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.
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.
1 answer:
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
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
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Definitions:
1. A real number can be represented on a number line.
2. A rational number can be represented as a fraction, with both the numerator and denominator as integers. The denominator cannot be zero.
3. An irrational number has decimals that go on indefinitely.
4. An integer is a real number that is countable.
5. A repeating decimal has a group of numbers that repeat indefinitely as decimals.
6. A complex number involves the use of the quantity i, defined as i² = -1.
Answers:
a. 7/8
Real, Rational.
b. √36
Real, Rational because its value is +6 or -6.
c. √24
Real, Irrational.
d. 0.75
Real, rational because 0.75 = 3/4.
e. 0
Real, rational
f. √(-100)
Complex, because √(-1) * √100 = +/- i√100
g.
Irrational, Repeating decimal because
h -18/6
Real, Integer, Rational because -18/6 = -3.
1. A real number can be represented on a number line.
2. A rational number can be represented as a fraction, with both the numerator and denominator as integers. The denominator cannot be zero.
3. An irrational number has decimals that go on indefinitely.
4. An integer is a real number that is countable.
5. A repeating decimal has a group of numbers that repeat indefinitely as decimals.
6. A complex number involves the use of the quantity i, defined as i² = -1.
Answers:
a. 7/8
Real, Rational.
b. √36
Real, Rational because its value is +6 or -6.
c. √24
Real, Irrational.
d. 0.75
Real, rational because 0.75 = 3/4.
e. 0
Real, rational
f. √(-100)
Complex, because √(-1) * √100 = +/- i√100
g.
Irrational, Repeating decimal because
h -18/6
Real, Integer, Rational because -18/6 = -3.
