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2 years ago

Evaluate 7p+6(p/q)2 q if p = 6 and q = 3. show your work and give an explanation for each step .

Mathematics

1 answer:

Degger [83]2 years ago

6 0

Answer:

63 is the required value.

Step-by-step explanation:

We need to find the value if p = 6 and q = 3 in the below expression i.e.

$7p+6(\dfrac{p}{q})^2-q$

Put p = 6 and q = 3 in the above expression.

$=7(6)+6(\dfrac{6}{3})^2-3\\\\=42+6(2)^2-3\\\\=42+24-3\\\\=63$

So, the value of the given expression is 63.

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Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic

Marina86 [1]

Answer:

Equation of Sphere = $x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

$(PA)^{2} = (2PB)^{2}$

$(PA)^{2} = 4 (PB)^{2}$

$(x - (-3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x $(x-6)^{2}$ + $(y-2)^{2}$ + $(z-(-3))^{2}$

Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

- ( 3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142) = 0

3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

7 0

3 years ago

PLS PLS PLS I NEED HELP FAAAAAAAASSSSST GIVING BRAINLIEST TO QUICKEST CORRECT

ElenaW [278]

Answer:

c hope this helps

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

|y| x-3 what is the vertex

lutik1710 [3]

Answer:

(3,0)

Step-by-step explanation:

put x-3=0 and solve for it whic hwould be x=3

8 0

3 years ago

What is the product of (3√8)(4√3)? Simplify your answer

andreyandreev [35.5K]

The answer is: 24√6 .
_______________________________
The question asks:
_______________________________
"What is the product of (3√8)(4√3)? Simplify your answer/

First, let us simplify: "√8"

"√8 = √4*√2 = 2√2 ;

So, "3√8 = 3*2√2 = 6√2" .

So, "what is the product of "(3√8)(4√3)"?

Rewrite, replacing the "(3√8)" with "6√2" ; as follows:

6√2* 4√3 = 6*4 *√2*√3 = 24 *√(2*3) = 24√6 .
______________________________________

3 0

2 years ago

PLEASE HELP..... I WILL GIVE BRAINLIEST!!

Yakvenalex [24]

For the first part:

Every shirt she grabs, will cost her dollars, so if she grabs 3 shirts, then the cost of the shirts is:

$12+12+12=3(12)$

With the same rationale, if she grabs 2 pairs of jeans, the cost of the jeans is:

$19+19=2(19)$

So, her total is:

$3(12)+2(19)$

If you subtract 3 from the total, then the expression is:

$3(12)+2(19)-3=36+38-3=71$

For the second part:

If she's paying 3 less for each shirt, then the cost of 3 shirts will become:

$(12-3)+(12-3)+(12-3)=3(12-3)$

In the same fashion, for the two jeans:

$(19-3)+(19-3)=2(19-3)$

So the expression for the total cost is:

$3(12-3)+2(19-3)=36-9+38-6=59$

For number three:

The amounts are different because the cost of the total purchase is different than the cost of each element that makes up the total purchase.

For number four:

If you're the owner, you want to give the smallest amount of discount (the one in part 1/a).

So you could clarify by saying there's 3 dollars of the TOTAL purchase's cost.

6 0

3 years ago