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3 years ago

Match the pairs of equivalent expressions.

Mathematics

2 answers:

Troyanec [42]3 years ago

5 0

Answer:

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Karo-lina-s [1.5K]3 years ago

3 0

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Can someone helllllppp me on 5 more problems like this n I’ll give u 20 dollars in cashapp plzzz I’m being serious

Vlada [557]

Answer:

y = x - 5

Step-by-step explanation:

$\rm Solve \: for \: y: \\ \rm \longrightarrow x - y= 5 \\ \\ \rm Subtract \: x \: from \: both \: sides: \\ \rm \longrightarrow x - y - x = 5 - x \\ \\ \rm \longrightarrow -y = 5 - x \\ \\ \rm Multiply \: both \: sides \: by \: -1: \\ \rm \longrightarrow - y \times ( - 1) = (5 - x) \times ( - 1) \\ \\ \rm \longrightarrow y = x - 5$

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3 years ago

Convert 5.3575 miles into kilometers

evablogger [386]

8.62206048 kilometers

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3 years ago

Read 2 more answers

A tank contains 180 gallons of water and 15 oz of salt. water containing a salt concentration of 17(1+15sint) oz/gal flows into

Stels [109]

Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

$\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}$

and flows out at a rate of

$\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}$

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

$\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))$

Multiply both sides by the integrating factor, $e^{t/180}$ , and rewrite the left side as the derivative of a product.

$e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))$

$\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))$

Integrate both sides with respect to t (integrate the right side by parts):

$\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt$

$\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C$

Solve for A(t) :

$\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}$

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

$\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}$

So,

$\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}$

Recall the angle-sum identity for cosine:

$R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)$

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

$R \cos(\theta) = -\dfrac{66,096,000}{32,401}$

$R \sin(\theta) = \dfrac{367,200}{32,401}$

Recall the Pythagorean identity and definition of tangent,

$\cos^2(x) + \sin^2(x) = 1$

$\tan(x) = \dfrac{\sin(x)}{\cos(x)}$

Then

$R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}$

and

$\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)$

so we can rewrite A(t) as

$\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}$

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

$24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}$

and

$24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}$

which is to say, with amplitude

$2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}$

6 0

2 years ago

A line passes through the point (-1,5) and the point (3,5), what is the equation of the line?

Lemur [1.5K]

Answer:

Step-by-step explanation:

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have a nice day

mark brainlist plzzzzz

8 0

3 years ago

who knows fraction on daily basic for a living because i need help thank you i will give you 50 point if you do?

e-lub [12.9K]

Answer:

EATING OUT: Have you ever gone out to eat with a group of friends but the waitress brings only one check? To divide up the bill, you’ll need to use fractions.

BACK TO SCHOOL SHOPPING: Your son really wants those new Lebron kicks and you’ve agreed to pay ½. How much are they if you find a ¼ off sale?

GROCERY SHOPPING: You set aside your grocery budget and made your list. Sales tax and coupons all use fractions.

MEAL PREP FOR THE FAMILY: Cooking for 4 people but the recipe serves 10? You’ll need to use fractions to divide the ingredients.

SPORTS: The NBA Finals are on. Fractions are used to determine statistics and shooting percentages.

CONTRACT WORK: Buying a car? Signing a lease on an apartment? Making your own jewelry and working with a supplier? For all of these things (and many others) you’ll need to use fractions when negotiating the contract rates.

FITNESS: Before starting a diet, you should know your Body Mass Index. This BMI number is calculated using fractions. Dieting? You’ll need fractions to know how many calories you are taking in vs. how many calories you are using.

JEWELRY: 24 karats is pure gold, and 18 karats is 18/24 which equals 75% gold. Using fractions to understand jewelry purity could save you money!

COCKTAILS: Good bartenders know how to mix drinks and fractions are used to determine how much of each ingredient is added.

PIZZA FOR THE KIDS: Mealtime doesn’t have to be a battle about who got more. Use fractions to split the pie evenly.

PAY: Did you recently get a raise? Does a quarter of your pay go towards healthcare? How much should you invest in retirement? Fractions will determine how much you actually take home.

MONEY IN GENERAL: A quarter is a ¼ of a dollar. Dimes are 1/10 of a dollar. If you know fractions, adding your money is quick and easy.

GAS TANK: If you’ve got an 1/8 of a tank, how much further can you drive? Prices to fill up also use fractions.

FAST FOOD: Can you eat two quarter-pounders with all of the toppings? You’ve just consumed a half a pound of meat.

PHOTOGRAPHY: Shutter speed is calculated using fractions of a second.

HOMEWORK ASSIGNMENTS: Your child got 38/51 questions correct. A solid understanding of fractions will help you determine if the child should be rewarded or grounded.

PRESCRIPTIONS: Whether you, your child, or your pet is sick, medicine dosages are often determined with a fraction of parts to weight. Different body sizes require different dosages.

PARTY PLANNING: Use fractions to determine how much food to get, how many drinks you’ll need on hand, and table settings.

CHECKING PROGRESS: Use fractions to determine rate of improvement. For example, if you called 25% more customers this month than last month, you might want to ask for a raise.

TIME: An hour and a half. A quarter of an hour. Time is commonly measured in fractions.

Step-by-step explanation:

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3 years ago