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3 years ago

What is the slope of the line passing through the points (1, -5) and (4,1)

Mathematics

2 answers:

Hoochie [10]3 years ago

8 0

1-(-5). 6
———- = —- = 2
4-1 3

never [62]3 years ago

3 0

The slope of the line passing through (1,-5) and (4,1) is 2

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Jon has 6 kites he and his friends will each fly one kite how many people in all will fly a kit

True [87]

Answer:

Step-by-step explanation:

One person will fly a kite for each of the 6 kites Jon has.

6 people in all will fly a kite.

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3 years ago

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:

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

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2 years ago

The point slope equation of a line is?

snow_tiger [21]

Answer:

$\text{The point-slope equation of a line is:}$

$C.\ y-y_0=m(x-x_0)$

$m-\text{slope}\\\\(x_0,\ y_0)-\text{point on a line}$

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3 years ago

CAN SOMEONE HELP ME PLEASE ASAP!?

faust18 [17]

Answer:

option 2 is correct given diagrm

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3 years ago

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bixtya [17]

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Step-by-step explanation:

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3 years ago