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Vadim26 [7]
1 year ago
15

The derivative of y with respect to x, when y = 3e^5x - 2 is:

Mathematics
1 answer:
Ede4ka [16]1 year ago
5 0
Answer: 15e^5x

Step - by - step

y=3e^5x - 2

By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].

d/dx [ 3e^5x ] + d/dx [ -2 ]

Evalute d/dx [ 3e^5x ]

Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].

3 d/dx [ e^5x ] + d/dx [ -2 ]

Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.

To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]

Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.

3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]

Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]

Multiply 5 by 3
15e^5x + d/dx [-2]

Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x
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Answer:

<h2>52500 kg</h2>

Step-by-step explanation:

Step one:

given data

mass of harvested peanuts = 14,000kg

size of land = 8-acre

Step two:

Required:

mass of harvested peanuts for a 30-acre land

let the mass be x

so, for 8-acre land the harvested mass is 14,000

hence for 30-acre land the harvested mass is x

cross multiply we have

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divide both sides by 8

x=420000/8

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3 years ago
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2m=p-q/r solve for r
Oduvanchick [21]

To solve for r, you would start by subtracting p from both sides.

2m - p = -q/r

Multiply everything by r.

2mr - pr = -q

Factor r out of the left side of the equation.

r(2m - p) = -q

Divide both sides by (2m - p).

r = \frac{-q}{2m-p} = \frac{q}{2m + p}.

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The regression equation for change in temperature, y, to amount of humidity in
mr_godi [17]

Answer:

Residual = 11.462

Since the residual is positive, it means it is above the regression line.

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The residual is simply the difference between the observed y-value which is gotten from the scatter plot and the predicted y-value which is gotten from regression equation line.

The predicted y-value is given as 20.7°

The regression equation for temperature change is given as;

y^ = 9.1 + 0.6h

h is the observed amount of humidity and it's given to be 23 percent or 0.23.

Thus;

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y^ = 9.238

Thus:

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6.15x = 123
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3 years ago
Can someone help please?
Vlada [557]

Answer:

Step-by-step explanation:

Vertex of the given parabola = (1, -4)

Since, vertex form of a parabola is given by,

y = (x - h)² + k

Here (h, k) is the vertex

Now substitute the coordinates (1, -4) in the equation.

y = (x - 1)²- 4 [Vertex Form]

Further solve this equation,

y = x² - 2x + 1 - 4

y = x² - 2x - 3 [Standard form]

Further write this equation in the factored form,

y = x² - 3x + x - 3

y = x(x - 3) + 1(x - 3)

y = (x + 1)(x - 3) [Factored form]

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