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Dimas [21]
2 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]2 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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In a certain​ lottery, an urn contains balls numbered 1 to 26. From this​ urn, 6 balls are chosen​ randomly, without replacement
expeople1 [14]

Answer:

\frac{1}{230230}

Step-by-step explanation:

Given that in a certain​ lottery, an urn contains balls numbered 1 to 26

From this​ urn, 6 balls are chosen​ randomly, without replacement.

Bet amount 1 dollar and he selects a set of six numbers.

If these match with those chosen from the urn he wins (order does not matter)

Total ways of choosing 6 out of 26 = 26C6 = \frac{26!}{20!6!} \\=230230

The way he selects = 1

Hence probability of winning  =\frac{1}{230230}

with one ticket

4 0
3 years ago
For the 2015 Intel Science Fair, two brothers in high school recruited 47 of their classmates to take part in a two-stage study.
kvv77 [185]

Answer:

a) 47

b) 3

c)  1

d) 2

e) 47

f) 3

Step-by-step explanation:

read the textbook

8 0
3 years ago
Read 2 more answers
Could you please help me!?
Alinara [238K]

Answer:

Answer: 42.5

Step-by-step explanation:

It says 1 inch equals 5 feet. So, every inch is on the map is an extra 5 feet in real space. So if you think about it, all this is is a simple multiplication problem.

Here is the math:

8.5 * 5 = 42.5

Think about it, for every inch there is on the map there is an extra 5 feet in real space. There is 8 inches, so we need 5 extra feet for each of those 8 inches. So what we get for 1 inch is 5 feet, for 2 inches 10 feet, 3 inches 15 feet, etc etc until we reach 8 inches. For the 0.5 inches alone that would equal 2.5 feet in real life since 1 inch is 5 feet.

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6 0
3 years ago
Find the equation of the line that goes through the points (3,8) and (9,16).
Aneli [31]

Answer:

4x-3y+12=0 is required eqn

Step-by-step explanation:

Let, 3,8 be x1,y1

9,16 be x2,y2

Now,

Eqn of st.line is y-y1 = y2-y2/x2-x1 * (x-x1)

y-8 = 16-8/9-3 * (x-3)

y-8 = 4/3*(x-3)

3y-24 = 4x-12

4x-3y+12=0 is required eqn

3 0
3 years ago
Simplify the complex fraction.
lilavasa [31]

Given:

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}

To find:

The simplified fraction.

Solution:

Step 1: Simplify the numerator

$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}

Step 2: Simplify the denominator

$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}

Step 3: Using step 1 and step 2

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}

Step 4: Using fraction rule:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}

$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}

Cancel the common factor r and t², we get

           $=\frac{64 r^{2} \cdot 9 }{16  \cdot 15 t^2 }

Cancel the common factors 16 and 3 on both numerator and denominator.

           $=\frac{4 r^{2} \cdot 3 }{  5 t^2 }

           $=\frac{12 r^{2}  }{  5 t^2 }

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2}  }{  5 t^2 }

The simplified fraction is \frac{12 r^{2}  }{  5 t^2 }.

5 0
3 years ago
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