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Given:

[tex]f(y)=e^{9y}+e^{-9y}[/tex]

To find:

The f'(y).

Solution:

Chain rule of differentiation:

[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]

Differentiation of exponential:

[tex]\dfrac{d}{dx}e^x=e^x[/tex]

We have,

[tex]f(y)=e^{9y}+e^{-9y}[/tex]

Differentiate with respect to y.

[tex]f'(y)=e^{9y}\dfrac{d}{dx}(9y)+e^{-9y}\dfrac{d}{dx}(-9y)[/tex]

[tex]f'(y)=e^{9y}\cdot 9(1)+e^{-9y}\cdot (-9)(1)[/tex]

[tex]f'(y)=9e^{9y}-9e^{-9y}[/tex]

Therefore, the differentiation of the given function is [tex]f'(y)=9e^{9y}-9e^{-9y}[/tex].

x = -2

−12x−2(x+9)=5(x+4)

Use the distributive property to multiply −2 by x+9.

−12x−2x−18=5(x+4)

Combine −12x and −2x to get −14x.

−14x−18=5(x+4)

Use the distributive property to multiply 5 by x+4.

−14x−18=5x+20

Subtract 5x from both sides.

−14x−18−5x=20

Combine −14x and −5x to get −19x.

−19x−18=20

Add 18 to both sides.

−19x=20+18

Add 20 and 18 to get 38.

−19x=38

Divide both sides by −19.

x=  

−19

38

​

Divide 38 by −19 to get −2.

x=−2

The required simplified value of x for the given equation is -2/19.

To determine the value of x that makes equation -12x - 2(x + 9) = 5(x + 4) true.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

-12x - 2(x + 9) = 5(x + 4)
-12x -2x  - 18 = 5x + 20
-14x - 18 = 5x  + 20
-14x - 5x = 20 - 18
-19x  = 2
x = -2/19

Thus, the required simplified value of x for the given equations is -2/19.

Learn more about simplification here: https://brainly.com/question/12501526

#SPJ2

Answer:

14.1

Step-by-step explanation:

[tex]\frac{\pi *angle*radius}{180}[/tex] here is a formula for finding the answer for the future

We know that the angle is 54 degrees and the radius is 15 units

So now that we have the formula we can plug in the numbers which would like this:

Calculate: 14.1371669412

Round to the nearest tenth = 14.1

Hope this helps :)

Answer:

f has no critical points.

Step-by-step explanation:

We are given:

[tex]f(x)=\cos(x)+2x[/tex]

A function has critical points whenever its derivative equals 0 or is undefined.

Differentiate the function:

[tex]f'(x)=-\sin(x)+2[/tex]

Since this will never be undefined, solve for its zeros:

[tex]0=-\sin(x)+2[/tex]

Hence:

[tex]\displaystyle \sin(x)=2[/tex]

Recall that the value of sine is always between -1 and 1.

Thus, no real solutions exist.

Therefore, f has no critical points.

Answer:

...

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

9 x 9 =81

88-81=7

There will be 7 muffins in the small box.

Answer:

438.501cm^3

Step-by-step explanation:

Given data

Height of can= 12cm

Radius= 3.5cm

The capacity of the can is expressed as

V= πr^2h

V= 3.14*3.5^2* 12

V= 3.14*12.25*12

V= 461.58cm^3

Hence the capacity is 461.58cm^3

We are also given that the juice amount to 95% of the capacity of the can

95/100*461.58= x

0.95*461.58=x

x=438.501cm^3

This means that the volume of the juice is 438.501cm^3

Answer:

72 ft^2

Step-by-step explanation:

A = bh

A = 12 ft * 6 ft

A = 72 ft^2

Answer:

72

Step-by-step explanation:

you have to do base times height

You can rule out both EGF and GEF because they are representing another segment of the graph.

The answer should be DGE. If you use DGE to draw a triangle starting from the first letter (D) and then go to E and then G, then E will be in the middle.

I was taught that the middle letter of any sequence of letters is the angle of said sequence because line DG and line GE connect to form it.

Answer:it is 50. Degrees

Step-by-step explanation:

High

Temperature

(degrees)

50°

Number of

Water Bottles

Sold

10

20

25

30

25

85°

85

90°

100°

Does the table showa proportional relationship? How do you know?

Answer:

a) El submarino se encuentra a una profundidad de 26 metros una hora después de haber comenzado el ascenso.

b) Al submarino le falta 1 hora y 5 minutos para llegar a la superficie.

Step-by-step explanation:

a) De acuerdo con el enunciado, la cantidad de metros ascendidos por el submarino es directamente proporcional al tiempo, entonces la profundidad del submarino a la hora de haber comenzado el ascenso se obtiene mediante la siguiente relación lineal:

[tex]h = 50\,m - \frac{2\,m}{5\,min}\times 60\,min[/tex]

[tex]h = 26\,m[/tex]

El submarino se encuentra a una profundidad de 26 metros una hora después de haber comenzado el ascenso.

b) En primer lugar, calculamos el tiempo total del viaje mediante la siguiente relación:

[tex]\frac{2\,m}{5\,min} = \frac{50\,m}{t}[/tex]

[tex]t = 50\,m\times \frac{5\,min}{2\,m}[/tex]

[tex]t = 125\,min[/tex] ([tex]2\,h\,5\,min[/tex])

El tiempo faltante para alcanzar la superficie se calcula mediante la siguiente sustracción:

[tex]\Delta t = 125\,min - 60\,min[/tex]

[tex]\Delta t = 65\,min[/tex] ([tex]1\,h\,5\,min[/tex])

Al submarino le falta 1 hora y 5 minutos para llegar a la superficie.

Answer:

75o

Step-by-step explanation:

2x+5 = 155 (parallel lines)

x=(155-5)/2=75 deg

Answer:

- 3

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

[tex]\frac{h(b)-h(a)}{b-a}[/tex]

Here [ a, b ] = [ - 1, 5 ] , then

h(b) = h(5) = - 5² +  5 + 4 = - 25 + 9 = - 16

h(a) = h(- 1) = - (- 1)² + (- 1) + 4 = - 1 - 1 + 4 = 2

average rate of change = [tex]\frac{-16-2}{5-(-1)}[/tex] = [tex]\frac{-18}{6}[/tex] = - 3

Answer:

1000 m

Step-by-step explanation:

Tom's distance = 400 m

Sophie's distance = 600 m

Hence. Distance per day = 600 - 400 = 200 m per days

In 5 days ;

200 m * 5 = 1000 m

Sophie travels 1000 m more

Answer:

Let's make both of them have a common denominator since we can't just identify by the looks of it.

2 x 4 =  8

          ___

5 x 4 = 20

11/20 > 8/20

11/20 is bigger.

Respuesta:

2x - 0.5x = 30

x = 20

Explicación paso a paso:

Llamemos "x" a la incógnita, el número desconocido.

Cuando nos referimos al doble de un número, es lo mismo que 2x.

Cuando nos referimos a la mitad de un número, es lo mismo que 0.5 x.

Consideremos que al doble de un número (2x) se le resta su mitad 0.5x) y se obtiene 30. La ecuación resultante es:

2x - 0.5x = 30

1.5x = 30

x = 30/1.5 = 20

Answer:

14

Step-by-step explanation:

You need to count by 4´s. So:

4, 8, 12, 16, 20.

3, 6, 9, 12, 14.

I lined them up for you to understand it easier

Answer:

this is the answer Hope's it helps

Answer:

He bought about 176 ounces or 22 cups, or 5.2 liters.

Step-by-step explanation:

1.) 4 * 28 = 112

2.) 112 + 64 = 176 (answer in ounces)

3.) 8 ounces in a cup

4.) 176 ÷ 8 = 22 (answer in cups)

5.) About 4.227 cups in a liter

6.) 22 ÷ 4.227 = 5.204636858

7.) Round to the nearest tenth = 5.2 (answer in liters)

Answer:

216 cm³

Step-by-step explanation:

1/3x + 63 = 5/8x

subtract 1/3x from each side; (1/3x = 8/24x  and  5/8x = 15/24x)

63 = 7/24x

7x = 63(24)

7x = 1512

x = 216

[tex]n^2 +6n-27 = n^2+6n-27+0\\~\\n^2+6n-27+0 = n^2+6n-27+(3n-3n) \\~\\n^2+6n-27+(3n-3n) = n^2+9n-3n-27\\~\\n^2+9n-3n-27 = n\cdot(n+9)-3\cdot(n+9) \\~\\n\cdot(n+9)-3\cdot(n+9) = (n+9)(n-3)[/tex]

The other side is n-3

Answer:

x = 40

Step-by-step explanation:

Both angles are opposites and will therefore have the same measurements.

Set your formula up as

142 = 3x + 22

142 - 22 = 3x

120 = 3x

120/3 = x

40 = x

You can also test this by placing 40 in place of x in your formula to check your work

3 * 40 + 22 = 142

Answer:

(x+5)²+(y+5)²=18

Step-by-step explanation:

r=√(-8+5)²+(-2+5)²=√(-3)²+(3)²=√9+9

=√18

the equation is :

(x+5)²+(y+5)²=18

Answer:

312ft

Step-by-step explanation:

Answer: the answer is 0.98.

Step-by-step explanation:

the equation 8/100 + 9/10 = 0.98.

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