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When y=125 and x=-3, what is the value of #root3y-3x^4#?

Answer 1

Abigail Allen

Let #x=-3#
Let #y=125#
#root3(y)-3x^4=#

#-238#

#root3(y) -3x^4#

Let's break this down starting with #y#.

#root3(125) = 5# because #n*n*n = n^3# and #root3(n^3)=n#.

#5^3=125# [how convenient :)]

#root3(125)=5#

Now #x#.

#3(-3)^4#

Recall PEMDAS: Parentheses first, then exponents. You have to take account for that negative.

#-3*-3*-3*-3 = 81#

#81*3=243#

Finally:

#5 - 243 = -238#

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Answer 2

Hazel Anglin

To find the value of ( \sqrt{3y} - 3x^4 ) when ( y = 125 ) and ( x = -3 ), substitute the given values into the expression:

[ \sqrt{3 \cdot 125} - 3 \cdot (-3)^4 ]

[ \sqrt{375} - 3 \cdot 81 ]

[ \sqrt{375} - 243 ]

[ \approx 19.364 - 243 ]

[ \approx -223.636 ]

So, the value of ( \sqrt{3y} - 3x^4 ) when ( y = 125 ) and ( x = -3 ) is approximately -223.636.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.