Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of
its square base. Nathan uses the formula for the volume of a pyramid to determine the dimensions of the sculpture: Here, a is the side length of the pyramid’s square base and h is its height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x3 +
x2 +
= 0 can be used to find that the length of the sculpture’s base is
centimeters.
Let x-----------> <span>the side length of a pyramid square base h-----------> t</span>he height of the sculpture <span>in the shape of a pyramid
we know that h=(x-3) Volume=162 cm</span>³ Volume=x² *(x-3)/3 then x² *(x-3)/3=162----------> x³-3x²=486----------> x³-3x²-486=0 x³-3x²-486=0-------- <span>this equation can be used to find the length of the sculpture’s base
using a graph tool-----------> </span>to find the solution x=9 cm -------------> see the attached figure h=(x-3)-----> h=9-3--------> h=6 cm
the answer is <span>the length of the sculpture’s base is 9 cm </span>the height of the sculpture is 6 cm
Mars orbits the Sun at an average distance (semi-major axis) of 228 million km (141.67 million mi), or 1.524 astronomical units (over one and a half times the distance between Earth and the Sun).