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3 years ago

if the area of a square is 144 feet and the perimeter of the triangle is 28 feet, what is the perimeter of the room's floor?

Mathematics

1 answer:

FinnZ [79.3K]3 years ago

4 0

Answer:

$52+12\pi$

Step-by-step explanation:

The diagram for the question is attached below

perimeter of the triangle is 28 feet

area of a square is 144 feet

Area of the square is side^2

$side ^2= 144$

take square root on both sides

side = 12

side of the square = 12

side is the diameter of the semicircle

Diameter = 12 , so radius = 12 divide 2 = 6

circumference of semicircle = $2\pi r=2\pi (6)=12\pi$

one side of the rectangle is calculated in the perimeter of triangle and other side is calculated using circumference

perimeter of other two side = 2(12)= 24

Total perimeter = $28+24+12\pi =52+12\pi$

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If y= 3x + 6, what is the minimum value of (x^3)(y)?

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Answer:

Given the statement: if y =3x+6.

Find the minimum value of $(x^3)(y)$

Let f(x) = $(x^3)(y)$

Substitute the value of y ;

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Distribute the terms;

$f(x)= 3x^4 + 6x^3$

The derivative value of f(x) with respect to x.

$\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)$

Using $\frac{d}{dx}(x^n) = nx^{n-1}$

we have;

$\frac{df}{dx} =(12x^3+18x^2)$

Set $\frac{df}{dx} = 0$

then;

$(12x^3+18x^2) =0$

$6x^2(2x + 3) = 0$

By zero product property;

$6x^2=0$ and 2x + 3 = 0

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then;

at x = 0

f(0) = 0

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x = -1.5

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3 years ago

Solve:<br><br> a.x3+x2-8x - 12x+2<br> b. x3-4x2-3x + 18x-3<br> c. x2 + 4x + 4<br> d. x2 - 6x + 9

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<h2>Steps:</h2>

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}$

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}$

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

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Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

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Now you can rewrite it as:

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Next, multiply:

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Next, divide:

$(\frac{f}{g})(x)=(x+2)^2$

And lastly, simplify:

A good tip: $(x+y)^2=x^2+2xy+y^2$

$(\frac{f}{g})(x)=x^2+4x+4$

<h2>Answer:</h2>

<u>The correct option is C. x² + 4x + 4.</u>

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