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3 years ago

What is the exact value of cos 112.5°?

1 answer:

3 0

We have 112.5 = 225/2; cos112.5 < 0 because 90 < 112.5 < 180;
cos 112.5 = cos(225/2);
We use the trigonometric formula: cos(x/2) = - $\sqrt{ \frac{1+cosx}{2} }$ ;
Then, cos(225/2) = - $\sqrt{ \frac{1+cos225}{2} }$ ;
We have the formula: cos(270 - x) = -sinx (because cos(a-b) = cosacosb + sinasinb);
Then, cos225 = cos(270-45) = -sin45 = - $\frac{ \sqrt{2} }{2} ;$
Finally, cos112.5 = - $\frac{ \sqrt{2- \sqrt{2} } }{2} ;$

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HELP!!!

ella [17]

Answer:

120

Step-by-step explanation:

We are given that the function for the number of students enrolled in a new course is $f(x) = 4^{x}-1$ .

It is asked to find the average increase in the number of students enrolled per hour between 2 to 4 hours.

We know that the average rate of change is given by,

$A = \frac{f(x)-f(a)}{x-a}$ ,

where f(x)-f(a) is the change in the function as the input value (x-a) changes.

Now, the number of students enrolled at 4 = f(4) = $f(x) = 4^{4}-1$ = 255 and the number of students enrolled at 2 = f(2) = $f(x) = 4^{2}-1$ = 15

So, the average increase $A=\frac{f(4)-f(2)}{4-2}$ = $A=\frac{255-15}{4-2}$ = $A=\frac{240}{2}$ = 120.

Hence, the average increase in the number of students enrolled is 120.

3 0

3 years ago

The polygons are regular polygons. What is the area of the shaded region to the nearest tenth? (see attachment)

Fynjy0 [20]

Area of shaded region = 2(4*4)=2*16=32 in squared

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8 0

3 years ago

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On March 1, 2022, Carla Vista Co. acquired real estate, on which it planned to construct a small office building, by paying $79,

const2013 [10]

Answer:

Cost of the land = $90,900

Step-by-step explanation:

Cash Paid for the construction = $79,000

Cost of demolition of the old warehouse = $8,000

Salvage (i.e Proceeds from the salvaged materials) = $1,660

Additional Expenditure before construction began

Attorney's fee = $1,160

Real estate broker's fee = $4,400

Architect's fee = $8,660 ( Note that this will be capitalized to building cost)

Driveways and parking lot = $13,800 ( Note that this is capitalized to land improvements)

Sum of additional expenditure = Attorney's fee + Real estate broker's fee

Sum of the additional expenditure = 1160 + 4400

Sum of the additional expenditure = $5,560

Cost of the land = Cash paid + cost of demolition + Additional expenditure - salvage

Cost of the land = 79000 + 8000 + 5560 - 1660

Cost of the land = $90,900

3 0

3 years ago

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Hola esta es mi pregunta

fenix001 [56]

Answer:

Step-by-step explanation:

hola

Cuando dos numeros tienen el mismo signo la respuesta siempre es positiva. cuando un signo es positivo y e lotro es negativo la respuesta siempre sera negativa. Esta es la regla para multiplicar numeros con signos diferentes. el orden de los signos no importa en multiplicacon siempre va ha ser la misma respuesta.

7 0

3 years ago

What is the following quotient? 5/√11-√3

kati45 [8]

ANSWER

$\frac{5( \sqrt{11} + \sqrt{3} )} {8}$