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2 years ago

1. A wooden box is to be built so that it measures 156 cm by 122 cm by 95 cm.

1 answer:

7 0

The amount of plywood needed to build the garbage bin is the surface area. Therefore, the amount of plywood needed is 90884 cm².

<h3>How to find the surface area of a rectangular prism</h3>

The wooden box is a rectangular prism. The amount of plywood used to construct the wooden box is the surface area of the box.

Therefore,

surface area of rectangular prism = 2(lw + lh + hw)

where

l = length
w = width
h = height

l = 156 cm

w = 122 cm

h = 95 cm

surface area of rectangular prism = 2((156 × 122) + (156 × 95) + (122 × 95))

surface area of rectangular prism = 2(19032 + 14820 + 11590)

surface area of rectangular prism = 2(45442)

surface area of rectangular prism = 90884 cm²

learn more on surface area here:brainly.com/question/27161212

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Find the limit (enter 'DNE' if the limit does not exist)

vaieri [72.5K]

Answer:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)=2$

Step-by-step explanation:

We need to first simplify the expression using rationalization(i.e. if a square root term exists in the denominator, then multiply and divide the whole expression by the denominator(but the change the sign of its middle term))

here, we need to find:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\right)$

first we'll rationalize our expression:

$\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\left(\dfrac{\sqrt{-2x^2-6y^2+1}+1}{\sqrt{-2x^2-6y^2+1}+1}\right)$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{(\sqrt{-2x^2-6y^2+1}+1)^2-(1)^2}$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-2x^2-6y^2+1-1}$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-(2x^2+6y^2)}$

$\sqrt{-2x^2-6y^2+1}+1$

this is our simplified expression, now we can apply our limits:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)$

$\sqrt{-2(0)^2-6(0)^2+1}+1$

$1+1$

$2$

the limit does exists and it is 2.

5 0

3 years ago

Simplify 5x(3x^2+2x-3)

Tcecarenko [31]

Answer:

$15x^3 +10x^2 - 15x$

Step-by-step explanation:

Hello!

Use the distributive property and multiply like terms.

<h3>Simplify</h3>

$5x(3x^2 + 3x - 3)$
$5x(3x^2) + 5x(2x) + 5x(-3)$
$15x^3 +10x^2 - 15x$

The simplified form is $15x^3 +10x^2 - 15x$ .

4 0

1 year ago

Read 2 more answers

Drina wrote the system of linear equations below.

zalisa [80]

Answer:

Option c, A square matrix

Step-by-step explanation:

Given system of linear equations are

$3x-2y=-2\hfill(1)$

$7x+3y=26\hfill(2)$

$-x-11y=46\hfill(3)$

Now to find the type of matrix can be formed by using this system

of equations

From the given system of linear equations we can form a matrix

Let A be a matrix

A matrix can be written by

A=co-efficient of x of 1st linear equation co-efficient of y of 1st linear equation constant of 1st terms linear equation

co-efficient of x of 2st linear equation co-efficient of y of 2st linear equation constant of 2st terms linear equation

co-efficient of x of 3st linear equation co-efficient of y of 3st linear equation constant of 3st terms linear equation $3\times 3$

which is a $3\times 3$ matrix.

Therefore A can be written as

A= $\left[\begin{array}{lll}3&-2&-2\\7&3&26\\-1&-11&46\end{array}\right] 3\times 3$

Matrix "A" is a $3\times3$ matrix so that it has 3 rows and 3 columns

A square matrix has equal rows and equal columns

Since matrix "A" has equal rows and columns Therefore it must be a square matrix

Therefore the given system of linear equation forms a square matrix

7 0

3 years ago

Read 2 more answers

A mother has two children whose ages differ by 5 years. The sum of the squares of their ages is 97. The square of the mother's

svetoff [14.1K]

Answer:

41 years old.

Step-by-step explanation:

Let x represent age of younger child.

We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be $x+5$ .

The sum of the squares of their ages is 97. We can represent this information in an equation as:

$x^2+(x+5)^2=97$

Let us solve for x.

$x^2+x^2+10x+25=97$

$2x^2+10x+25-97=0$

$2x^2+10x-72=0$

Divide both sides by 2:

$x^2+5x-36=0$

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x+9)(x-4)=0$

$(x+9)=0 ; (x-4)=0$

$x=-9 ; x=4$

Since age cannot be negative, therefore, age of younger child is 4 years.

Age of older child would be $x+5\Rightarrow4+5=9$

Therefore, the age of older child would be 9 years.

We have been given that the square of the mother's age can be found by writing the squares of the children's ages one after the other as a four-digit number.

Square of 4: $4^2=16$