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3 years ago

9

Why is 20 to 40 is a 100% increase but 40 to 20 is a 50% decrease

2 answers:

Artyom0805 [142]3 years ago

7 0

I think it because how the order change

murzikaleks [220]3 years ago

6 0

Its because 20 is doubling its self. Its using 100% of its number, While 40 is decreasing by 50%. Half of forty is 20. Half equals 50%.

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A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

Is 1.88 rational or is it irrational

Anna11 [10]

Answer:

1.88 is a irrational number

3 0

4 years ago

- help help help help help help!!!!

Viefleur [7K]

Answer:

B would be -7

Step-by-step explanation:

Because 6 times -7 equals -42

4 0

3 years ago

Read 2 more answers

a) change 12 out of 40 to a percentage . b) change 33 out of 60 to a percentage .

viktelen [127]

Answer:

30%, and 55%

Step-by-Step explanation:

12/40=30%

33/60=55%

7 0

4 years ago

Read 2 more answers

Determine the vertex of the function f(x)=2(x+1)(x+7). You must show all algebraic steps for full marks

notsponge [240]

Answer:

vertex (-4,-18)

Step-by-step explanation:

f(x)=2(x+1)(x+7)

f(x)=2(x^2+8x+7)

f(x)=2x^2+16x+14

f(x)=2(x^2+8x)+14

f(x)=2(x^2+8x+4^2-4^2)+14

f(x)=2(x^2+8x+4^2)+2(-4^2)+14

f(x)=2(x^2+8x+4^2)+2(-4^2)+14

f(x)=2(x^2+8x+4^2)-18

f(x)=2(x+4)^2-18

vertex form:

f(x)=a(x-h)^2+k

h=-4

k=-18

vertex (-4,-18)

8 0

3 years ago