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3 years ago

What is the value of the expression below? (5^1/2)^2

Mathematics

1 answer:

Readme [11.4K]3 years ago

5 0

Answer:

using the laws of exponents,

in this case the exponents or the powers will multiply

and therefore,

the answer is 5^1

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What can you say about the y-values of the two functions f(x)=-5^x +2 and g(x)=-5x^2+2?

Kryger [21]

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B) The maximum y-value of f(x) approaches 2

C) g(x) has the largest possible y-value

Step-by-step explanation:

f(x)=-5^x+2

f(x) is an exponential function.

Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞

Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→

Lim x→ -∞ f(x) = 2

Then the maximun y-value of f(x) approaches 2

g(x)=-5x^2+2

g(x) is a quadratic function. The graph is a parabola

g(x)=ax^2+bx+c

a=-5<0, the parabola opens downward and has a maximum value at

x=-b/(2a)

b=0

c=2

x=-0/2(-5)

x=0/10

x=0

The maximum value is at x=0:

g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2

The maximum value of g(x) is 2

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The a value is the starting value of 100. The b value must be a decimal lower than 1 because it is decreases.

If you substitute in 8 for x, you will see that the output is about 50 (half of 100).

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