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Andrew [12]
3 years ago
11

11. Use the fact that 19 X 33 = 627 to solve the problems and justify your reasoning

Mathematics
1 answer:
topjm [15]3 years ago
8 0
<h2>19 X 33 = 627,  justified.</h2>

Step-by-step explanation:

We have,

19 × 33 = 627

Use the fact and justify.

L.H.S. = 19 × 33

= (20 - 1) (20 + 13)

Using the identity,

(x - a)(x + b) = x^{2} - (a - b)x - ab

Here, x = 20, a = 1 and b = 13

= 20^{2} - (1 - 13)20 - 1(13)

= 400 - (- 12)20 - 13

= 400 + 240 - 13

= 640 - 13

= 627

= R.H.S., justified.

Thus,  19 X 33 = 627,  justified.

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Yes because 3 x 27= 81 or 81 / 3= 27.
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Will give you 10 points, thank for the help!
Alla [95]

Answer:

Step-by-step explanation:

Area of the shaded region will be "(area of rectangle) - (area of triangle)"

Area of rectangle: 8 ft * 5 ft = 40 ft^2

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A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f
NNADVOKAT [17]

Answer:

26 - \sqrt{181} cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares,  in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}

x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}

x = \frac{624 \pm \sqrt{104256}}{24}

x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}

x = \frac{624 \pm 8*3*\sqrt{181}}{24}

x_1 = \frac{624 + 24*\sqrt{181}}{24}

x_1 = 26 + \sqrt{181}

x_2 = \frac{624 - 24*\sqrt{181}}{24}

x_2 = 26 - \sqrt{181}

But x_1 > 33, then is not the correct answer.

5 0
2 years ago
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