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ludmilkaskok [199]
3 years ago
13

a rectangular sheet is 62cm long and 42cm wide from each of its corners a square of side 6cm is cut out and an open box is made

fromthe remaing sheet . find the volume of the rectangular sheet

Mathematics
1 answer:
Alla [95]3 years ago
4 0

Answer:

The volume of rectangular box is 9,000 cubic centimeters

Step-by-step explanation:

Given as :

The length of the rectangular sheet = L = 62 cm

The width of the rectangular sheet = B = 42 cm

Let The volume of rectangular box = v cubic centimeters

From each corner of sheet a square of 6 cm is cut out and an open box made

So, The length of box = L' = (L - 6 - 6)

i.e L' = (62 - 6 - 6)

Or, L' = 50 cm

Or, Length of the box = 50 cm

And The width of the box = B' = (B - 6 - 6)

i.e B' = (42 - 6 - 6)

Or, B' = 30 cm

Or width of the box = 30 cm

And,

The height of the box = H = 6 cm

∴ volume of rectangular box = Length of box × Breadth of box × Height of  box

i.e v = L' × B' × H

Or, v = 50 cm × 30 cm × 6 cm

Or, v = 9,000 cm³

So, The volume of rectangular box = v = 9,000 cm³

Hence, The volume of rectangular box is 9,000 cubic centimeters Answer

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Mandarinka [93]

Answer:

  • As the slopes of both lines 'm' and 'n' are the same.

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

Step-by-step explanation:

We know that the slope-intercept of line equation is  

y=mx+b

Where m is the slope and b is the y-intercept

Given the equation of the line m

y = 1/2x - 4

comparing with the slope-intercept form of the line equation

y  = mx + b

Therefore,

The slope of line 'm' will be = 1/2

We know that parallel lines have the 'same slopes, thus the slope of the line 'n' must be also the same i.e. 1/2

Checking the equation of the line 'n'

x-2y=4

solving for y to writing the equation in the slope-intercept form and determining the slope

x-2y=4

Add -x to both sides.

x - 2y + (-x) = 4+(-x)

-2y = 4 - x

Divide both sides by -2

\frac{-2y}{-2}=\frac{-x+4}{-2}

y=\frac{1}{2}x-2

comparing ith the slope-intercept form of the line equation

Thus, the slope of the line 'n' will be: 1/2

  • As the slopes of both lines 'm' and 'n' are the same.

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

3 0
2 years ago
In 2013 Traci joined a swim club. The fees were £600 per year in 2013. Each year the fees increase by 6%. Calculate, to nearest
balandron [24]

Answer:

715 pounds

Step-by-step explanation:

<em>FV = solve</em>

<em>PV = 600</em>

<em>I% = 6</em>

<em>K = 1, N = 3 </em>(2013 - 2016 = 3 years)

Plug it in:

<em>FV = 600 x [ 1 + (6/100 x 1)]³</em>

= 600 x ( 1 + 0.06)³

= 600 x (1.06)³

FV = 714.61, 715 to the nearest dollar.

<em>Therefore, the fee in 2016 is 715 pounds.</em>

6 0
3 years ago
What is the equation for the line of reflection <br><br> A. X=6<br> B. Y=6<br> C. Y=x<br> D. Y=2
PilotLPTM [1.2K]

Answer:

x = 6

Step-by-step explanation:

The line of reflection is x = 6.

5 0
3 years ago
Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.
grandymaker [24]

Answer:

Lines a and b are parallel

Lines a and c are perpendicular

Lines d and c are perpendicular

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

Part 1) Find the slope of Line a

we have the points

(-3,4) and (3,6)

substitute in the formula

m=\frac{6-4}{3+3}

m=\frac{2}{6}

simplify

m_a=\frac{1}{3}

Part 2) Find the slope of Line b

we have the points

(-10,-3) and (-8,3)

substitute in the formula

m=\frac{3+3}{-8+10}

m=\frac{6}{2}

m_b=3

Part 3) Find the slope of Line c

we have the points

(0,5) and (3,-4)

substitute in the formula

m=\frac{-4-5}{3-0}

m=\frac{-9}{3}

m_c=-3

Part 4) Find the slope of Line d

we have the points

(4,-7) and (13,-4)

substitute in the formula

m=\frac{-4+7}{13-4}

m=\frac{3}{9}

simplify

m_d=\frac{1}{3}

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Remember that

If two lines are parallel then their slopes are the same

If two lines are perpendicular then their slopes are opposite reciprocal

we have

m_a=\frac{1}{3}

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m_d=\frac{1}{3}

therefore

Lines a and b are parallel (slopes are equal)

Lines a and c are perpendicular (slopes are opposite reciprocal)

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