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artcher [175]
3 years ago
11

How do I find x and y in this equation

Mathematics
1 answer:
zalisa [80]3 years ago
7 0
X= 8 radical 5 and y= 8 radical 10
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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
Read 2 more answers
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
Read 2 more answers
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<br> Remove grouping symbols and combine like terms.<br> 4a2 - 3[2b - 3b(b - 1)]
kvasek [131]
Answer:
4a^2 - 15b + 9b^2

Step by step explanation:
8 0
3 years ago
Read 2 more answers
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.

<u>∆x = 1.5</u>

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.

__

<u>∆x = 0</u>

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
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