The digit 7 is in the tens place so 74 will become either 70 or 80 after rounding off to the nearest ten. Draw a number line with 3 numbers on it: 70, 75 and 80. (Both possible rounded off numbers and the number in the middle.

3 0

3 years ago

Given the kite below, if NO = 5 and OM = 12, what is the value of NM?

tester [92]

Answer:

NM = 13

Step-by-step explanation:

pythagorean theorem: $a^{2} + b^{2} = c^{2}$

a or NO = 5

b or OM = 12

c or NM = ?

plug in what is known:

⇒ $5^{2} + 12^{2} = c^{2}$

⇒ $25 + 144 = c^{2}$

⇒ 169 = $c^{2}$

square root each side of the equation:

⇒ $\sqrt{169} = \sqrt{c^{2} }$

solve:

⇒ 13 = c

6 0

3 years ago

The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP dt = P(a

LuckyWell [14K]

Answer:

Decreases

Step-by-step explanation:

We need to determine the integral of the DE;

$dP/dt=P(aP-b)$

$dP=P(aP-b)dt$

$1/(dP^2-bP)dP=dt$

We can solve this by integration by parts on the left side. We expand the fraction 1/P²:

$1/(d-b/P)\cdot{P^2} dP$

let

$u=d-b/P$

$du/dP=b/P^2$

$dP=$ $\int\limits {P^2/b} \, du$

$P=lnu/b$

Substitute u in:

$P=ln(d-b/P)/b$

Therefore the equation is:

$ln(d-b/P)/b=t$

We simplify:

$d-b/P=e^b^t$

$P=b/(d-e^b^t)$

As t increases to infinity P will decrease

6 0

3 years ago