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3 years ago

Can someone answer this soon?!?

Mathematics

1 answer:

Sever21 [200]3 years ago

6 0

First get all the terms on the same side:

$x^2 + 7x - 4 = 0$

Now solve using the quadratic formula which is:

$\frac{-b±\sqrt{b^2 - 4ac} }{2a}$

Plug in the values:

$\frac{-7± \sqrt{49-4(1)(-4)} }{2}$

So the answer is:

$\frac{-7 ± \sqrt{65} }{2}$

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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

Find the missing terms of the following geometric sequence. Assume all terms are positive. (Hint: The geometric mean of the fi

alexandr1967 [171]

1.5,4.6,13.5,40.5,121.5

7 0

2 years ago

Please answer all three questions Pleaseeeeee tysmm <3

oee [108]

Answer: 2 3/4 > 2.68 is correct (only)

Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68

The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.

Sqrt(63) = 7.93, and 7.93 > 8.11 is false.

Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2

6 0

1 year ago

If 7x + 3 = 24, what is the value of 5 - 4x?

Iteru [2.4K]

Answer:

Step-by-step explanation:

7x + 3= 24

7x= 24-3

7x= 21

x= 21/7

x= 3

Then we have that

5-4x

5-4(3)

5-12

Answer= -7

3 0

2 years ago

Which theorem shows how the triangles are similar:

yan [13]

Answer:

AA similarly is correct....

6 0

3 years ago