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natka813 [3]
3 years ago
11

3.

Mathematics
1 answer:
Naddik [55]3 years ago
4 0
A, D, E, and F are greater than -5
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Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2
Anastaziya [24]

Answer:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

Step-by-step explanation:

we would like to figure out the derivative of the following:

\displaystyle  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

to do so, let,

\displaystyle y =  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

By simplifying we acquire:

\displaystyle y =  3 -  \frac{2}{x}  -  \frac{1}{ {x}^{2} }

use law of exponent which yields:

\displaystyle y =  3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} }

take derivative in both sides:

\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  (3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} } )

use sum derivation rule which yields:

\rm\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  3 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

By constant derivation we acquire:

\rm\displaystyle  \frac{dy}{dx} =  0 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

use exponent rule of derivation which yields:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ - 1 -1} ) -     ( - 2 {x}^{  - 2 - 1} )

simplify exponent:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ -2} ) -     ( - 2 {x}^{  - 3} )

two negatives make positive so,

\displaystyle  \frac{dy}{dx} =   2 {x}^{ -2} +      2 {x}^{  - 3}

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

\displaystyle  \frac{dy}{dx} =   \frac{2 }{x^2}+       \frac{2}{x^3}

simplify addition:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

and we are done!

5 0
3 years ago
If the measure of angle 2 is 3x, and the measure of 1 is 5x - 12 what is the measure of angle 9 ?
Mariana [72]
3x+5x-12=180
8x=180+12
8x=192
x=192/8
x=24

angle 1 = 5x-12
=5(24)-12
=120-12
=108

angle 2= 3x =3*24=72

angle 1 = angle 9
angle 9= 108
8 0
3 years ago
6. A regular pyramid has a square base. The perimeter of the base is 64 inches and the height of the pyramid is 12 inches. What
hichkok12 [17]

The volume is 1024. the base lengths are all 16 inches

4 0
2 years ago
Solve this question in the following photo​
katovenus [111]

Answer:

55/43

Step-by-step explanation:

(x/y) = 7/3, (x^2/y^2)=49/9, multiply by 3 above and multiply 2 below, 3x^2/2y^2=147/18. Next apply C&D and you will get (3x^2+2y^2)/(3x^2-2y^2)=(147+18)/(147-18)=165/129=55/43

6 0
2 years ago
If the length of a rectangle is 120 m and the diagonal measures 130 m what is the perimeter and area of the rectangle
Leviafan [203]

Answer:

Step-by-step explanation:

width=√(130²-120²)=√[10²(13²-12²)]=10√(13+12)(13-12)=10√(1×25)=10×5=50 m

perimeter=2(120+50)=2×170=340 m

area=120×50=6000 m²

5 0
3 years ago
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