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sleet_krkn [62]

3 years ago

8

Smith cell phone company advertises device for 3 cents per minute plus a monthly fee of $29.95. If sara's phone bill for october

was $38.95, find the number of minutes she used

1 answer:

hjlf3 years ago

6 0

$38.95-$29.95= $9
$9= 900¢
900¢/3¢= 300
Ans: She used 300 minutes.

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a box of cereal weighs 550 g. There is enough cereal for 10 servings. How many grams of cereal are there per serving?

prisoha [69]

Answer:

55 grams per serving

Step-by-step explanation:

To find the number of grams per serving, we take to total grams and divide by the number of servings. The total grams is 550 and the number of servings is 10

grams per servings = 550/10 = 55 grams per serving

7 0

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A new iPhone 13 is on sale for $999. You get a 10% discount for being a student. But, you are buying the phone at the Apple Stor

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3 0

3 years ago

21 less than tree-fifths of a number

MissTica

Answer:

$\frac{3}{5}x - 21$

Step-by-step explanation

Three-fifths of a number means $\frac{3}{5}x$ and 21 less than that number means $\frac{3}{5} x - 21$ .

3 0

3 years ago

Which value of x is in the solution set of the following inequality. -3x +5 >7

Vadim26 [7]

I’m not sure if this was a typo, but A and B are the same answer. A and B are correct, because when you solve this the answer has to be anything less than -0.6.

8 0

3 years ago

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago