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3 years ago

(6Q) Find the domain and range.

Mathematics

1 answer:

Rudik [331]3 years ago

8 0

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function $f(x) = 2x + cosx$

Note that f(x) is the sum of two continuous functions $h(x) = 2x$ and $g(x) = cosx$

The domain and range of h(x) are all real numbers

The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]

Then the domain of $f(x) = h(x) + g(x)$ will be the intersection of the domains of the function $h(x) = 2x$ and the function $g(x) = cosx$ .

Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)

The range of f(x) will be equal to the union of the range of g(x) and h(x)

Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)

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An equilateral ∆ has sides of length 16 cm. Find the length of an altitude.

inn [45]

The length of the altitude is $8\sqrt{3}$

Explanation:

Let ABC be an equilateral triangle.

It has sides of length 16 cm

Let AD be the altitude of the triangle.

We need to determine the length of an altitude.

Let AC = 16 cm and CD = 8 cm

Let us consider the right angled triangle ADC

Using the Pythagorean theorem, we have,

$AC^2=AD^2+DC^2$

Substituting the values, we get,

$16^2=AD^2+8^2$

$256=AD^2+64$

$192=AD^2$

$8\sqrt{3}=AD$

The length of the altitude is $8\sqrt{3}$

5 0

3 years ago

On a number line, what is the distance between -0.6 to -0.4?

Mila [183]

Answer is B
-0.6- (-0.4)= -0.6+0.4= -0.2

4 0

3 years ago

Read 2 more answers

What is the volume of a sphere that has a radius of 11.5 units?

Brut [27]

Answer:

6370.63 is the volume

Step-by-step explanation:

V=4

3πr3=4

3·π·11.53≈6370.6263

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3 years ago

I need helping answering 15. I need to create a table and graph the function.

Alekssandra [29.7K]

ANSWER and EXPLANATION

We want to order the functions from widest to narrowest:

$\begin{gathered} y=3x^2 \\ y=2x^2 \\ y=4x^2 \end{gathered}$

To do this, we have to plot the graphs of the functions by using a table of values.

Let us find the values of the functions for values of x = -2, 0, 2

For the first function:

$\begin{gathered} y=3x^2 \\ \Rightarrow x=-2: \\ y=3(-2)^2=3*4 \\ y=12 \\ \Rightarrow x=0: \\ y=3(0)^2=3*0 \\ y=0 \\ \Rightarrow x=2: \\ y=3(2)^2=3*4 \\ y=12 \end{gathered}$

Hence, its table is:

For the second function:

$\begin{gathered} y=2x^2 \\ \Rightarrow x=-2: \\ y=2(-2)^2=2*4 \\ y=8 \\ \Rightarrow x=0: \\ y=2(0)^2=2*0 \\ y=0 \\ \Rightarrow x=2: \\ y=2(2)^2=2*4 \\ y=8 \end{gathered}$

Hence, its table is:

For the third function:

$\begin{gathered} y=4x^2 \\ \Rightarrow x=-2: \\ y=4\left(-2\right)^2=4*4 \\ y=16 \\ \Rightarrow x=0: \\ y=4(0)^2=4*0 \\ y=0 \\ \Rightarrow x=2: \\ y=4(2)^2=4*4 \\ y=16 \end{gathered}$

Hence, its table is:

Now, let us plot the graphs of the functions:

Therefore, from the graph, we see that the order of the functions from widest to narrowest is: