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3 years ago

What is the coefficient in the expression shown?

Mathematics

1 answer:

ikadub [295]3 years ago

3 0

Answer:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression.

Step-by-step explanation:

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago

Can someone please explain proportions?

nirvana33 [79]

Proposition is

A statement or assertion that exppresses a judment or opinion

8 0

3 years ago

Jamal simplified ...

brilliants [131]

$\bf \sqrt{75x^5y^8}\qquad 
\begin{cases}
75=3\cdot 25\\
\qquad 3\cdot 5^2\\
x^5=x^{4+1}\\
\qquad x^4x^1\\
\qquad (x^2)^2x\\
y^8=y^{4\cdot 2}\\
\qquad (y^4)^2
\end{cases}\implies \sqrt{3\cdot 5^2\cdot (x^2)^2x(y^4)^2}
\\\\\\
5x^2y^4\sqrt{3x}$

4 0

3 years ago

Please help out , i’ll mark the brainliest answer

Len [333]

Answer:

Step-by-step explanation:

7) The tangent angles are 90° each.

The angles of a quadrilateral add up to 360°, so ? = 360°-90°-90°-73° = 107°.

8) Solve this the same way as question 7). ? = 360°-90°-90°-57° = 123°.

Questions 9) and 10) are cut off, so I assume you don't need to know those.

4 0

3 years ago

Read 2 more answers

The image shows three sets of stuffed bears. Each set represents a term of the sequence (1, 4, 7, . . .) What is the next term i

frosja888 [35]

Next term = 10

You add 3 to each term to get the next

1+3 = 4

4+3 = 7

7+3 = 10

etc etc

The domain of the sequence is 1,2,3,4,... basically the set of positive whole numbers. This is known as the set of natural numbers or counting numbers. We don't include 0. The domain is the set of possible inputs for 'n' in the formula mentioned below.

The range is the sequence of values shown.

The formula to generate the sequence is

an = 3n-2

as shown by these steps below

an = a1 + d(n-1)

an = 1 + 3(n-1)

an = 1+3n-3

an = 3n-2

To get any term you want, plug in a whole number for n. For example, plug in n = 4 to get...

an = 3n-2

a4 = 3*4-2

a4 = 12-2

a4 = 10

Showing that the fourth term is 10 as found earlier above.

3 0

3 years ago