Answer:
log(32/125)
=log32 - log125 [log(x/y)=log(x) - log(y)]
=log(2)^2 - log(5)^3
=2log2-3log5 [log(x)^p=p log x]
=2a-3b
Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:
Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t
Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0
Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles
So after 70 min's of driving, Dale will be 36.5 miles from his destination.
If Aneesha travels at a rate of
50 miles............................1h
and 1mile=5280ft, therefore 50 miles = 264000 ft
and 1 h =3600 seconds we can say that Aneesha travels
264,000 ft in 3600 seconds or
264,000/3600= 73.33 ft/s
Morris travels 3 ft per second less than her
so 73.33-3=70.33 ft/s for Morris
Answer:
The first option, the mayor will lose by a large percentage.
Step-by-step explanation:
If you look at the numbers, You can see that the two best answers which are excellent and satisfactory are low, and in total equal 28.
Being compared to the lower ratings which are needs improvement and unsatisfactory are high, and in total equal 52.
Seeing this, this shows that the mayor will lose the election the with more than half of the people voting for someone else.
All the other options excluding the first one, say that he will win by a close call, a big percent, or a close call again.
which just leaves the first option saying that he will lose by large percent, which is true.
