Radical Functions Assignment help

Please complete the following questions. It is important that youshow all work you did to solve the problems when you submit your work.This includes any calculations, diagrams, or graphs that helped yousolve it.

Writing in Math Refer to the informationon page 435 to explain how rational exponents can be applied toastronomy. Explain how to write the formula in radical form and simplify it.Writing in Math Refer to the informationon page 442 to describe how the cost and the number of unitsmanufactured are related. Rewrite the manufacturing equation C = 10n2/3+ 1500 as a radical equation, and write a step-by-step explanation ofhow to determine the maximum number of chips the company could make for$10,000. Ideas
te pressions
rational
onents in radical
n and vice versa.
plify expressions
ponential or
cal form
Astronomers refer to the space
around a planet where the planet’s
gravity is stronger than the Sun’s as
the sphere of influence of the planet.
The radius r of the sphere of
influence is given by the formula
M,13
r=D
where M, is the mass
of the planet, M is the mass of the
Sun, and D is the distance between the planet and the Sun.
Ms
Page
435
Rational Exponents and Radicals You know that squaring a numbe
and taking the square root of a number are inverse operations. But how
would you evaluate an expression that contains a fractional exponent
such as the one above? You can investigate such an expression by
assuming that fractional exponents behave as integral exponents.
1
– 52.62 Write the square as multiplication.
Add the exponents
= blor b Simplity
Thus, b is a number whose square equals b. So b2 = Vo.
deas
quations
ng radicals
equalities
ng radicals
Computer chips are made from the element silicon, which is found in
sand. Suppose a company that manufactures computer chips uses the
formula C = 10m
+ 1500 to estimate the cost C in dollars of
producing n chips. This can be rewritten as a radical equation.
cabulary
ation
solution
quality
Solve Radical Equations Equations with radicals that have variables in
the radicands are called radical equations. To solve this type of equation,
raise each side of the equation to a power equal to the index of the
radical to eliminate the radical.
It is very important that you check your solution. Sometimes you will
obtain a number that does not satisfy the original equation. Such a
number is called an extraneous solution.
Page
EXAMPLE Solve Radical Equations
Solve each equation.
a. Vx+1 +2 = 4
VX+1 +2 = 4 Original equation
VX + 1 = 2 Subtract 2 from each side to isolate the radical.
(Vx + 1) = 22 Square each side to eliminate the radical.
x + 1 = 4
Find the squares
Subtract from each side.
4142
= 3