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3 years ago

Question 1

Mathematics

1 answer:

Alexxx [7]3 years ago

8 0

Answer:

Water needed for pool = 486 cubic feet

Plastic liner required for the pool = 298.3 feet

Step-by-step explanation:

Top view of the pool is a composite figure, having one rectangle and a trapezoid.

1). Water needed for the pool = volume of the pool

Volume of the pool = Area of the base × Depth

= (Area of the rectangle + Area of the trapezoid)× depth

Area of the trapezoid = $\frac{1}{2}(b_{1}+b_{2})\times h$

= $\frac{1}{2}(11+9)\times (12-1.5)$

= 105 ft²

Area of the rectangle = Length × width

= 11 × 1.5

= 16.5 ft²

Now, volume of the pool = (105 + 16.5) × 4

= 121.5 × 4

= 486 cubic feet

b). Liner required = surface area of the pool excluding top

= Surface area of the walls + Area of the pool base

= (Perimeter of the pool) × depth + area of the base

= (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5

= 176.8 + 121.5

= 298.3 square feet

Therefore, amount of water required = 486 cubic feet

liner needed = 298.3 square feet

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. Given ????(5, −4) and T(−8,12):

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b) $y = \dfrac{13x}{16}+ \dfrac{37}{2}$

Step-by-step explanation:

Given two points: $S(5,-4)$ and $T(-8,12)$

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: $y = mx + c$ where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST we first need to find the gradient of ST, using the gradient formula.

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

$m = \dfrac{12 - (-4)}{(-8) - 5}$

$m = \dfrac{-16}{13}$

to find the perpendicular of this gradient: we'll use:

$m_1m_2=-1$

both $m_1$ and $m_2$ denote slopes that are perpendicular to each other. So if $m_1 = \dfrac{12 - (-4)}{(-8) - 5}$ , then we can solve for $m_2$ for the slop of ther perpendicular!

$\left(\dfrac{-16}{13}\right)m_2=-1$

$m_2=\dfrac{13}{16}$ :: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope $m$ and the points $(x,y)$ . And plug into the equation: $(y - y_1) = m(x-x_1)$

side note: you can also use the $y = mx + c$ to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

$(y - y_1) = m(x-x_1)$

we have the slope of the perpendicular to ST i.e $m=\dfrac{13}{16}$