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wariber [46]
2 years ago
10

Minimize Q=3x2+3y2​, where x+y=6.

Mathematics
1 answer:
weeeeeb [17]2 years ago
5 0

Answer:

+(x + y) {}^{2}  = 6 {}^{2} \\ x {}^{2} + 2xy + y {?}^{2}  = 36

x {}^{2}  + y {}^{2}  = 36 - 2xy

q = 3(x {}^{2}  + y {}^{2} )

q = 3(36 - 2xy) = 108 - 6xy

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SO
Xelga [282]

Answer:

D. y=162.5

Step-by-step explanation:

0.75 ->25

4.875->y

y= (4.875*25)/0.75

y=162.5

6 0
3 years ago
A rectangular prism has a base area 56 ft.² and a volume of 840 ft.³ the length of the base is longer than the width if the sum
suter [353]

Answer:

The length of the base in feet is 8 ft.

Step-by-step explanation:

The volume V of the rectangular prism is given by

V = l × w × h

But Area, A = l × w

∴ V = A × h

Where A is the base area and h is the height

From the question

A = 56 ft.²  and V = 840 ft.³

∴ 840 ft.³ = 56 ft.² × h

840 ft.³ / 56 ft.² = h

15 ft. = h

∴ h = 15 ft.

Hence, the height of the rectangular prism is 15 ft.

Also, from the question

the sum of the length and the width of the base is equal to the height

i.e l + w = h

where l is the length of the base and w is the width of the base

Then, l + w = 15 ------ (1)

Also, A = l × w

Then, 56 = l × w ------- (2)

From equation (1)

l + w = 15

Then, w = 15 - l ------- (3)

Substitute this into equation (2)

56 = l × w

56 = l × (15-l)

56 = 15l - l²

Then,

l²- 15l + 56 = 0

l² -8l -7l + 56 = 0

l(l - 8) -7(l - 8) = 0

(l - 7)(l - 8) = 0

l - 7 = 0 OR l - 8 = 0

∴ l = 7 OR l = 8

Substitute the values of l into equation (3)

w = 15 - l

when l = 7

w = 15 - 7

w = 8

and when l = 8

w = 15 - 8

w = 7

From the question, the length of the base is longer than the width

∴ l = 8 and w = 7

Hence, the length of the base in feet is 8 ft.

6 0
2 years ago
What does it mean to have diagonals bisect each other?
Degger [83]

Answer:

I think your answer would be A

Step-by-step explanation:

8 0
2 years ago
Liam had a container of oatmeal that contained 5 and one-half cups of oatmeal. Liam ate StartFraction 4 over 9 EndFraction cup o
Solnce55 [7]
3 and two half I hope you get a good answer
4 0
2 years ago
Read 2 more answers
Urgenttttt please I need it fast​
dolphi86 [110]

Answer:

Below in bold.

Step-by-step explanation:

c) 3 x (9^2)^3/4 x ((81^3)^5/6

= 3 x 81^3/4 x 81^15/6

= 3 x 81^(3/4 + 15/6)

= 3 x 81^13/4

= 3 x 3^13

= 3^14

= 4,782,969.

f) (5x^-1y^2)^-2 / (25 x^2 y - 1)^2

=  5^-2 x^2y^-4 / 625 x^4y^-2

=  5^-2 x^-2 y^-2 / 5^4

= 5^-6 x^-2y^-2

= 0.000064x^-2y^-2.

5 0
2 years ago
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