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2 years ago

Calculate the following derivative if f(x) = sin(x) and g(x) = 5x + 4.

Mathematics

1 answer:

gayaneshka [121]2 years ago

8 0

Answer:

Rewrite the function as an equation.

−

Use the slope-intercept form to find the slope and y-intercept.

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The slope-intercept form is

, where

is the slope and

is the y-intercept.

Find the values of

and

using the form

−

The slope of the line is the value of

, and the y-intercept is the value of

Slope:

y-intercept:

−

Any line can be graphed using two points. Select two

values, and plug them into the equation to find the corresponding

values.

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Choose

to substitute in for

to find the ordered pair.

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Replace the variable

with

in the expression.

(

)

(

)

−

Simplify the result.

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The

value at

Choose

to substitute in for

to find the ordered pair.

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Replace the variable

with

in the expression.

(

)

(

)

−

Simplify the result.

Tap for more steps...

−

The

value at

−

Create a table of the

and

values.

−

Graph the line using the slope and the y-intercept, or the points.

Slope:

y-intercept:

−

Step-by-step explanation:

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A cylindrical water bottle has a diameter of 5 in. and a height of 9 in. What is the capacity of the water bottle in cubic inche

VikaD [51]

The answer will be 388.6 because you will use the formula V=pi.r^2.h.
pi we know is 3.14 we also know that radius is half the diameter so half of 5 is 2.5 and the height is 9 so here is what we have so far. V=3.14x2.5^2x9.
2.5x2.5=13.75 13.75x3.14=43.175 43.175x9=388.575 and if we round that it will be 388.6 so your answer is 388.6

3 0

3 years ago

Graficar con la tabla de valores Y= -2x+1

prohojiy [21]

Step-by-step explanation:

Slope: −2

y-intercept: (0,1)

Answer:

8 0

3 years ago

Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

Question 1:

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

Question 2:

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

8 0

3 years ago

The graph of f(x) is shown. which graph represents g(x) = f(2x)

Temka [501]

A because its twice bigger than the real one

5 0

3 years ago

Read 2 more answers

8x^2+23=823 whats going to be the answer I got 0 am I right?

Naily [24]

1) No; you are incorrect. "0" is NOT a solution.

Plug in "0" for "x" ;

8*0² + 23 =? 823? ;

8*0 + 23 =? 823? ;

0 + 23 = ? 823 ? ; No! ; "0 + 23 = 23 " ; NOT "823" .
_________________________________________________
2) The answers: x = 10, -10 ; or, write as: x = ± 10 .
_________________________________________________

To solve:

GIven: 8x² + 23 = 823 ;

Subtract "23" from EACH SIDE of the equation:
_____________________________________________
8x² + 23 - 23 = 823 - 23 ;
to get:
8x² = 800 ;

Now, divide EACH SIDE of the equation by "8" ;

8x² / 8 = 800 / 8 ;

to get: x² = 100 ;

Take the "square root" of EACH SIDE of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;

√(x²) = √(100) ;

x = ± 10 .

The answers: x = 10, -10 ; or, write as: x = ± 10 .
_____________________________________________________

5 0

3 years ago