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2 years ago

Find the length of a diagonal of a square if its area is 162 square feet.

Mathematics

1 answer:

bearhunter [10]2 years ago

5 0

Answer:

9sqrt(2) ft or 12.73 ft

Step-by-step explanation:

A = L^2

sqrt(162) = 9sqrt(2)

The diagonal of a square is equal to the side length.

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An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. Find the dimensions of such a box if

murzikaleks [220]

Answer:

6 in x 6 in x 3 in.

Step-by-step explanation:

Given

V = xyz = 108 ⇒ z = 108/(xy)

The amount of the material used is

S = xy + 2yz + 2xz

Put value of z from the volume

S = xy + 2y*108/(xy) + 2x*108/(xy) = xy + 216/x + 216/y

Now, we find the relative minimum of the function S(x,y)

First, we find the critical point. Set Sx = 0 and Sy = 0

and solve this system:

Sx(x,y) = y - (216/x²) = 0

Sy(x,y) = x - (216/y²) = 0

From the first equation we have

y = 216/x²

Put it in the second equation and find x

x - (216/(216/x²)²) = 0

⇒ x*(1 - (x³/216)) = 0

⇒ x₁ = 0 and x₂ = 6

Now, we can find y as follows

y₁ = 216/(0)² which is undefined

y₂ = 216/(6)² = 6

Hence, the only critical point of S is (6, 6). Next, we calculate the second ordered derivatives that we need for the second derivative test:

Sxx(x,y) = 432/x³

Sxy(x,y) = 1

Syy(x,y) = 432/y³

Applying the second derivative test

D(6, 6) = Sxx(6, 6)*Syy(6, 6) - S²xy(6, 6) = 2*2 - 1² = 4 -1 = 3 > 0

Sxx(6, 6) = 2 > 0

Since D(6, 6) > 0 and Sxx(6, 6) > 0 we can conclude that S has a relative minimum at (6, 6).

z coordinate is:

z = 108/(xy) = 108 / (6*6) = 3

Finally, the dimentions of a box are 6 in x 6 in x 3 in.

6 0

3 years ago

Please answer these and find the slope intercept form for each one.

damaskus [11]

1. 5/y=2/3x +3
2. y= 7/1-4
3. y=2/5x8
4. y=-3/4 +1 I could be wrong but I think this is right

5 0

2 years ago

Pleas help with what I just recently posted

Delvig [45]

Answer:

Circumference is 18.84 feet. Area is 28.26 square feet.

Step-by-step explanation:

Given:

Radius of the circle, $r=3\textrm{ ft}$

The value of $\pi$ is 3.14.

Now, circumference of a circle of radius $r=3$ is given as:

$Circumference=2\pi r=2\times 3.14\times 3=18.84\textrm{ ft}$

Also, area of the circle of radius $r=3$ is given as:

$Area=\pi r^{2}=3.14\times (3)^{2}=3.14\times 3\times 3=28.26\textrm{ }ft^{2}$

Therefore, the circumference of the circle is 18.84 feet and area of the circle is 28.26 square feet.

5 0

3 years ago

Helpppppp:((((((this is due tomorrow and I still didn’t turn it in. Pls help if you can and take ur time but pls don’t take too

Arlecino [84]

#3 is < , =, =
#6 4L= 4,000ml
9L= 9,000ml
6g=6000mg

5 0

2 years ago

NOBODYS HELPING ME ANSWER THIS AND I NEED AN ANSWER ASAP :((( IVE ASKED 2 TIMES ANYWAYS ILL GIVE BRAINLIEST AND 15+

KengaRu [80]

Answer:

1) 2/3

2) y= 2x+4

Step-by-step explanation:

For number one, use the formula $\frac{(y_{2}-y_{1} ) }{(x_{2}-x_{1} ) }$ .

Insert the given coordinates into the formula.

7-1/10-1= 6/9

Simplify 6/9.

6/9÷3= 2/3

For the second one, I used desmos calculator.

Hope this helps! :)

6 0

3 years ago