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tatyana61 [14]
3 years ago
6

What is the domain of f(x) = -(x-6)^2-30

Mathematics
1 answer:
son4ous [18]3 years ago
3 0

Answer:

(-∞, ∞)

Step-by-step explanation:

To find the domain, we find how far along the x axis the line goes.

Specifically, we're looking for when x <em>doesn't</em> exist, because that's much easier.

So we're looking for when x is undefined. In order to have something undefined, you need the \sqrt{-something}, or \frac{anything}{0}.

As we can see, there's no part where x is undefined. Therefore, the domain is

(-∞, ∞)

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How do i solve for y and x?
Akimi4 [234]

Answer:

You use the facts about a 30, 60, 90 triangle.

Step-by-step explanation:

The angles in a triangle add up to 180.

90+30+x=180

120+x=180

x=60

This is a 30-60-90 right triangle.

The side opposite the 30 degree angle is a.

The side opposite the 90 degree angle (hypotenuse) is 2a.

The side opposite the 60 degree angle is a\sqrt{3}

We know the side opposite the 90 degree angle.

2a = 12\sqrt{3}

Divide by 2.

a=6\sqrt{3}

a is the side opposite the 30 degree angle (y)

Because we know a, we can find a\sqrt{3}.

6\sqrt{3 } (\sqrt{3})

The square roots cancel, leaving 3.

6 times 3 is 18.

Therefore, the side opposite the 60 degree angle (x) is 18.

4 0
3 years ago
Read 2 more answers
Evaluate the expression a•b for a =24 and b=8
Butoxors [25]

\huge\text{Hey there!}


\mathsf{a\times b}}

\mathsf{= 24\times8}

\mathsf{= 192}


\huge\textbf{Therefore, your answer should be:}

\huge\boxed{\mathsf{192}}\huge\checkmark


\huge\text{Good luck on your assignment \& enjoy your day!}


<h3>~\frak{Amphitrite1040:)}</h3>
4 0
2 years ago
The number of daily sales of a product was found to be given by S = 600xe−x2 + 600 x days after the start of an advertising camp
Elena-2011 [213]

Answer:

a. 20520

b. 12600

Step-by-step explanation:

Given the function S = 600xe^-x² + 600.

a. To find the average, we have to find the definite integral of the function because average, as it is known, is the sum of data points divided by the size of its dataset, this can be used for discrete data. Integral formula is just the continuous form of average, so we are using integral because we were given an interval of x= 0 to X = 30.

Let's integrate 100xe^x² first. Let –x² = u, this means –2xdx = du and we have dx = –du/2x. Also, when x = 0, u = –(0)² = –0 and when x = 30, u = –(30)² = –900. When we make our substitutions we have:

–600(xe^udu)/2x = –600(e^udu)/2 upon integrating that we have –600(e^u)/2. Applying our interval we have

–600[(e^900)/2 – (e^0)/2] ≈ – [– 3.7 – (1/2)] = –600 (–4.2) = 600 x 4.2 = 2520

Now let's integrate 600, with the interval x = 0 to x = 30 (we are using this interval here because the substitution we made didn't affect this).

We have, upon integrating:

600x.

Substituting our intervals we have:

600(30 – 0) = 600 x 30 = 18000.

Adding that up we have: 2520 + 18000 = 20520.

b. The same method is needed, just difference of interval.

Therefore, after integrating the first component with intervals u = 900 to u = 2500 (from x² = u) we have:

–600[(e^2500)/2 – (e^900)/2] ≈ –600[2.7 – 3.7] = –600(–1) = 600.

Then for the second component:

600x using x = 30 to x = 50

600(50 – 30) = 600 x 20 = 12000.

Adding that up we have:

12000 + 600 = 12600.

4 0
3 years ago
Write two perfect squares that each have a value greater than100 and less than 200
Trava [24]

Answer:

121, 144

Step-by-step explanation:

√121= 11

√144= 12

6 0
2 years ago
Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact<br><br> C=.
Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

(2x+5y)dx+(5x-4y)dy=0

Now the above differential equation can be re-written as

P(x,y)dx+Q(x,y)dy=0

Checking for exactness we should have

\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}

\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5

\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)

The value of \phi (y) can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c

5 0
3 years ago
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