Answer:
0.32km
Step-by-step explanation:
The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.
This is written mathematically as:
S = 356√d
What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?
S = 200km/hr
Hence:
200km/hr = 356√d
Divide both sides by 356
200/356 = 356√d/356
√d = 200/356
Square both sides
(√d)² = (200/356)²
d =(0.5617977528)²
d = 0.3156167151km
Approximately = 0.32km
So, if Dylan has x dollars and he bought 3 tickets with them, the tickets were priced at k dollars per ticket. If he bought 5 tickets with the x dollars and saved 12 total dollars, it would be the same as buying the tickets with x-12 dollars, so we have:
So, with this we have:
If we're looking for a number that satisfies these constraints, we can work with modular arithmetic. We have:
So, we can use the chinese remainder theorem here. So, we clearly have x=3k, which means:
So, since we have x=3k, we also have x=3(5j+4)=15j+12.
So, clearly j=0 won't work so we should have j=1. That means our money per ticket for the five tickets is:
And our money per three tickets is:
This is easily verifiable. Three tickets needs 27 dollars and 5 tickets needs 15 dollars, which is 12 less than 27 dollars. So we have our money per three dollar ticket at 6 more than money per five dollar.
Patterns can be used to determine products of a number of a power of 10 by following it to obtain easily the answer. When you multiply a number by the power of 10 you just have to write the number then add the number of corresponding number of 0s to the end which will be the same number as the power used.
Hope this helped : )
Answer:
He burnt 1000 calories per hour when playing basketball.
Step-by-step explanation:
Let B be calories burned playing basketball, and C calories burned canoing.
1800 = B + 2C
3200 = 2B + 3C
From 1st equatipn, we get that B = 1800 - 2C
Replacing into the 2nd equation, we have:
3200 = 2(1800-2C) + 3C
3200 = 3600 - 4C + 3C
3200 = 3600 - 1C
C = 3600 - 3200
C = 400
Knowing C, we find B.
B = 1800 - 2C = 1800 - 2*400 = 1800 - 800 = 1000 calories.
Answer:
3. Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over the course of
2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind
by 4 points. All other times, the two teams were tied.
(a) What is the average score of Adrian’s favorite team relative to its opponent using the observations
Adrian made during the game? Show your work neatly.
(b) Explain what this value means about Adrian’s favorite team’s performance
Step-by-step explanation:
