Answer:
24 mph for both 60 miles and 40 miles.
Step-by-step explanation:
We need to find how long it takes to get to college and from it.
Speed x time (x) = Distance (60)
30x = 60
x=2
It takes two hours to get to college
20x = 60
x = 3
It takes 3 hours to get back. It's a total of 5 hours, 2 hours at 30mph and 3 at 20. Now we need to find the average
30+30+20+20+20=120
120/5= 24
The average speed for the round trip is 24.
To do the second part, we follow the same process, but replace 60 with 40 for distance.
30x=40
x= 1.33
20x=40
x=2
We can add the total distance and divide by total time to find the average.
The total distance is 80. Time is 3.33
80/3.33=24
The average speed is still 24.
Answer:
BDE- 85
EDG- 50
FDG- 60
CDA- 85
Step-by-step explanation:
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
No, Vijay cannot fit all cubes into the box.
Solution:
Total number of cubes = 50
Volume of each cube = 1 cubic inch
Number of cubes fit in the bottom of the box = 12
Area of the box<em> = l</em> × <em>b</em> = 12 square inch
Height of the box = 4 inch
Volume of the box = <em> l</em> × <em>b </em>× h
= 12 × 4
Volume of the box = 48 cubic inch
So, 48 cubes can only fit in the box.
Hence, Vijay cannot fit 50 cubes into the box.
Division Problem: 90 people were invited to the party.
1. How many tables are needed, if each table can seat 8 people?
2. How many tables will be completely full?
3. How many people will be at an incomplete table?
Solution:
You have that 90=8·11+2 (8 - divisor, 11 - quotient, 2 - remainder).
Since the quotient is 11, 12 tables are needed, 11 tables will be completely full and the last 12th table will be incomplete, only 2 people will be at this table.
Answer: 1. 12 tables, 2. 11 tables, 3. 2 people
