Make a graph on f(x)=−3/2(x+1)(x−5)

Mathematics

1 answer:

Murrr4er [49]3 years ago

8 0

Answer:

explanation below

Step-by-step explanation:

f(x) = −3/2(x+1)(x−5) = -3/2 (x²-4x-5) = -3/2 (x²-4x+4-9) = -3/2 ((x-2)² - 9)

f(x) = -3/2 (x-2)² + (-3/2)*(-9) = -3/2 (x-2)² + 13.5

There are points to be referenced for the graph:

vertex (2 , 13.5) axis of symmetry: x = 2

roots: (-1 , 0) (5 , 0)

-3/2 : curve downward

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6) the circular base of a hemisphere of radius 2 rests on the base of a square pyramid of height 6. the hemisphere is tangent to

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The length of the square base is thus $2 x 3\sqrt{2}/2 = 3\sqrt{2}$ = A

<h3>What is hemisphere?</h3>

Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.

EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.

Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.

OM/2 = 6/EP

OM = 6/EP x 2

OM = $6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}$