Choose the best unit of measure to find the capacity of a swimming pool.

Using the Principle of Mathematical Induction, prove that . n ^2 − n is even for n ≥ 1

Tamiku [17]

Base case: if n = 1, then

1² - 1 = 0

which is even.

Induction hypothesis: assume the statement is true for n = k, namely that k ² - k is even. This means that k ² - k = 2m for some integer m.

Induction step: show that the assumption implies (k + 1)² - (k + 1) is also even. We have

(k + 1)² - (k + 1) = k ² + 2k + 1 - k - 1

… = (k ² - k) + 2k

… = 2m + 2k

… = 2 (m + k)

which is clearly even. QED

8 0

3 years ago

The discriminate of a quadratic is given as b² - 4ac is equal to 0. Select the best description below.

zzz [600]

Answer:

2) the quadratic has one x intercept

Step-by-step explanation:

D = 0 => has twin quadratics as one x intercept

8 0

2 years ago

Guys can you do this i want to spend time with my brother just do 4 and 5

nirvana33 [79]

Cristiano Ronaldo 'instructs agent to seal transfer' amid Man Utd and Real Madrid links

6 0

3 years ago

Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the

Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

$y=Ce^{kt}$ . We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is $\frac{dy}{dt}$ . Thus, the change in the concentration of salt is found in

$\frac{dy}{dt}=$ inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

$3(\frac{y}{400})$