An expression is shown 30×8×103 P.s the three is in top of the 10 What is the value of the expression
1 answer:
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The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.
The mass of the particles moving in river is proportional to the sixth power of 2, or
miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship 
, for some constant k.
For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.
So, the key here is proportional. We can set up two proportions and cross multiply.
Cancelling our x's (because we don't need to solve for them), we have
To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.
![\sqrt[6]{y^6} = \sqrt[6]{960}](https://tex.z-dn.net/?f=%20%5Csqrt%5B6%5D%7By%5E6%7D%20%3D%20%20%5Csqrt%5B6%5D%7B960%7D%20)
Using a calculator, we see that![\sqrt[6]{960} = 3.14 \ miles \ per \ hour](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B960%7D%20%3D%203.14%20%5C%20miles%20%5C%20per%20%5C%20hour)
.
The mass of the particles moving in river is proportional to the sixth power of 2, or
For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.
So, the key here is proportional. We can set up two proportions and cross multiply.
Cancelling our x's (because we don't need to solve for them), we have
To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.
Using a calculator, we see that
Answer:
<h2>B. 468</h2>Step-by-step explanation:
We have
If |r| < 1, then the formula of a sum of an infinite geometric sequence is:
Substitute:
Answer:
a. 73; b. 48.9; c. 2; d. 33.8; e. 73
Step-by-step explanation:
Assume the function was
S(t)= 73 - 15 ln(t + 1), t ≥ 0
a. Average score at t = 0
S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73
b. Average score at t = 4
S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9
c. Average score at t =24
S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7
d. Percent of answers retained
At t = 0. the students retained 73 % of the answers.
At t = 24, they retained 24.7 % of the answers.
e. Maximum of the function
The maximum of the function is at t= 0.
Max = 73 %
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