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2 years ago

Can anyone plz help me plz:

Mathematics

1 answer:

dexar [7]2 years ago

7 0

The range of the data can be calculate by subtracting the min from the max. In this case, the min is 10 and the max is 90. The range is 90 - 10, or 80.

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How to differentiate ?

Bas_tet [7]

Use the power, product, and chain rules:

$y = x^2 (3x-1)^3$

• product rule

$\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}$

• power rule for the first term, and power/chain rules for the second term:

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}$

• power rule

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3$

Now simplify.

$\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}$

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

$\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) = \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)$

Differentiate both sides and you end up with the same derivative:

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2$

7 0

2 years ago

What is the coefficient of x2 in the expansion of (x + 2)3?

wolverine [178]

One way is that you can just factor it out: (x+2)(x+2)(x+2)
For the first pair, you get $x^2+4x+4$ .
Then do $(x^2+4x+4)$ * $(x+2)$
That will be $x^3+6x^2+12x+8$
So the answer is 6

4 0

3 years ago

Find the surface of each pyramid

Genrish500 [490]

Where’s the picture at

6 0

3 years ago

1. Rich wants to buy a coat priced at x dollars. It is on sale for 20% off. He must

alexandr1967 [171]

Answer: $x-0.20x+0.0725x$

Step-by-step explanation:

Let x be the price. 20% (0.20) 7.25% (0.0725)

$x-0.20x+0.0725x$

6 0

2 years ago

Can anyone help me with this

stepladder [879]

Answer:

Step-by-step explanation

I'd say it's PQR and TSR cause they match up in terms of the order of vertexes, and then you've got the angles of P and T that are in the middle of PR and TR, which are equal, and the sides PQ and TS. The angles are in between the sides.

8 0

3 years ago