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Neporo4naja [7]
3 years ago
8

If f(x) = f(x)g(x), where f and g have derivatives of all orders, show that f'' = f ''g + 2f 'g' + fg''.

Mathematics
1 answer:
Nadya [2.5K]3 years ago
5 0
Differentiating once, we have

f'(x)=f'(x)g(x)+f(x)g'(x)

Differentiating again,

f''(x)=f''(x)g(x)+f'(x)g'(x)+f'(x)g'(x)+f(x)g''(x)
f''(x)=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x)

as needed.
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Solve for the value of r. (8r+6)° (9r-7)​
lukranit [14]

Answer:

r = 13

Step-by-step explanation:

these angles are vertical and are congruent

8r + 6 = 9r - 7

6 = r - 7

13 = r

8 0
3 years ago
Could the lengths 6,8, and 15 represent the sides of a triangle?
kupik [55]

No, because the sum of two sides must be larger than the third.

3 0
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The manufacturer of Pepsi claims that its 2-liter bottles contain, on average, no more than 250 calories. A sample of 20 2-liter
Stels [109]

Answer:

Yes, Sample information does indicate that a 2-liter bottle of Pepsi contains more than 250 calories  

Step-by-step explanation:  

Null Hypothesis [H0] : u < 250  

Alternate Hypothesis [H1] : u > 250 {One Tail}  

t = (x' - u) / [ sd / √n ]  

= (255 - 250) / (5.6 / √20)  

5 / (5.6 /√20)  

= 3.99  

As t ie 3.99 > t value 1.65 ie for one tail 95% confidence level. So, we reject the null hypothesis & conclude that it contains more than 250 calories.  

4 0
3 years ago
Maggie is creating a cushion for a circular stool. The stool has a diameter of 14 inches. If she needs fabric to extend 2 inches
Marianna [84]

Answer:

396 in.^2

Step-by-step explanation:

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We need to find the surface area of the cylinder.

diameter = 14 in.

radius = diameter/2 = 7 in.

height = 2 in.

A = 2(pi)r^2 + 2(pi)rh

A = 2(3.14159)(7 in.)^2 + 2(3.14159)(7 in.)(2 in.)

A = 395.84 in.^2

A = 396 in.^2

8 0
3 years ago
Look at this system of equations. How can the system be changed so that the two equations have equal x-coefficients?
Volgvan
I believe the correct answer from the choices listed above is option A. The <span>system can be changed so that the two equations have equal x-coefficients by multiplying </span><span>both sides of the top equation by 2 resulting to 6x + 4y = 24. Hope this answers the question.</span>
5 0
3 years ago
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