About how much farther away from the Sun is Earth than Mercury? Write your answer in standard form and scientific notation.

The approximate distance from each planet to the Sun is given below.
Mercury: 35,983,610
Earth: 92,957,100
Neptune: 2,798,842,000

No, it is not.

Hope it helped! :)

we are given

[tex]f(x)=e^x sin(x)[/tex]

(a)

Firstly, we will find critical numbers

so, we will find derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

now, we can set it to 0

and then we can solve for x

we get

[tex]x=\frac{3\pi }{4} ,x=\frac{7\pi }{4}[/tex]

now, we can draw a number line and then locate these values

and then we can find sign of derivative on each intervals

increasing intervals:

[tex][0,\frac{3\pi}{4} )U(\frac{7\pi}{4} , 2\pi][/tex]

Decreasing interval:

[tex](\frac{3\pi}{4} ,\frac{7\pi}{4} )[/tex]

(b)

Local maxima:

It is the value of x where function changes from increasing to decreasing

so, local maxima is at

[tex]x=\frac{3\pi}{4}[/tex]

Local minima:

It is the value of x where function changes from decreasing to increasing

so, local minima is at

[tex]x=\frac{7\pi}{4}[/tex]

now, we will plug critical numbers and end values into original function

and we get

At x=0:

[tex]f(0)=e^0 sin(0)[/tex]

[tex]f(0)=0[/tex]

At [tex]x=\frac{3\pi}{4}[/tex]:

[tex]f(\frac{3\pi}{4})=e^{\frac{3\pi}{4}} sin(\frac{3\pi}{4})[/tex]

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

At [tex]x=\frac{7\pi}{4}[/tex]:

[tex]f(\frac{7\pi}{4})=e^{\frac{7\pi}{4}} sin(\frac{7\pi}{4})[/tex]

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

At [tex]x=2\pi [/tex]:

[tex]f(2\pi)=e^{2\pi} sin(2\pi )[/tex]

[tex]f(2\pi )=0[/tex]

Global maxima:

It is the largest value among them

so, we get

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

Global minima:

It is the largest value among them

so, we get

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

(c)

now, we can find second derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

[tex]f''(x)=\frac{d}{dx}\left(e^x\sin \left(x\right)+e^x\cos \left(x\right)\right)[/tex]

[tex]=\frac{d}{dx}\left(e^x\sin \left(x\right)\right)+\frac{d}{dx}\left(e^x\cos \left(x\right)\right)[/tex]

[tex]=e^x\sin \left(x\right)+\cos \left(x\right)e^x+e^x\cos \left(x\right)-e^x\sin \left(x\right)[/tex]

[tex]f''(x)=2e^x\cos \left(x\right)[/tex]

now, we can set it to 0

and then we can solve for x

[tex]f''(x)=2e^x\cos \left(x\right)=0[/tex]

so, we get

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

now, we  can draw number line and locate these values

and then we can find sign of second derivative on each intervals

concave up intervals:

[tex][0,\frac{\pi}{2})U(\frac{3\pi}{2}, 2\pi][/tex]

Concave down intervals:

[tex](\frac{\pi}{2} ,\frac{3\pi}{2})[/tex]

Turning points:

All values of x for which concavity changes

so, we get turning points at

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

fff

[tex]f(x) = e^x sin (x)[/tex]

To find increasing and decreasing intervals we take derivative

[tex]f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)[/tex]

Now we set the derivative =0  and solve for x

[tex]e^x(sinx+cosx)=0[/tex]

sinx + cosx =0

divide whole equation by cos x

[tex]\frac{sinx}{cosx} + \frac{cosx}{cosx} =0[/tex]

tanx +1 =0

tanx = 1

[tex]x=\frac{3\pi }{4}[/tex] and  [tex]x=\frac{7\pi}{4}[/tex]

Now we pick a number between 0 to  [tex]\frac{3\pi }{4}[/tex]

Lets pick  [tex]\frac{\pi }{2}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))[/tex]

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, [tex]x=\frac{3\pi }{4}[/tex])

Now we pick a number between   [tex]\frac{7\pi}{4}[/tex] to 2pi

Lets pick  [tex]\frac{11\pi}{6}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))[/tex]

= 116 is positive

So the graph of f(x) is increasing on the interval [tex](\frac{7\pi }{4}, 2\pi)[/tex]

Increasing interval is [tex](0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)[/tex]

Decreasing interval is [tex](\frac{3\pi}{4}, \frac{7\pi}{4})[/tex]

(b)

The graph of f(x) increases and reaches a local maximum at [tex]x=\frac{3\pi}{4}[/tex]

The graph of f(x) decreases and reaches a local minimum at [tex]x=\frac{7\pi}{4}[/tex]

(c)

f(0) = 0

[tex]f(2\pi)=0[/tex]

[tex]f(\frac{3\pi }{4})=7.46[/tex]

[tex]f(\frac{7\pi}{4})=-172.64[/tex]

Here global maximum at [tex]x=\frac{3\pi}{4}[/tex]

Here global minimum at [tex]x=\frac{7\pi}{4}[/tex]

Since the ratio is as simple as 1:2, just double each Euro value.

1:2, 2:4, 5:10, 10:20.

Answer:

$4,$10,$20.

Step-by-step explanation:

y=-1x-6 is your answer

b represents rate of change

Answer:

rate of change

Step-by-step explanation:

Answer:

The answer is 8.

Step-by-step explanation:

If is

[tex]\sqrt{r^{64}}=\sqrt{r^{32\cdot2}}=\sqrt{(r^{32})^2}=r^{32}[/tex]

Used:

[tex](a^n)^m=a^{nm}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]

If is

[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]

2(x+1) = 2x+5

2x + 2 = 2x = 5

2 ≠ 5

Answer

B. No solution

100th customer is your answer

Find the first number that shows up on both answers when they are added

Add 20 each time for $5 gift card:

20, 40, 60, 80, 100

Add 50 each time for $10 gift card:

50, 100

------------------------------------------------------------------------------------------------------------

As seen above, the first number that shows up on both is 100, therefore, 100 is your answer

hope this helps

9*54=486  

10x50=500

So, either 450 or 500.

Positive. The distance from a number to zero is always positive

Positive. The distance from a number to zero is always positive . hope that helps

Do you need all the coordinates or just A' and B'

Answer:

18 rolls of nickles

Step-by-step explanation:

One roll of dimes would be the same value as 2 rolls of nickles. If she has 9 rolls of dimes, she would have 18 rolls of nickles.

Dont forget to thanks and rate!

Alysha has 13 nickel rolls.

Let x be the number of dime rolls and y be the number of nickel rolls.

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.

Each dime roll has 50 dimes, then x dime rolls are worth 50×10×x=500x cents or $5x.

Each nickel roll has 40 nickels, and then y nickel rolls are worth 40×5×y=200y cents or $2y.

A. The total value of Alysha's rolls is 500x+200y cents or $(5x+2y).

If the total value of the coins is $71 and she has 9 rolls of dimes, then x = 9 and 5×9+2y=71.

⇒45+2y=71

⇒2y=71-45

⇒2y=26

⇒y=13

Therefore, Alysha has 13 nickel rolls.

To learn more about the linear equation visit:

https://brainly.com/question/19549073.

#SPJ2

Alysha has a collection of dime and nickel rolls that she'd like to take to the bank. Each dime roll has 50 dimes and each nickel roll has 40 nickels.

a) Write an equation to represent the total value of

b) If the total value of the coins is $71 and she has 9 rolls of dimes, how many does she have?

$1.25x + $10 + $15 (less than or equal to) $50

Answer:

So, with the reaming 25 dollars she can play at max 20 games.

Step-by-step explanation:

Given that

Amount Courtney has to spend = $ 50

Amount Spent on Admission = $ 10

Amount Spent on Snacks = $ 15

Price of a Game at Share = $ 1.25

Now, lets find the total amount spent by her already

Amount Spent = 50 - 10 - 15 = $ 25

Suppos x represent the number of games so, we can represent the remaining amount and in term of games that can be purchased by using it

[tex]1.25x\leq25[/tex]

the above inequality can be simplified as follows

[tex]x\leq\frac{25}{1.25}[/tex]

[tex]x\leq20[/tex]

So, with the reaming 25 dollars she can play at max 20 games.

x=16/3 or 5.33333333

Answer:

Step-by-step explanation:

multiply by 3 the whole equation

6×3 = (x)×3  + (2/3) ×(3)

18 =3x + 2

subtracting 2 both sides

18-2 = 3x +2-2

16= 3x

dividing by 3 both sides

16/3 = 3x / 3

16/3 = x

Answer:

6

Step-by-step explanation:

The approximate distance in km between her house and her job is 9 km.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles

It is given that :

The distance on a map between a student’s house and her job is 6 cm.

also, on the same map, the distance between her house and her school is 8 cm.

The scale of the map = 8cm : 12km

Therefore, Distance between the house and the job = (12 x 6) / 8 = 9m

To learn more about scale drawings, please check: brainly.com/question/26388230

#SPJ5

I think it is 25 sorry if im wrong

Answer:

There were 25 guest in Dan's party.

Step-by-step explanation:

We are given the following information in the question:

Number of classmates came to Dan’s birthday party = 5

Number of friends from his summer camp = Number of classmates came to Dan’s birthday party = 5

Number of relatives in Dan's party =

Let x be the number of relatives, then,

[tex]\displaystyle\frac{x}{3} = 5\\\\x = 15[/tex]

Total number of guest in Dan's party =

[tex]\text{Number of classmates came to Dan’s birthday party} +\\ \text{Number of friends from his summer camp } + \\\text{Number of relatives}\\= 5 + 5 + 15\\=25[/tex]

Hence, there were 25 guest in Dan's party.

Hey there!

The slope of the equation is -4.

This is because each time x increases by 1, y increases by -4.

You can typically find the slope right in front of the x value in equations that look like this one.

Hope this helps!

[tex]|\Omega|=20\cdot19=380\\|A|=4\cdot12=48\\\\P(A)=\dfrac{48}{380}\approx0.13[/tex]

Solve:

(3x    −   4)(2x^2     +      2x    −   1)

Simplify:

(3x     −      4)(2x^2      +       2x     −    1)

=      (3x     +    −4)(2x^2     +        2x        +        −1)

=   (3x)(2x^2)    +   (3x)(2x)   +   (3x)(−1)    +    (−4)(2x2)   +    (−4)(2x)     +     (−4)(−1)

=      6x^3    +   6x^2    −   3x    −  8x^2   −   8x   +   4

Answer   =      6x^3    −   2x^2     −   11x   +   4

Hope that helps!!!!                                         : )

Final answer:

The product of (3x - 4) and (2x² + 2x - 1) is calculated by multiplying each term in the first polynomial by each term in the second and combining like terms, resulting in the final expression 6x³ - 2x² - 11x + 4.

Explanation:

The product of the polynomials (3x − 4) and (2x2 + 2x − 1) is obtained by applying the distributive property, otherwise known as FOIL (First, Outer, Inner, Last) method in this context. Each term in the first polynomial is multiplied by each term in the second polynomial and then the results are summed together. The step-by-step calculation is as follows:

Multiply the First terms: (3x) × (2x2) = 6x3.

Multiply the Outer terms: (3x) × (2x) = 6x2.

Multiply the Inner terms: (− 4) × (2x2) = − 8x2.

Multiply the Last terms: (− 4) × (− 1) = 4.

Once these calculations are done, we combine like terms:

6x3 (no like terms to combine here)

6x2 − 8x2 = -2x2

(3x) × (2x) = 6x2 (already accounted for in the previous step)

(3x) × (−1) = -3x

(− 4) × (2x) = − 8x

4 (no like terms to combine here)

So, adding all these up, we get:

6x3 − 2x2 − 3x − 8x + 4

Combining the x terms, we have:

− 3x − 8x = − 11x, so the final answer is:

6x3 − 2x2 − 11x + 4

You can solve this using long division. The answer should end up being 2.3.

Answer:

2.3

Step-by-step:

[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]

Answer:

For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x

Step-by-step explanation:

step 1: 3(x - 5)² - 2 + 4x

step 2: 3(x - 5)(x - 5) - 2 + 4x

For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x

d. distribute the 3 to each term in the parentheses by multiplying.

First, simplify within parentheses: [tex]\(3(2x - 6 - x)^2 = 3(x - 6)^2\)[/tex]. Next, expand the exponent to get [tex]\(3x^2 - 36x + 108\)[/tex].

Sure, let's break down the steps:

Given expression:

[tex]\[ 3(2x - 6 - x)^2 - 24x \][/tex]

Step 1: Simplify within the parentheses.

[tex]\[ 3(2x - 6 - x)^2 = 3(x - 6)^2 \][/tex]

Step 2: Expand the exponent.

[tex]\[ 3(x - 6)^2 = 3(x^2 - 12x + 36) \][/tex]

[tex]\[ = 3x^2 - 36x + 108 \][/tex]

Now, combine this result with the given expression:

[tex]\[ 3x^2 - 36x + 108 - 24x \][/tex]

Step 3: Combine like terms.

[tex]\[ = 3x^2 - 60x + 108 \][/tex]

So, the simplified expression is:

[tex]\[ 3x^2 - 60x + 108 \][/tex]

The correct question is:

sharina simplified the expression 3(2x – 6 – x 1)^2 – 2 4x. in step 1 she simplified within the parentheses. in step 2 she expanded the exponent. which is a possible next step?

a. simplify the expression by adding and subtracting from left to right.

b. combine like terms within the parentheses.

c. combine all x-terms.

d. distribute the 3 to each term in the parentheses by multiplying.

the height of (my favorite animal if i might add) an adult male giraffe can grow up to 16-20 feet while the females grow up to 15 feet

Answer:

Statistical question.

Step-by-step explanation:

Given question

Is in, how tall are giraffes?

Statistical question is that type of question which have more than one possible answers. The answer of statistical question is the collection of various  points of data. The answer of statistical question depends on variety and situations. The answer of statistical question may be range . Answer of statistical question are more than one.

Non statistical question is that type of question which have only one answer.

For example, the value of 2+2

Answer: 2+2=4

It has only one answer .Therefore , it is non statistical question.

Given question is a statistical question because the height of all giraffes are not same . Height of some giraffes are same and some giraffes have same height. The height  of female giraffes are smaller than the height of male giraffes.

The range of  height of male giraffes lies between 16 feet to 20 feet.

Step 1 = Distributive Property ( multiplying the 2 by each term in parenthesis)

Step 2 = Addition Property ( adding like terms)

Step 3 = Addition Property (adding 34x to each side)

Step 4 = Division Property. ( dividing both sides by 17)

the distance from home would not change while he was stopped, so it would be a flat line.  the two possibilities are  B and C  or D and E.  He stopped for a soda then played catch (which would also be a flat line since he would be the same distance from home) so it must be B and C

Choice A

Answer:

A

Step-by-step explanation:

because D and E is when he's playing catch and right after he went home.

Sine, Cosine, Tangent, Cosecant (opposite of Sine), Secant (opposite of Cosine), and Cotangent (opposite of Tangent)

Hello, Jssoyg! I've solved the problem for you below. I hope it helps.

Slope equation is[tex]\frac{y2 - y1}{x2 - x1}[/tex]. The two points are (0,1) and (4,2), so the equation becomes [tex]\frac{2 - 1}{4 - 0} = \frac{1}{4}[/tex]. We now know that the slope is 1/4, so now let's write it in the [tex]y = mx + b[/tex] format. Plug in the m, x, and y values:[tex]2 = 4*\frac{1}{4} + b[/tex].

This becomes [tex]2 = 1 + b[/tex] which means b = 1.

Your answer is y = 1/4x + 1. Hope this was helpful. :D

Answer: The correct reason for [tex]\angle4\cong \angle7[/tex] is property of corresponding angles and the reason for [tex]\angle4+\angle6=180[/tex] is substitute [tex]\angle7=\angle4[/tex] and the third error is the forget the property that the sum of consecutive interior angles is 180.

Explanation:

It is given that m is parallel to n.

When  two parallel lines intersected by a transversal eight angles are produced as shown in the given figure, where m and n are parallel and l is the transversal line.

In this case corresponding angles are congruent. Example [tex]\angle1\cong \angle5[/tex],[tex]\angle2\cong \angle6[/tex] etc.

So, [tex]\angle4\cong \angle7[/tex] by the property of corresponding angles.

[tex]\angle7+\angle6=180[/tex] because these are supplementary angles.

Substitute [tex]\angle7=\angle4[/tex]

[tex]\angle4+\angle6=180[/tex]

So, the correct reason is substitution.

Hence proved [tex]\angle4+\angle6=180[/tex]

The third error is the forget the property that the sum of one side interior angles is 180. Since the alternate interior angles are congruent therefore the consecutive interior angles are supplementary angles around the sum of consecutive interior angles is 180 degree.

with the distributive property of multiplication you can take ba+ca and rewrite it as a(b+c)=ab+ac=ba+ca