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3 years ago

the length of a rectangle is four times its width. the rectangle has an area of 1024cm^2 work out the width of the rectangle

Mathematics

2 answers:

olga2289 [7]3 years ago

7 0

The width is 16 so the length is 64 (TO clarify W=16)

Hope this helps :)

Papessa [141]3 years ago

6 0

Answer:

Area of a rectangle is given by:

$A = lw$ ....[1]

where

l is the length

w is the width of the rectangle respectively.

As per the statement:

the length of a rectangle is four times its width.

⇒ $l = 4w$

It is also given that: area of rectangle is 1024 cm square

Substitute the given values in [1] we have;

$1024=(4w)w$

⇒ $1024=4w^2$

Divide both sides by 4 we have;

$256 = w^2$

$w^2 =256$

Taking square root both sides we have;

$w = \sqrt{256} = 16$ cm

Therefore, the width of the rectangle is, 16 cm

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The least common factor of 8 and 56, 12 and 30, 16 and 24, and 9 and 15

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The lcf of 8 and 56 is 2, the lcf of 12 and 30 is 2, the lcf of 16 and 24 is 2, and the lcf of 9 and 15 is 3.

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3 years ago

Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

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PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

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$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
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$a=1,b=-4,c=0$

This is the standard form

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3 years ago

How does h

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Answer:

h(t) = 16t changes 16 units every t. in the interval t=7 to t=2,

if its asking for:

$\int\limits^2_7 {16t} \, dt$