The value of `sqrt20` is between ______ and _____

vampirchik [111]

To verify the identity we need the following identities:

i) $\displaystyle{ \cot(x)= \frac{\cos x}{\sin x}$

ii) $\displaystyle{ \sin (x-y)=\ sinx\cdot\ cosy -\ siny\cdot\ cosx$

iii) $\displaystyle{ \cos (x-y)=\ cosx\cdot \ cosy +\ sinx\cdot\ siny$ .

Also, we have know that $\displaystyle{ \sin \frac{ \pi }{2}=1$ and $\displaystyle{ \cos \frac{ \pi }{2}=0.$

Thus, $\displaystyle{ \cot(x-\frac{\pi}{2})= \frac{\cos (x-\frac{\pi}{2})}{\sin (x-\frac{\pi}{2})}$

By (ii) and (iii) we have:

$\displaystyle{ \frac{\cos (x-\frac{\pi}{2})}{\sin (x-\frac{\pi}{2})}= \frac{\ cosx\cdot \ cos\frac{\pi}{2} +\ sinx\cdot\ sin\frac{\pi}{2}}{\ sinx\cdot\ cos\frac{\pi}{2} -\ sin\frac{\pi}{2}\cdot\ cosx} = \frac{\ sinx}{-\cos x}$

by simplifying $\displaystyle{ \sin \frac{ \pi }{2}=1$ and $\displaystyle{ \cos \frac{ \pi }{2}=0.$

Now, $\displaystyle{ \frac{\ sinx}{-\cos x}$ is clearly -tanx.

4 0

3 years ago

A new building is being constructed at UT Austin. It is 200 feet tall, and has a

Mariana [72]

Answer:

Walkway is 3 feet wide.

Step-by-step explanation:

Given:

Length of the building is 150 ft

width of the building is 100 ft

walkway is x ft wide.

Total area(around and including the building) = 16536 square feet

Solution:

Length of the total area will be = length of the building + width of walkway from 2 sides = $150 +2x$

Width of the total area will be = width of the building + width of walkway from 2 sides = $100 +2x$

Now Total area(around and including the building) = Length of the total area $\times$ Width of the total area

$(150+2x)\times(100+2x)=16536\\15000+300x+200x+4x^2=16536\\500x+4x^2=16536-15000\\4(125x+x^2)=1536\\125x+x^2= \frac{1536}{4}=384\\$

$x^2+125x-384=0\\x^2-3x+128x-384=0\\x(x-3)+128(x-3)=0\\(x-3)(x+128)=0\\$

Now solving for both equation we get.

$x+128=0\\x=-128\\x-3=0\\x=3$

Now, We get 2 values for x which -128 and 3 but the width of the building can't be in negative value hence we will consider value of x be 3.

∴ Width of the walkway is 3 ft.

4 0

3 years ago

Read 2 more answers

Graphing Exponential Function in Exercise ,sketch the graph of the function.See example 3 and 4.

OLga [1]

Answer:

The black curve is the graph for given function.

Step-by-step explanation:

We are given the following function in the question:

$f(x) = 4^{x}$

We have to graph this function.

Properties of function:

The given function is an exponential function of the form $f(x) = b^x$ , where b is the base and x can be any real number.
Here, $b = 4$
It passes through the point (0,1).
Since $b > 1$ , the graph of function will will increase as we move from left to right.
The domain for given function is all real numbers.
The range for the given function is $(0,\infty)$