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Rom4ik [11]
2 years ago
5

How many tiles with dimensions 14 cm and 9 cm will be needed to fit in a rectangular

Mathematics
1 answer:
marta [7]2 years ago
5 0

Answer:

96 tiles

Step-by-step explanation:

The number of tiles measured  14 cm and 9 cm that will fit into a rectangular

region whose length and breadth are 168 cm and 72 cm may be computed as a ratio of the areas of the two rectangles.

Hence number of tiles

= 168 * 72/14 * 9

= 12 * 8

= 96 tiles

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Find the circumference of a circle if the radius is 2 inches.
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Answer:

12.566368 units

Step-by-step explanation:

2(pi)r = C

2(pi)(2) = C

4(pi) = C

4(3.141592) = C

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The zeros of function dare -3 and 8. Which expression could be a factor of function d?
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Answer:

(x + 3)

Step-by-step explanation:

Using the zero product property

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(x-a)(x-b) =0

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3 years ago
How do you convert a fraction to decimal
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Find dy/dx if f(x) = (x + 8)^3x.
vlabodo [156]
This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...

Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.

Let y = (x+8)^(3x)

Take the natural log of both sides:

ln(y) = ln((x+8)^(3x))

By laws of logarithms, this can be rearranged:

ln(y) = 3xln(x+8)

Next, differentiate both sides. By implicit differentiation:

d/dx(ln(y)) = 1/y dy/dx

The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):

d/dx(3xln(x+8)) = d/dx(uv)

du/dx = 3

Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:

v = ln(a)
da/dx = 1
dv/da = 1/a

By chain rule:

dv/dx = dv/da * da/dx = 1/a = 1/(x+8)

Finally, use the product rule:

d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)

This overall produces the equation:

1/y * dy/dx = 3x/(x+8) + 3ln(x+8)

We want to solve for dy/dx, achievable by multiplying both sides by y:

dy/dx = y(3x/(x+8) + 3ln(x+8))

Since we know y = (x+8)^(3x):

dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))

Neatening this up a bit, we factorise out 3/(x+8):

dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))

Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.

I hope this helped you :)
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3 years ago
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