How do I find x and y in this equation

Solve this equation pls

Aleksandr-060686 [28]

Answer:

${ \rm{y = \frac{3 \sqrt{x} + 2x}{ {4x}^{2} } }} \\$

• We are gonna use the quotient rule

${ \boxed{ \bf{ \frac{dy}{dx} = \frac{ {\huge{v} } \frac{du}{dx} - { \huge{u}} \frac{dv}{dx} }{ {v}^{2} } }}} \\$

u is (3√x + 2x)
v is 4x²
du/dx is 3/2√x
dv/dx is 8x

• Therefore:

${ \rm{ \frac{dy}{dx} = \frac{(4 {x}^{2})( \frac{3}{2 \sqrt{x} }) - (3 \sqrt{x} + 2x)(8x) }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{(6 {x}^{2})( {x}^{ - \frac{1}{2} } ) - (24 {x}^{ \frac{3}{2} } + 16 {x}^{2} ) }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{ 6 {x}^{ \frac{3}{2} } - {24x}^{ \frac{3}{2} } - {16x}^{2} }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{ - 18 {x}^{ \frac{3}{2} } - 16 {x}^{2} }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = - 2 {x}^{ \frac{3}{2} } (9 + 8 {x}^{ \frac{4}{3} } ) \div 16 {x}^{4} }} \\ \\ { \boxed{ \boxed{ \rm{ \: \: \frac{dy}{dx} = - \frac{8 \sqrt{ {x}^{ \frac{8}{3} }} + 9}{8x {}^{ \frac{8}{3} } } \: \: }}}}$

5 0

2 years ago

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What is f(x) = 7x2 + 42x written in vertex form?

amid [387]

Answer:

$\boxed{\boxed{y = 7(x+3)^2-63}}$

Step-by-step explanation:

The general vertex form of parabola is,

$y=a(x-h)+k$

where,

(h, k) is the vertex of the parabola.

The given function is,

$\Rightarrow f(x) = 7x^2 + 42x$

$\Rightarrow y = 7x^2 + 42x$

$\Rightarrow y = 7(x^2 + 6x)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2$

$\Rightarrow y = 7(x+3)^2-7\cdot 9$

$\Rightarrow y = 7(x+3)^2-63$

This is vertex form the given function.

7 0

3 years ago

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Need help with all parts please show you work for each part

bezimeni [28]

Vinegar is the x or horizontal oil is the y or vertical
$\frac{3}{2} = \frac{y}{x} \\ 3x = 2y \\ y = \frac{3}{2} x$
the point represent the amount of vinegar and oil so for 1 tbsp vinegar you need 1.5tbsp oil

4 0

2 years ago

HELP QUICK Remove grouping symbols and combine like terms. 4a2 - 3[2b - 3b(b - 1)]

kvasek [131]

Answer:
4a^2 - 15b + 9b^2

Step by step explanation:

8 0

3 years ago

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Drag the ordered pair that are 5.5 units apart.

Alexus [3.1K]

Answer:

(-1.5, -3.5) and (-1.5, 2)

Step-by-step explanation:

The x-coordinates in increasing order are ...

-3, -1.5, 5

The distances between pairs of these coordinates are ...

-1.5 -(-3) = 1.5

5 -(-3) = 8

5 -(-1.5) = 6.5

Clearly, any pair with x = 5 is too far away from any pair with a different x-value.

∆x = 1.5

If the distance between pairs is 5.5, then the distance formula tells us the y-coordinate differences for pairs with x-coordinates of -3 and -1.5 must be ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

5.5 = √(1.5^2 +(y2 -y1)^2) . . . substitute known values

30.25 = 2.25 +(y2 -y1)^2 . . . . square both sides

√28 = (y2 -y1) . . . . . . . . . . . . . . subtract 2.25 and take the square root

This value is irrational. Clearly none of the y-coordinates is irrational, so there are no point pairs with x-coordinates -3 and -1.5 that are 5.5 units apart.

__

∆x = 0

If the x-coordinates are the same, then the y-coordinates must differ by 5.5 in order for the points to be 5.5 units apart. The coordinates in order are ...

for x = -1.5, y = -3.5, 2, 2.5 . . . . . differences of 5.5, 6, 0.25

for x = 5, y = -3.5, 1.5 . . . . . . . difference of 5

The only pair we can find that is 5.5 units apart is ...

(-1.5, -3.5) and (-1.5, 2).

6 0

2 years ago