interior angles are:

$\dfrac{33}{36}\times 180^\circ =165^\circ\\\dfrac{3}{36}\times 180^\circ =15^\circ$

We can then say that the measure of all eight angles formed by the parallel lines and transversal starting from the upper left in a clockwise rotation is:

$15^\circ,165^\circ,15^\circ,165^\circ, 15^\circ,165^\circ,15^\circ,165^\circ$

4 0

2 years ago

A ladder reaches the top of a 20 foot building. the ladder is 4.5 feet away from the building. how long is the ladder?

KATRIN_1 [288]

Answer:

C

Step-by-step explanation:

do that with pithagoras:

20² + 4,5² = x²

400 + 20,25 = x²

420,25 = x²

x = $\sqrt{420,25}$

x ~ 20,5

Letter C: 20,5 feet

4 0

2 years ago