55% of what number is 231

From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh

Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

Step-by-step explanation:

Volume = height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V= 4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so, 4 (3x² - 60x +225)=0

3x² - 60x+225=0 (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5 (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

7 0

4 years ago

Solve this for 50 points

Bingel [31]

3< -5x+2x
3< -3x
-3x>3
3x> -3
X> -1

4 0

3 years ago

Read 2 more answers

When a number is stated as a percentage, it means that number represents a portion of

dedylja [7]

100. Percent means out of hundred, so one percent means one out of a hundred, two percent means two out of a hundred, etc.

6 0

3 years ago

9. what is the measure of QSR

Scilla [17]

<h3>Answer: C) 142 degrees</h3>

=======================================================

Explanation:

Extend segment MN such that it intersects side ST. Mark the intersection as point A. See the diagram below.

We're given that angle MNT is 72 degrees. The angle TNA is equal to 180-(angle MNT) = 180 - 72 = 108 degrees, since angles MNT and TNA add to 180.

For now, focus entirely on triangle TNA. We see from the diagram that T = 34 and we just found that N = 108. Let's find angle A

A+N+T = 180

A+108+34 = 180

A+142 = 180

A = 180-142

A = 38

So angle NAT is 38 degrees.

----------------------------

Since segment MA is an extension of MN, and because MN || SQ, this means MA is also parallel to SQ.

We found at the conclusion of the last section that angle NAT was 38 degrees. Angles QST and NAT are corresponding angles. They are congruent since MA || SQ. This makes angle QST to also be 38 degrees

----------------------------

The angles QSR and QST are a linear pair, so they are supplementary

(angle QSR) + (angle QST) = 180

angle QSR = 180 - (angle QST)

angle QSR = 180 - 38

angle QSR = 142 degrees

5 0

3 years ago

You are asked to build an open cylindrical can (i.e. no top) that will hold 364.5 cubic inches. To do this, you will cut its bot

Vilka [71]

Generate a function for the height of the cyliner as a function of radius. Use this function to generate a function of r for the material used. Take the derivative of that function, set it to zero, and solve for r.

V=πr2hh=d h=d=2r h=2r V=πr22r

V(r,h)=180.5=πr2h⟹h=180.5/πr2⟹A(r)=r(r+h)=r2+180.5/πr

A(r)=2r(2r+h)=4r2+361/πr

A′(r)=8r−361/πr2

3 0

3 years ago