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Arlecino [84]
2 years ago
9

P and W are twice-differentiable functions with P(7)=2(W(7)). The line y=9+2.5(x-7) is tangent to the graph of P at x=7. The lin

e y=4.5+2(x-7) is tangento to the graph of WQ at x=7. Let m be a function such that m(x)=x(W(x)). Find m'(7).
Mathematics
1 answer:
fiasKO [112]2 years ago
4 0

Using the product rule, we have

m(x) = x W(x) \implies m'(x) = xW'(x) + W(x)

so that

m'(7) = 7W'(7) + W(7)

The equation of the tangent line to <em>W(x)</em> at <em>x</em> = 7 has all the information we need to determine <em>m'</em> (7).

When <em>x</em> = 7, the tangent line intersects with the graph of <em>W(x)</em>, and

<em>y</em> = 4.5 + 2 (7 - 7)   ==>   <em>y</em> = 4.5

means that this intersection occurs at the point (7, 4.5), and this in turn means <em>W</em> (7) = 4.5.

The slope of this tangent line is 2, so <em>W'</em> (7) = 2.

Then

m'(7) = 7\cdot2 + 4.5 = \boxed{18.5}

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Dennis_Churaev [7]
Pretty sure it’s the second option because length would be 3w+2
and width would be w+1 and with area you have to multiply so it would just be the (w+1)(3w+2)
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Which graph represents the function of f(x) = 9x 2 -36/3x+6 Please help
UkoKoshka [18]
The function is:

             (9x^2 - 36)
f(x) = ---------------------
                3x + 6

You can simplify that function to a linear function for all x for which 3x + 6 ≠ 0

=> x ≠ - 2.

So, for x ≠ - 2, you can do:


             (9x^2 - 36)
f(x) = --------------------- =
               3x + 6

              9(x^2 - 4)
f(x) = ---------------------
                3(x + 2)

             3(x + 2)(x - 2)
f(x) = --------------------- = 3(x - 2) = 3x - 6
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So, the graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2 as the function is not defined for x = -2. That is the second graph of the second picture.


6 0
3 years ago
What is 21/25 in a fraction
Vlad [161]

21/25 is already a fraction and if you wanted it to be simplified, its already simplified to be 21/25.

5 0
3 years ago
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Add or subtract as indicated 5/x-2 - 3/x-2
algol [13]

Option a: \frac{2}{x-2} is the right answer

Step-by-step explanation:

The given expression is:

\frac{5}{x-2} - \frac{3}{x-2}

As the denominators of both terms are same, the LCM will be x-2

so

\frac{5-3}{x-2}

Subtracting

\frac{2}{x-2}

Hence,

Option a: \frac{2}{x-2} is the right answer

Keywords: Polynomials, fractions

Learn more about polynomials at:

  • brainly.com/question/9231234
  • brainly.com/question/9214411

#LearnwithBrainly

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3 years ago
How many non-square numbers lie between the 215to the power of 2 and 216 to the power of 2
Vaselesa [24]

There are 430 non square numbers that lie between 215^{2} and 216^{2}.

Given two numbers 215^{2} and 216^{2} and we are require to find non square numbers that lie between them.

Numbers can be consecutive numbers or non consecutive numbers. In our question we will find the consecutive numbers.

Square numbers are those numbers whos square is in a proper number means decimal should not be there.

First number=215^{2}

Second number=216^{2}

First we have to find the exact value of numbers by finding the square of these numbers.

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Numbers that  lie between them=(46656-46225)-1

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Hence 430 numbers lie between 215^{2} and 216^{2}.

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