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3 years ago

9 + a = 113 find the solution

Mathematics

1 answer:

alukav5142 [94]3 years ago

5 0

Answer: a=104

Step-by-step explanation:

104+9=113

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Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Anestetic [448]

Answer:

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

$2x,2y,2z$

Volume = $8xyz$

Maximize volume subject to

$x^2+y^2+z^2 =1$

i.e. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Use Lagrangian multipliers , we have

$∇f(x,y,z)=λ∇g(x,y,z)$ at the maximum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dividing we get

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Similarly $y^2=z^2$

Thus we get $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Hence dimensions are

(2x,2y,2z)

So dimensions are

$\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } )$

3 0

3 years ago

You have $6 and earn $0.50 for each cup of orange juice you sell. Write an equation in two variables that represents the total a

natta225 [31]

A = 0.50j + 6.......u r correct

he started with 6....and he is selling each cup (j) for 0.50

so lets say he sold 10 cups...u would sub in 10 for j
A = 0.50(10) + 6
A = 5 + 6
A = 11......and he would have $ 11

6 0

3 years ago

Hey, I would appreciate it if you can help me with these problems, been stuck on it for a few days

Makovka662 [10]

Answer:

Explained below.

Step-by-step explanation:

The formula for average rate of change is:

$\frac{f(b) - f(a)}{b - a}$

1. $\frac{f(b) - f(a)}{b - a}$ = $\frac{f(2) - f(1)}{2 - 1}$ = $\frac{100 - 40}{2 - 1}$ = $\frac{70}{1}$ = 70

2. $\frac{f(b) - f(a)}{b - a}$ = $\frac{f(4) - f(2)}{4 - 2}$ = $\frac{180 -110}{4 - 2}$ = $\frac{70}{2}$ = 35

3. $\frac{f(b) - f(a)}{b - a}$ = $\frac{f(8) - f(6)}{8 - 6}$ = $\frac{350 -230}{8 - 6}$ = $\frac{120}{2}$ = 60

4. $\frac{f(b) - f(a)}{b - a}$ = $\frac{f(10) - f(8)}{10 - 8}$ = $\frac{390 -350}{10 - 8}$ = $\frac{40}{2}$ = 20

5. Their average speed was the greatest during the first to second hour.

6. Their average speed was the least during the eight to tenth hours.

7. $\frac{f(b) - f(a)}{b - a}$ = $\frac{f(10) - f(1)}{10 - 1}$ = $\frac{390 -40}{10 - 1}$ = $\frac{350}{9}$ = 38.89 or 38.9

Hope that helps!

6 0

3 years ago

What is the perimeter of a rectangle with a length of 3.5 yd and a width of 9 yd?

SCORPION-xisa [38]

Perimeter means all the way around.....
so:
3.5 + 9 + 3.5 + 9
= 25

5 0

3 years ago

Solve the equation y2 - y - 5=-3 using the quadratic formula.

VLD [36.1K]

Answer: 0

Explanation:

4 0

3 years ago