Answer: y - 3 = 0.041(x - 27)
Step-by-step explanation:
y = log3 x; (27, 3)
Step 1
Find the point of tangency.
It's given as (27,3)
Step 2
Find the first derivative, and evaluate it at x=27
Differentiating log3 x.
Note we can't directly differentiate log3 x, we need to convert it to natural log = ln.
Using change of base.
Log3 x = lnx/ln3
So,
d(lnx/ln3)/dx = 1/ln3 × 1/x
f'(x) = 1/xln3
f'(27) = 1/27ln3 = 0.041
The slope of the tangent line at this point is m= 0.041
Step 3
Find the equation of the tangent line at (27,3) with a slope of m=0.041
y−y1 = m(x - x1)
y - 3 = 0.041(x - 27)
Answer:
the sum is 24
hope this helps
Step-by-step explanation:
First subtract the constant to the other side to simplify it for now
y-5=-x^2+6x
Then pull out a common factor so the coefficient is x^2
y-5=-1(x^2-6x)
Next you take 1/2 of the b value (-6) and square it to find your c value
[1/2(-6)]^2=9
After that plug 9 into your equation as your c value
y-5=-1(x^2-6x+9)
Adding the C-value (9) causes the equations to become unbalanced so you need to balance them back out by minus 9 to the other side
y-14=-1(x^2-6x+9)
Now you want to simplify the equation on the right side.
y-14=-1(x-3)^2
Finally you want to add the constant back to the right side.
y=-1(x-3)^2+14 <——— vertex form
maximum=(3,14)
Answer: The area of the larger square is 9 times the area of the smaller square.
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
Total consumed = 1/4 + 1/5
= 5/20 + 4/20
= 9/20 of the salad they eat
1 - 9/20
= 11/20 of the salad is left
10/20 is half so more than half the salad is left