![kimjooin02](/avatars/11074.jpg)
kimjooin02
02.09.2021 •
Mathematics
A high school basketball game between the Raiders and the Wildcats was tied at the end of the first quarter. The number of points scored by the Raiders in each of the four quarters formed an increasing geometric sequence, and the number of points scored by the Wildcats in each of the four quarters formed an increasing arithmetic sequence. At the end of the fourth quarter, the Raiders had won by one point. Neither team scored more than 100 points. What was the total number of points scored by the two teams in the first half
Solved
Show answers
More tips
- H Health and Medicine Get Rid of Warts: Simple and Effective Ways...
- S Style and Beauty How to Choose the Perfect Hair Color?...
- C Computers and Internet Best iPad Games: Our Opinion...
- A Animals and plants Man s Best Friend: Which Dog Breed Is the Most Friendly?...
- H Health and Medicine 10 Simple Techniques on How to Boost Your Mood...
- G Goods and services How to Choose the Right High Chair for Your Baby?...
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
- S Style and Beauty How to braid friendship bracelets?...
Answers on questions: Mathematics
- M Mathematics The area of a square garden is 1/49 km cubed. How long is each side?...
- B Biology What happen to the energy that was not passed on to the next tropic asap...
- M Mathematics The volume of a cube is determined by the formula V=s^3 where s is the length of one side. Find the inverse formula. Use it to find the side length of a cube with a...
- G Geography Which of the following countries has a marine west coast climate? italy, portugal, ireland, or greece...
Ответ:
5 and 14.
Step-by-step explanation:
We know that the Raiders and Wildcats both scored the same number of points in the first quarter so let a,a+d,a+2d,a+3d be the quarterly scores for the Wildcats. The sum of the Raiders scores is a(1+r+r^{2}+r^{3}) and the sum of the Wildcats scores is 4a+6d. Now we can narrow our search for the values of a,d, and r. Because points are always measured in positive integers, we can conclude that a and d are positive integers. We can also conclude that $r$ is a positive integer by writing down the equation:
a(1+r+r^{2}+r^{3})=4a+6d+1
Now we can start trying out some values of r. We try r=2, which gives
15a=4a+6d+1
11a=6d+1
We need the smallest multiple of 11 (to satisfy the <100 condition) that is 1 (mod 6). We see that this is 55, and therefore a=5 and d=9.
So the Raiders' first two scores were 5 and 10 and the Wildcats' first two scores were 5 and 14.
Ответ:
Step-by-step explanation: you will need
240^2 / 2(70*40 + 70*50 + 40*50) = 3.46 sheets