Answer:
(-7 ± 
√(-23)) / 4
Step-by-step explanation:
Unless you have to show your work, you don't really have to use the quadratic formula unless it is unfactorable.
2x² + 9 = -7x (Add 7x to both sides)
2x² + 7x + 9 = 0 ( The quadratic formula is (-b ± √(b^2 - 4ac))/2a )
A = 2
B = 7
C = 9
(-7 ± √(49 - 72))/4
= (-7 ± √(-23))/4 (Which simplifies to an imaginary answer, proving that this is, indeed, unfactorable)
= (-7 ± √(-23))/4
The trick here is to use an appropriate substitution. Let u=a^3.
Then du/da=3a^2, and du=3a^2da.
We can now make two key substitutions: In (3a^2)da/(1+a^6), replace 3a^2 by du and a^6 by u^2.
Then we have the integral of du/(1+u^2).
Integrating, we get arctan u + c. Substituting a^3 for u, the final result (the integral in question) is arctan a^3 + c.
Check this by differentiation. if you find the derivative with respect to a of arctan a^3 + c, you MUST obtain the result 3a^2/(1+a^6).
Answer: Reflect Y-Axis & 10 Units Down
Step-by-step explanation:
Answer: 11.1 m
Step-by-step explanation:
This can be solved by the Pythagorean theorem where;
c² = a² + b²
c is the hypotenuse which is the distance from the top of the building to the tip of the shadow.
a is the height
c is the length
32² = 30² + b²
b² = 32² - 30²
b² = 1,024 - 900
b² = 124
b = √124
b = 11.1 m
Simple interest formula
Interest = Pit = $50
P=principal (initial investment)
i=annual interest rate = 0.04
t=time in years = 6 months = 0.5 years
Substitute values,
$50 = P*0.04*0.5
Solve for P
P=$50/(0.04*0.5)=$2500
