Ask question

Ask question

All categories

3 years ago

5

In the continental United States, The ratio of states border an ocean to states that do not border an ocean is 7:9. How many of

the states border an ocean?

1 answer:

luda_lava [24]3 years ago

7 0

The answer is 7 because the first part of the ratio says amount of states that border an ocean.

You might be interested in

Please help<br> 4(x+8)+2=1/2(8x+60)

user100 [1]

Answer:

This is a contradiction

7 0

2 years ago

A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

$\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}$

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for <em>S</em>.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for <em>C</em> :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick <em>P</em> such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

5 0

3 years ago

Find the nth term of this sequence, 3, 6, 9, 12

miss Akunina [59]

Answer:

$\large\boxed{\sf n^{th} \ term =3n}}$

Step-by-step explanation:

Find common difference from subtracting any term in the sequence with the previous term.

$\large{\sf 6-3}=3$

Apply nth term formula.

$\large{\sf a_n=a_1+(n-1)d$

$\large{\sf d=3 \ \ a_1=3}$

$\large{\sf a_n=3+(n-1)3$

$\large{\sf a_n=3+3n-3$

$\large{\sf a_n=3n}$

3 0

3 years ago

Read 2 more answers

For which of the following increasing functions f does (f-1)'(20) = 1/5

aalyn [17]

Answer:

D f(x)= e^x+ 5x + 19

Step-by-step explanation:

D f(x)= e^x+ 5x + 19

5 0

3 years ago

Consider the conditional statement: "If I skip dinner, then I won't sleep well tonight."

STALIN [3.7K]

Answer:

I won't sleep well tonight, if l skip dinner.

8 0

3 years ago

Read 2 more answers