Answer:
3 seconds
Step-by-step explanation:
To find the highest point, we want to find the vertex of the parabola. Since the function will be negative, the vertex will represent the highest point.
To find the vertex we want this equation in vertex form:
y=a(x−h)2+k
and the vertex will be (h,k)
We can expand the equation h(x)=-(x+1)(x-7) to be:
To get the vertex form we need to complete the square.
The vertex form is :
so our vertex is (3,16)
This means the highest point will be 16 when x = 3
Integrate indefinite integral:
Solution:
1. use substitution
=>
=>
=>
=>
2. decompose into partial fractions
where A=1/2, B=1/2, C=-1
3. Substitute partial fractions and continue
4. back-substitute u=e^x
Note: log(x) stands for natural log, and NOT log10(x)
Answer:
y = -2x+4
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
= (-4-2)/(4-1)
= -6/3
= -2
point slope form
y-y1 = m(x-x1)
y-2 = -2(x-1)
distribute
y-2 =-2x +2
add 2 to each side
y-2 +2 =-2x+2+2
y = -2x+4
in slope intercept form
y = -2x+4
Answer:
At a point on the ground 50 feet from the foot of a tree, the angle of elevation to the top of the tree is 53°. Find the height of the tree to the nearest foot.
I got 50xtan53 = 66.35 nearest foot ? would I use tan or sin since I'm finding the foot of the tree
Step-by-step explanation:
.
To get started, we will use the general formula for bacteria growth/decay problems:
where:
A_{f} = Final amount
A_{i} = Initial amount
k = growth rate constant
t = time
For doubling problems, the general formula can be shortened to:
Now, we can use the shortened formula to calculate the growth rate constant of both bacteria:
Colby (1):
per hour
Jaquan (2):
per hour
Using Colby's rate constant, we can use the general formula to calculate for Colby's final amount after 1 day (24 hours).
Note: All units must be constant, so convert day to hours.
Remember that the final amount for both bacteria must be the same after 24 hours. Again, using the general formula, we can calculate the initial amount of bacteria that Jaquan needs:
