How to determine if possible if(

Please i need help :( <br> What is the Y- intercept of the graph of the linear function ?

emmainna [20.7K]

Answer:

Looks like -6

Step-by-step explanation:

4 0

3 years ago

The daily average temperature in Santiago, Chile, varies over time in a periodic way that can be modeled approximately by a trig

natali 33 [55]

Answer:

a) the trigonometric function is;

$y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5$

b) $y = 28.36^0 \ C$ ( to two decimal places)

Step-by-step explanation:

This data can be represented by the sinusoidal function of the form :

$\mathbf{y = A sin (Bt -C)+D}$

where A = amplitude and which can be determined via the formula:

$A = \dfrac{largest \ temperature - lowest \ temperature}{2}$

$A = \dfrac{29-14}{2}$

$A = \dfrac{15}{2}$

A = 7.5° C

where B = the frequency;

Since the data covers a period of 3 days ; then $\dfrac{2 \pi}{B } =365$

$B = \dfrac{2 \pi}{365}$ ( where 365 is the time period )

The vertical shift is found by the equation D;

D = $\frac{largest \ temperature + lowest \ temperature}{2}$

D = $\frac{29+14}{2}$

D = 21.5

Replacing the values of A ; B and D into the above sinusoidal function; we have :

$y = 7.5 sin (\frac{2 \pi}{365}t -C) + 21.5$

From the question; when it is 7th of the year ( i.e January 7);

t = 7 and the temperature (y) = 29° C

replacing that too into the above equation; we have:

$29= 7.5 sin (\frac{2 \pi}{365}*7 -C) + 21.5$

$29= 7.5 sin (\frac{14 \pi}{365} -C) + 21.5$

$\frac{29-21.5}{7.5}= sin (\frac{14 \pi}{365} -C)$

$1= sin (\frac{14 \pi}{365} -C)$

$sin^{-1}(1)= (\frac{14 \pi}{365} -C)$

$\frac{\pi}{2}= (\frac{14 \pi}{365} -C)$

$C= (\frac{14 \pi}{365} -\frac{\pi}{2})$

$C= (\frac{28 \pi- 365 \pi}{730} )$

$C= \frac{-337 \pi}{730}$

Thus; the trigonometric function is;

$y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5$

Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :

$y = 7.5 sin ( \frac{2 \pi}{365}*31+ \frac{337 \pi}{730})+ 21.5$

$y = 7.5 sin ( \frac{62 \pi}{365}+ \frac{337 \pi}{730})+ 21.5$

$y = 7.5 sin ( \frac{124 \pi+ 337 \pi }{730})+ 21.5$

$y = 7.5 sin ( \frac{461 \pi }{730})+ 21.5$

$y = 7.5 *( 0.915)+ 21.5$

$y = 6.8689+ 21.5$

$y = 28.36^0 \ C$ ( to two decimal places)

7 0

3 years ago

Read 2 more answers

The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?

IrinaVladis [17]

G(x) would involve a translation left 1 and up 1.

g(x) is written in vertex form, which is

g(x) = a(x-h)²+k, where (h, k) is the vertex. Since
g(x) = 4(x-8)²+9, the vertex is at (8, 9). Comparing this to the vertex of f(x), which is at (9, 8), it is left 1 and up 1.

7 0

3 years ago

You spend 30 minutes reading emails. You then spend 3 hours watching television. write the ratio of the amount of time spent rea

oksano4ka [1.4K]

Ten minutes to 1 hour

8 0

3 years ago

A barn is shaped like a rectangular prism with a triangular prism on top as shown. The exterior four walls and two triangular fa

NemiM [27]

Answer:

Step-by-step explanation:

A barn is in form of rectangular prism

Given the dimension

Height H = 20 ft

Length L = 84 ft

Width W = 38 ft

Triangular prism dimensions

Height H = 12 ft

Length L = 84 ft

Width W = 19 ft

Given that,

1 gallon covers 232 Square feet

1 gallon = 232 ft²

So, we need to total surface area to be shaded

First for the rectangular prism, only the four exteriors wall that can be painted, the bottom and the top where the triangular rest on cannot be painted,

So, Area of rectangular prism

A = 2(LW + LH + WH)

But in this case, no length and width covers so, LW = 0

A = 2(LH + WH)

A1 = 2(84 × 20 + 38 × 20)

A1 = 2(1680 + 760)

A1 = 2 × 2440

A1 = 4880 ft²

Now, area to be covered in the triangular prism

Only two regular face is needed to be covered

Then,

Area of a triangle is ½b×h

Then, the two sides to be cover will have

A2 = 2 × (½ × 19 × 12)

A2 = 228ft²

So, total area to be painted is

A = A1 + A2.

A = 4880 + 228

A = 5108 ft²

So,

1 gallon = 232ft²

x gallon = 5108ft²

Cross multiply

x gallon = 5108ft² × 1gallon / 232ft²

x gallon = 22.017

So, approximate 22 gallon will be enough, but for design reason, it is advisable to get 23 gallons,

5 0

3 years ago