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3 years ago

What is the derivative of y^3+xe^4=3x^2-10?

Mathematics

1 answer:

Pani-rosa [81]3 years ago

7 0

Answer:

${y}^{3} + x {e}^{4} = 3 {x}^{2} - 10$

introduce dy/dx :

$\frac{d( {y}^{3} + x {e}^{4} ) }{dx} = \frac{d( {3x}^{2} - 10) }{dx} \\ \\ 3 {y}^{2} \frac{dy}{dx} + {e}^{4} = 6x - 0 \\ \\ {3y}^{2} \frac{dy}{dx} = 6x - {e}^{4} \\ \\ { \boxed{ \boxed{\frac{dy}{dx} = \frac{6x - {e}^{4} }{ {3y}^{2} } }}}$

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A submarine dives at a constant speed of 10 m/s at a diving angle measured from the vertical

valina [46]

Answer:

155.3 m

Step-by-step explanation:

θ: is the angle measured from the vertical = 75 °

v = is the speed of the submarine = 10 m/s

t = 1 min

The deep of the front end of the submarine at the end of a 1-minute drive is given by the following ratio:

$cos (\theta) = \frac{x}{d}$

<u>Where:</u>

d: is the distance traveled by the submarine in 1 minute

x: is the deep to find

The distance, d, is:

$d = v*t = 10 \frac{m}{s}* 1 min * \frac{60 s}{1 min} = 600 m$

Now, the deep is:

$cos (75) = \frac{x}{600}$

$x = cos(75)*600 = 155.3 m$

Therefore, the deep of the front end of the submarine at the end of a 1-minute drive is 155.3 m.

I hope it helps you!

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3 years ago

I want a tutor can I have some one help me

jekas [21]

Answer:

If you want add me on discord >>> fun54658#0871

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3 years ago

Read 2 more answers

Which graph shows the result of dilating this figure by a factor of 4 about the origin? On a coordinate plane, rectangle A B C D

Andrei [34K]

Answer:

Second option: On a coordinate plane, rectangle A'B'C'D' prime has points $(-4,4),(12,4),(12,-4),(-4,-4)$

(See the graph attached)

Step-by-step explanation:

For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.

In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:

$A(-1,1)\\\\B(3,1)\\\\C(3,-1)\\\\D(-1,-1)$

Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:

$A'=((-1)(4),(1)(4))=(-4,4)\\\\B'=((3)(4),(1)(4))=(12,4)\\\\C'=((3)(4),(-1)(4))=(12,-4)\\\\D'=((-1)(4),(-1)(4))=(-4,-4)$