Pls help urgently extra points and mark brainlist easy reading

A function is given. Determine the average rate of change of the function between the given values of the variable: f(x)= 4x^2;

nevsk [136]

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------$

$\bf f(x)= 4x^2 \qquad 
\begin{cases}
x_1=3\\
x_2=3+h
\end{cases}\implies \cfrac{f(3+h)-f(3)}{(3+h)~-~(3)}
\\\\\\
\cfrac{[4(3+h)^2]~~-~~[4(3)^2]}{\underline{3}+h-\underline{3}}\implies \cfrac{4(3^2+6h+h^2)~~-~~4(9)}{h}
\\\\\\
\cfrac{4(9+6h+h^2)~~-~~36}{h}\implies \cfrac{\underline{36}+24h+4h^2~~\underline{-~~36}}{h}
\\\\\\
\cfrac{24h+4h^2}{h}\implies \cfrac{\underline{h}(24+4h)}{\underline{h}}\implies 24+4h$

8 0

3 years ago

A scale model of a ramp is a right triangular prism as given in this figure. in the actual ramp, the triangular base has a heigh

kakasveta [241]

The surface area of the actual ramp including the underside is 16.8 ft²

The height of the actual ramp = 1.2 feet

The height of the model = 6 cm

<h3>What is the surface area of a right triangular prism?</h3>

A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.

The surface area of a right triangular prism

= (Perimeter of the base × Length of the prism) + (2 × Base Area)

Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm

Actual base = 16 cm × 0.2 ft/cm = 3.2 ft

convert the units

9 cm = 9 cm × 0.2 ft/cm = 1.8 ft

10 cm = 10 cm × 0.2 ft/cm = 2 ft

The surface area of a right triangular prism

= (Perimeter of the base × Length of the prism) + (2 × Base Area)

Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)

= 16.8 ft²

Hence, the surface area of the actual ramp including the underside is 16.8 ft²