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Anettt [7]
2 years ago
6

Trig. Functions: y= 3 cos(x) -5 Show work and Determine: Domain: Range:

Mathematics
1 answer:
babymother [125]2 years ago
5 0

Step-by-step explanation:

y = 3cos(x) - 5

Domain = 2sin(x)

Range = 5

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Y equals the quotient of the quantity x squared plus 4 times x and the quantity x cubed minus 5.
koban [17]

Given:

Consider the completer question is "Find the derivative \dfrac{dy}{dx} for y=\dfrac{x^2-4x}{x^3-5}."

To find:

The derivative \dfrac{dy}{dx}.

Solution:

Chain rule: \dfrac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)

Quotient rule: \dfrac{d}{dx}\dfrac{f(x)}{g(x)}=\dfrac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}

We have,

y=\dfrac{x^2-4x}{x^3-5}

Differentiate with respect to x.

\dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{x^2-4x}{x^3-5}\right)

Using chain rule and quotient rule, we get

\dfrac{dy}{dx}=\dfrac{(x^3-5)\dfrac{d}{dx}(x^2-4x)-(x^2-4x)\dfrac{d}{dx}(x^3-5)}{(x^3-5)^2}

\dfrac{dy}{dx}=\dfrac{(x^3-5)(2x-4)-(x^2-4x)(3x^2)}{(x^3-5)^2}

\dfrac{dy}{dx}=\dfrac{2x^4-4x^3-10x+20-3x^4+12x^3}{(x^3-5)^2}

\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}

Therefore, the required answer is \dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}.

4 0
2 years ago
What is 56/74 in simplest form?
leonid [27]


56/74 in simplest form

56/74×2/2=28/37

Therefore, 56/74 in simplest form is 28/37.

8 0
3 years ago
For this item, complete the choice matrix by clicking the appropriate answer in each row.
Vesna [10]
That person is really smart good job
8 0
3 years ago
Read 2 more answers
What is the answer to -5x+5y=-10 and 3x-3y=5 using substitution
IceJOKER [234]

Answer:

for the 1st one the answer is x= 3 y=1 and the second one is x= 5 and y = 3 and 1/3

Step-by-step explanation: so basically for the first one -5 times x which is 3 is -15 right? and then 5 times y which is 1 is 5 right so -15 plus 5 = -10

second one is x = 5 and y = 3 and 1/3 because 5*x which is 5 is = to 15 right? and then 3 times y which is equal to 3 and 1/3 is equal to 10 which when you do 15-10 in pretty sure it equals 5 correct me if im wrong

Hope this helps xD ;)

7 0
3 years ago
A city’s population, P, is modeled by the function P(x) = 78,500( 1.02 )x where x represents the number of years after the year
Levart [38]
Population 78500
Increased by 2%
3 0
3 years ago
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