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Dimas [21]
3 years ago
6

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnig

ht and the high and low temperature during the day are 54 and 36 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Mathematics
1 answer:
Paraphin [41]3 years ago
5 0

Answer:

D = 9sin(2π(t + a)/24) + 45

Step-by-step explanation:

Let's find the average temperature;

(54 + 36)/2 = 45°

Amplitude = 54 - 45 = 9

From the wave equation, we can write the temperature as;

D = 9sin(2π(t + a)/24) + 45

Where;

D is the temperature

t is the time in hours after midnight

a is a "phase" that is used to set the time at which temperature(D) occurs

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B
Keith_Richards [23]
AD that is the answer
6 0
2 years ago
Brooklyn has a goal to save $8,000 to buy a new entertainment system. In order to meet that goal, she deposited $4,132.79 into a
densk [106]
To see how much interest she'll get after a quarter:

$4132.79 + ($4132.79 × 0.048) = $4331.16

After two quarters:
$4331.16 + ($4331.16 × 0.048) = $4359.06

You can keep going until eventually reaching $8000 then see how many quarters has passed. That's a lot of calculator work!

There's another way that uses less calculation, but more algebra. I call it the exponential formula method! There's this general formula for stuff that increases exponentially, like virus, population, and MONEY:

m= d {e}^{tc}

M is money, d is deposit, t is time taken, and c is just some unknown constant related to the interest rate. There's also the natural logarithm form of this equation, which will come in handy later:

ln( \frac{m}{d} ) = tc

Alright first we gotta find that constant c for this equation to be useful! Let's plug in stuff we know.

ln( \frac{4331.16}{4132.79} ) = (0.25)c

We know how much she'll have after one quarter (0.25 years), and we know how much she deposited initially.

After pressing some buttons on the calculator we'll find that c = 0.1875.

Great! Now we can use that formula to find how many years (t) it'll take to reach M=$8000. To save time I'm going to use the natural log form:

ln( \frac{8000}{4132.79} ) = t(0.1875)

That will give us t = 3.522 which means it'll take approximately 3.5 years for her deposit to reach $8000!
5 0
3 years ago
Read 2 more answers
At the market, 2.4 pounds of peas cost 1.68 dollars. How much does one pound of peas cost?
babunello [35]
.7

because you need to get the original unit price which is 0.7 then multiply that by 1 and get your answer
6 0
4 years ago
Include work pleaseeeee
Angelina_Jolie [31]
Okay so to represent juice we are going to use X, and to represent water we are going to use Y.

We also know that the first two starting equations are:

6x + y = 135

4x + 2y = 110

We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:

y = -6x +135

Now you can take that equation and plug into either one of the starting two equations.  I chose the second equation.  We just substitute what y equals in for y in the equation, so we have:

4x + 2(135 - 6x) =  110

Now solve

4x + 270 -12x = 110

-8x + 270 = 110

Subtract 270 from both sides

-8x = -160

Now divide by -8 on both sides

x = 20

We can now confirm that juice costs $20

Now lets plug that into the equation where we solved for y, to get the actual value of y.

y = 135 - 6(20)

y = 135 - 120

y = 15

The price of water costs $15

From this we can conclude that the cost of juice is $20 and the price of water is $15

5 0
3 years ago
a pile of sand has a weight of 90kg The sand is put into a small bag, a medium bag and a large bag in the ratio of 2 : 3 : 7 Wor
just olya [345]
Hi there!

To split 90 kilos in the ratio of 2 : 3 : 7 we must first realise that we have a total of 2 + 3 + 7 = 12 parts, in which we must split the total 90 kilos.

12 parts equal 90 kilo, and therefore
1 part equals 90 / 12 = 7.5 kilos.

1 part equals 90 / 12 = 7.5 kilos, and therefore
2 parts equal 7.5 × 2 = 15 kilos.

1 part equals 90 / 12 = 7.5 kilos, and therefore
3 parts equal 7.5 × 3 = 22.5 kilos.

1 part equals 90 / 12 = 7.5 kilos, and therefore
7 parts equal 7.5 × 7 = 52.5 kilos.

Hence, 90 kilos in the ratio of 2 : 3 : 7
gives 15 kg, 22.5 kg and 52.5 kg.

~ Hope this helps you!
3 0
3 years ago
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