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mr Goodwill [35]
3 years ago
15

The state where you live has a 6% sales tax. If you purchase a car for $9,800, what will you pay, including tax? (this is a two-

step problem.)
Mathematics
1 answer:
mestny [16]3 years ago
5 0

Answer: $10,388

Step-by-step explanation:

The first step is to calculate the tax for the car:

9,800*0.06=588

The second step is to add the price of the car and the corresponding tax:

9,800+588=10,388

So, you will pay $10,388.

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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
I-ready testing need help ASAP!
Leto [7]

Answer:

-11/12

Step-by-step explanation:

5 0
2 years ago
Given the trinomial, what is the value of the coefficient 'B' in the factored form?
Zepler [3.9K]

Answer:

B=9  (I'll solve right now, just so you get the answer)

Step-by-step explanation:

2x^2+14xy-36y^2=2(x+By)(x-2y)

Expand right side by distributing

(2x+2By)(x-2y)

Use the FOIL method to simplify (first, outside, inside, last):

(a+b)(c+d)=ac+ad+bc+bd

(2x*x)+(2x*(-2y))+(2By*x)+(2By*(-2y))\\\\

Simplify

2x^2-4xy+2Byx-4By^2

Re-insert

2x^2+14xy-36y^2=2x^2-4xy+2Byx-4By^2

Cancel out 2x^2

14xy-36y^2=-4xy+2Byx-4By^2

Move all terms to one side

14xy-36y^2+4xy-2Byx+4By^2=0

Simplify

18xy-36y^2-2Byx+By^2=0

Factor out the common term 2

2(9xy-18y^2-Byx+2By^2)

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3 years ago
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