Find the volume of the darkly shaded region
1 answer:
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Step-by-step explanation:
To write the equation in LaTeX in form y = ab^x or for y = abx .........(1)
(a) LaTeX: y=3\sqrt{4^{2x}} y = 3 4 2 x can be written in mathematical form as
; y = 342x
on comparing with equation (1) we get a =3 and b =4
⇒y = 34^x or
(b) LaTeX: y=\frac{\sqrt[3]{5^{3x}}}{2} y = 5 3 x 3 2 can be written in mathematical form as
; y = 342x
on comparing with equation (1) we get a =0.5 and b =5
⇒y =
(c)LaTeX: y=8^{x+2} y = 8 x + 2 can be written in mathematical form as
on comparing with equation (1) we get a =64 and b =8
y =
(d)LaTeX: y=\frac{3^{2x+1}}{\sqrt{3^{2x}}} can be written in mathematical form as
=
=
on comparing with equation (1) we get a =3 and b =3
y =
Answer: 10 ft
Explanation
As two right triangles (a triangle with a 90º angle) are formed, to know the distance between AB we have to calculate BC, AC and subtract.
0. Calculating BC
We have a 30º angle and an adjacent side 5√3ft (as the hypotenuse is the side opposite to the 90º angle). Thus, using the tangent function where:
we can find the opposite side, which is BC. Replacing the values and simplifying we get:
Thus, the segment BC measures 5ft.
<em>2. Calculating segment AC</em>.
In this case, our hypotenuse changes. However, we are still looking for the opposite side. Using the tangent function as before we get:
<em>3. Calculating the distance between A and B</em>