The Oakland Avenue is approximately what the time you think is it now though you have 120 days to
Answer:
d. None of the above.
Step-by-step explanation:
The period is the change in x required to make a change of 2π in the argument to the sine function:
2x = 2π
x = π
The frequency is the reciprocal of the period, so is 1/π. There are no matching answer choices.
Step-by-step explanation:
Area of the square = a²
= 20²
= 400cm²
Area of the circle = πr²
= 22/7 × 9²
= 22/7 × 81
= 254.57cm²
Area of the shaded region = Area of the square - Area of the circle
= 400cm² - 254.57cm²
= 145.43cm²
This is a tricky question to answer without diagrams and there are useful videos online. A regular triangular prism has an equilateral triangle as its base with edge length 7cm, forming a prism with a total height of 11cm. We wish to calculate the area of the 3 equal triangular faces.
The formula for area of a triangle is 0.5 x base x height. We have the base (7cm) but the problem is we do not have the height (or slant length) of the lateral faces, we only have the height of the entire prism. We must first calculate the slant length by building a triangle inside the prism which goes from the centroid of the base (the inradius) to the centre of an edge. As the base is an equilateral triangle finding the inradius is much more difficult than for a square pyramid.
inradius = 1/6 x (SQRT of 3) x length
inradius = 1/6 x (SQRT of 3) x 7cm = 2cm
We now have a right angle triangle with base = inradius, height = height of prism, and hypotenuse = slant length we need.
Use pythag to calculate hypotenuse a^2 + b^2 = c^2
2^2 + 11^2 = c^2
4 + 121 = c^2
c= SQRT(125) = 11.18cm
We now have the missing slant length or height of the lateral triangles of the prism. We can find the area of one face and multiply it by 3 to get the total surface area of the lateral faces of the pyramid.
base = 7cm
height = 11.18cm
area of triangle = 0.5 x 7 x 11.18 = 39.13cm^2
Multiply this area by 3 to get the sum of all 3 lateral triangle surface areas, total area = 117.39cm^2