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3 years ago

Point x is the circumcenter of triangle ABC

Mathematics

2 answers:

sergejj [24]3 years ago

5 0

The answer is 5.3 cm.

AlladinOne [14]3 years ago

3 0

Answer:

XB ≈ 5.3 cm

Step-by-step explanation:

From the diagram :

In ΔXNC,

m∠XNC = 90°

Now, m∠XNC + m∠XNB = 180° ( Sum of angles forming a linear pair is supplementary )

⇒ 90° + m∠XNB = 180°

⇒ m∠XNB = 180° - 90°

⇒ m∠XNB = 90°

Now, in right angled ΔXNB Applying Pythagoras theorem , We have

XB² = NB² + XN²

⇒ XB² = 4.2² + 3.2²

⇒ XB² = 27.88

⇒ XB = 5.28 cm

⇒ XB ≈ 5.3 cm

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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Kobotan [32]

Answer:

The dimension of the box is 18.66 in by 2.66 in by 1.17 in.

Step-by-step explanation:

Given that, The cardboard is 21 in. long and 5 in. wide.

Assume,x be the length of the each sides of the square .

Then the length of the box is = (21-2x) in.

The breadth of the box is =(5-2x) in.

The height of the box is = length of side of the square

= x in.

The volume of the box = length × wide × height

=(21-2x)(5-2x)x

=(105-52x+4x²)x

=( $105 x-52x^2+4x^3$ )

Let

V= $105 x-52x^2+4x^3$

Differentiating with respect to x

$V'=105-104x+12x^2$

Again differentiating with respect to x

$V''=-104+24x$

To find the dimension of the box, we set V'=0

$105-104x+12x^2=0$

Applying the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , here a=12, b= -104 and c =105

$\Rightarrow x=\frac{-(-104)\pm\sqrt{(-104)^2-4.12.105}}{2.12}$

$=\frac{104\pm 76}{24}$

=7.5, 1.17

For x= 7.5 , the wide of the box will be negative.

∴x=1.17 in.

$V''_{x=1.17}=-104+(24\times 1.17)$

Since at x= 1.17, V''<0 , therefore at x=1.17 in. the volume of the given box will be maximum.

The length of the box is = [21-(1.17×2)]=18.66 in.

The wide of the box is = [5-(1.17×2)]=2.66 in.

The height of the box is = 1.17 in.

The dimension of the box is 18.66 in by 2.66 in by 1.17 in.

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4 years ago

Ms. Hawkinson is planning to take more pictures of her students. She bought 8 rolls of film and 2 camera batteries for $23.00. T

charle [14.2K]

Answer:

1 Roll = $2.50

1 Battery = $1.50

Step-by-step explanation:

From the question we know that,

8 Rolls + 2 Batteries = $23, and

6 Rolls + 2 Batteries = $18

We can subtract the two equations to obtain a third equation,

(8 Rolls + 2 Batteries) - (6 Rolls + 2 Batteries) = $23 - $18

(8 - 6) Rolls + (2 - 2) Batteries = $23 - $18

2 Rolls = $5

Divide RHS and LHS by 2, to obtain the cost of a roll,

2 Rolls / 2 = $5 / 2

1 Roll = $2.50

If one roll costs $2.50 then 6 rolls cost $15,

6 x $2.50 = $15

We plug in this value into the second equation,

$15 + 2 Batteries = $18

Subtract both sides by $15,

$15 + 2 Batteries - $15 = $18 - $15

2 Batteries = $3

Divide RHS and LHS by 2 to obtain the final answer,

2 Batteries / 2 = $3 / 2

1 Battery = $1.50

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3 years ago

A video game that usually costs $50 is on sale for $32 50 What percent of the regular price is the discount

slava [35]

Answer:

65 percent

Step-by-step explanation:

50 and is for sale at 32.50 dollars

ok to now this

32.5/50=0.65 multiply by 100

65 percent

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AfilCa [17]

She will need to buy 36 cups of sugar.

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A plastic toy submarine is held 15 centimeters below the water surface in a bath tub. The submarine is let go and rises 15 centi

Effectus [21]

Answer:

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3 years ago

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