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3 years ago

What is the x intercept of 27= -3x

Mathematics

2 answers:

madam [21]3 years ago

5 0

The x intercept is negative 9

ZanzabumX [31]3 years ago

4 0

The answer would be x = -9

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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

The solution set of the inequality 2x − y > 2 consists of all the points __ ? the line __ ?

GalinKa [24]

Answer:

b - below; y = 2x − 2

Step-by-step explanation:

2x − y > 2
2x - y + y - 2 > 2 + y - 2
2x - 2 > y
y < 2x - 2

Solution is the points below the line y = 2x - 2

Correct option is:

b - below; y = 2x − 2

7 0

3 years ago

Could someone explain how to do this, I have no idea how...

alexira [117]

Answer:

2a²

Step-by-step explanation:

Pair 'like' terms with 'like' terms, ie numbers go with numbers, and 'a's go with 'a's.

Lets deal with the top of the fraction first:

4ax3a³

Rearrange it so you have numbers beside numbers and 'a's beside 'a's:

(4x3)x(axa³)

12x(a⁴) (because nᵃxnᵇ=nᵃ⁺ᵇ)

12a⁴

Now, instead of (4ax3a³)/6a², we have 12a⁴/6a²

First divide the numbers: 12/6 =2

Now divide the 'a' parts: a⁴/a²=a² (because nᵃ/nᵇ=nᵃ⁻ᵇ)

Now we have 2a²

7 0

3 years ago

The area in square feet of a rectangular field is x²-110x+3000. The width, in feet, is x−50. What is the length, in feet?

ioda

x-60 is the length. Multiply you get x2-110x=3000 this is a quadratic equation.

7 0

3 years ago

Questlon 10 of 10

Juli2301 [7.4K]

The answer is 75 degrees. These are supplementary angles so
180-105 = 75

8 0

2 years ago