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BaLLatris [955]
3 years ago
12

You have an aquarium in the shape of a rectangular prism. The base is 4 feet by 3 feet. The height is 2 feet. How many square fe

et of glass were used to build the aquarium? (The top of the aquarium is open.)
Mathematics
1 answer:
fiasKO [112]3 years ago
6 0
Since it is about only the outer part of the aquarium which is made of glasses we need to calculate the total surface area.

Surface area of the base = 4*3 = 12 square feet

Surface area of the shorter length of wall = 3*2 = 6 square feet
since it has another wall in opposite side. It has to be multiplied with 2.
6*2 = 12 square feet

Surface area of the longer length of wall = 4*2 = 8 square feet
since it has another wall in opposite side. It has to be multiplied with 2.
8*2 = 16 square feet

Therefore the total surface area that need to be covered with glasses
12+12+16 = 40 square feet

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A table can be represented with a linear function equation as y = mx + b, where m is the slope and b is the y-intercept.

<h3>How to Represent a Table with Linear Function?</h3>

Assuming we have a table of values as shown in the image attached below, to write an equation of linear function for the table, do the following:

Pick two pairs of values, say, (1, 5) and (2, 25) and find the slope (m):

Slope (m) = change in y / change in x = (25 - 5)/(2 - 1)

Slope (m) = 20

Find the y-intercept (b) by substituting (x, y) = (1, 5) and m = 20 into y = mx + b:

5 = 20(1) + b

5 = 20 + b

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-15 = b

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Write the equation of the linear function by substituting m = 20 and b = -15 into y = mx + b:

y = 20x - 15

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a. There are 0 or 2 real positive roots for the equation and

b. There are 0 or 2 real negative roots for the equation.

<h3>What is the Descartes'rule of sign?</h3>

Descartes' rule of sign states that

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  • The number of real negative zero of a polynomial f(x) is the number of sign changes of the coefficients of f(-x) or an even number less than the number of sign changes of the coefficients of f(-x)

<h3>How to find the number of possible positive and negative roots are there for the equation?</h3>

Given the equation 0 = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1, writing it as a polynomial function, we have f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

<h3>a. The number of positive roots</h3>

So, to find the number of positive roots, we find the number of sign changes of the polynomial f(x).

So, f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, -2, + 8, -4, -1, there are two sign changes from -2 to + 8 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real positive roots.

So, there are 0 or 2 real positive roots for the equation.

<h3>b. The number of negative roots</h3>

So, to find the number of negative roots, we find the number of sign changes of the polynomial f(-x).

So, f(-x) = −8(-x)¹⁰ − 2(-x)⁷ + 8(-x)⁴ − 4(-x)² − 1

= −8x¹⁰ + 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, +2, + 8, -4, -1, there are two sign changes from -8 to + 2 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real negative roots.

So, there are 0 or 2 real negative roots for the equation.

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