Answer:
I don't know if this is absolutely correct but i got 1.35 by dividing 1 2/3 by 2 1/4
Step-by-step explanation:
The proffesional runner can run 50/12 miles or 4 1/6.
To figure this out turn both mixed numbers into improper fractions (denominator x whole number + numerator) and multiply both of the improper fractions ( numerator x numerator denominator x denominator )
Firstly, you've got to expand the brackets, this becomes;
8a-4= -10a+ 50
You've then got to eliminate the -10a and you do this by adding 10a to both sides,
This then becomes 18a-4=50
You've then got to add 4, to eliminate this, which then becomes 18a=54
You've then got to divide both sides by 18, and this becomes 3.
Therefor, a=3
Hope this helps :)
Answer:
The given statement is FALSE.
Step-by-step explanation:
If the original expression is defined for all values of x , then this implies there is no real value of x such that the original expression is not defined.
Hence, the original expression has domain all real values x
Now, the simplified form which is obtained by simplifying the original expression may not have the same domain as the original expression.
So, if original expression is defined on some value of x then it might be possible that the simplified expression may not be defined on that value of x.
So, we need to specify the absolute value in the simplified expression.
Hence the given statement is FALSE.
Answer:
∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)
Step-by-step explanation:
Start with the Maclaurin series for cos x.
cos x = ∑ₙ₌₀°° (-1)ⁿ x²ⁿ / (2n)!
Substitute ⅓ x².
cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓ x²)²ⁿ / (2n)!
cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓)²ⁿ x⁴ⁿ / (2n)!
cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)
Multiply by 8x.
8x cos (⅓ x²) = ∑ₙ₌₀°° 8x (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)
8x cos (⅓ x²) = ∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)
