Algebra
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Matrix
Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(t)=−105125t
Evaluate
y=−16t2×10t3×5
Simplify
More Steps
Evaluate
−16t2×10t3×5
Multiply the terms
More Steps
Evaluate
16×10×5
Multiply the terms
160×5
Multiply the numbers
800
−800t2×t3
Multiply the terms with the same base by adding their exponents
−800t2+3
Add the numbers
−800t5
y=−800t5
Interchange t and y
t=−800y5
Swap the sides of the equation
−800y5=t
Change the signs on both sides of the equation
800y5=−t
Divide both sides
800800y5=800−t
Divide the numbers
y5=800−t
Use b−a=−ba=−ba to rewrite the fraction
y5=−800t
Take the 5-th root on both sides of the equation
5y5=5−800t
Calculate
y=5−800t
Simplify the root
More Steps
Evaluate
5−800t
To take a root of a fraction,take the root of the numerator and denominator separately
58005−t
Simplify the radical expression
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Evaluate
5800
Write the expression as a product where the root of one of the factors can be evaluated
532×25
Write the number in exponential form with the base of 2
525×25
The root of a product is equal to the product of the roots of each factor
525×525
Reduce the index of the radical and exponent with 5
2525
25255−t
Multiply by the Conjugate
2525×52545−t×5254
Calculate
2×525−t×5254
Calculate
More Steps
Evaluate
5−t×5254
The product of roots with the same index is equal to the root of the product
5−t×254
Calculate the product
5−254t
An odd root of a negative radicand is always a negative
−5254t
Simplify the radical expression
−55125t
2×52−55125t
Calculate
50−55125t
Divide the terms
More Steps
Evaluate
50−5
Cancel out the common factor 5
10−1
Use b−a=−ba=−ba to rewrite the fraction
−101
10−5125t
Calculate
−105125t
y=−105125t
Solution
f−1(t)=−105125t
Show Solution
Solve the equation
Solve for t
Solve for y
t=−105125y
Evaluate
y=−16t2×10t3×5
Simplify
More Steps
Evaluate
−16t2×10t3×5
Multiply the terms
More Steps
Evaluate
16×10×5
Multiply the terms
160×5
Multiply the numbers
800
−800t2×t3
Multiply the terms with the same base by adding their exponents
−800t2+3
Add the numbers
−800t5
y=−800t5
Swap the sides of the equation
−800t5=y
Change the signs on both sides of the equation
800t5=−y
Divide both sides
800800t5=800−y
Divide the numbers
t5=800−y
Use b−a=−ba=−ba to rewrite the fraction
t5=−800y
Take the 5-th root on both sides of the equation
5t5=5−800y
Calculate
t=5−800y
Solution
More Steps
Evaluate
5−800y
To take a root of a fraction,take the root of the numerator and denominator separately
58005−y
Simplify the radical expression
More Steps
Evaluate
5800
Write the expression as a product where the root of one of the factors can be evaluated
532×25
Write the number in exponential form with the base of 2
525×25
The root of a product is equal to the product of the roots of each factor
525×525
Reduce the index of the radical and exponent with 5
2525
25255−y
Multiply by the Conjugate
2525×52545−y×5254
Calculate
2×525−y×5254
Calculate
More Steps
Evaluate
5−y×5254
The product of roots with the same index is equal to the root of the product
5−y×254
Calculate the product
5−254y
An odd root of a negative radicand is always a negative
−5254y
Simplify the radical expression
−55125y
2×52−55125y
Calculate
50−55125y
Divide the terms
More Steps
Evaluate
50−5
Cancel out the common factor 5
10−1
Use b−a=−ba=−ba to rewrite the fraction
−101
10−5125y
Calculate
−105125y
t=−105125y
Show Solution
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