Answer: See explanation
Step-by-step explanation:
a. how old is Cheryl?
Cheryl's age = d + 5
b. how old is Brandon?
d + 5 + 2
= d + 7
c. what was the difference in their ages 5 years ago?
Cheryl age five years ago = d
Brandon's age five years ago = d + 2
Difference = d + 2 - d = 2 years
d. what is the sum of their ages now?
Cheryl's age = d + 5
Brandon age = d + 7
Sum = d + 5 + d + 7
= 2d + 12
e. what will the sum of their ages be two years from now?
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Sum = d + 7 + d + 9
= 2d + 16
f. what will the difference of their ages be two years from now
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Difference = Brandon age - Cheryl age
= (d + 9) - (d + 7)
= 2 years.
Answer:

Step-by-step explanation:
Given:

Solving for
:

Hi there!

We are given:
cos(7x)cos(4x) = -1 - sin(7x)sin(4x)
Begin by moving all terms with variables to one side:
cos(7x)cos(4x) + sin(7x)sin(4x) = -1
The corresponding trig identity is cos(A - B). Thus:
cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1
cos(3x) = -1
cos = -1 at π, so:
3x = π
x = π/3
We can also find another solution. Let 3π = -1:
3x = 3π
x = π
Thus, solutions on [0, 2π) are π/3 and π.
In this case, we cannot simply take the average speed by
adding the two speeds and divide by two.
What we have to do is to calculate the time required
going to school and the return trip home.
We know that to calculate time, we use the formula:
t = d / v
where,
d = distance = 4.8 km = 4800 m
v = velocity
Let us say that the variables related to the trip going
to school is associated with 1, and the return trip home is 2. So,
t1 = 4800 m / (22.6 m / s)
t1 = 212.39 s
t2 = 4800 / (16.8 m / s)
t2 = 285.71 s
total time, t = t1 + t2
t = 498.1 s
Therefore the total average velocity is:
= (4800 m + 4800 m) / 498.1 s
= 19.27 m / s = 19.3 m / s
Answer:
19.3 m/s