The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval [0, 700).

Answer:

-

Step-by-step explanation:

Forget using calculators.

Test each point by plugging its coordinates into the equation, and checking if the equation holds true.

Don't bother testing (-3,0), because you can't take the square root of -3.

Answer:

2.

Step-by-step explanation:

(-2)×4=-8

-2×4=-8

~~~~~~~~

Answer:

16 and 16 is the correct answer

Answer:

25

Step-by-step explanation:

F(x) = 2x^2- 5x-8

Let x=-3

f(-3) = 2 (-3)^2 -5(-3) -8

          =2(9) +15 -8

          =18+15-8

          =25

Answer:

Step-by-step explanation:

Garden is two times as long as it is wide.

L = 2W

Perimeter is 120 feet

2L + 2W = 120

L +W = 60

(2W) + W = 60

3W = 60

W = 20 feet

L = 2W = 40 feet

Answer:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                                     [tex]\displaystyle \lim_{x \to c} x = c[/tex]

L'Hopital's Rule

Differentiation

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

We are given the limit:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}[/tex]

When we directly plug in x = 0, we see that we would have an indeterminate form:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}[/tex]

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}[/tex]

Plugging in x = 0 again, we would get:

[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}[/tex]

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}[/tex]

Substitute in x = 0 once more:

[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}[/tex]

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

C. [tex]k[/tex] is greater than zero.

Step-by-step explanation:

We know that graph is obtained from the function of the form [tex]f(x) = a\cdot (x+k)^{1/n} + c[/tex]. According to the graph and if [tex]x + k = 0[/tex], we find that:

[tex]x = -k[/tex] (1)

[tex]x < 0[/tex] (2)

By (1) and (2):

[tex]-k < 0[/tex]

[tex]k > 0[/tex]

Hence, correct answer is C.

Answer:

Hello,

Step-by-step explanation:

[tex]\dfrac{3^{n+1}+9}{3^{n-1}+1} \\\\=\dfrac{9*(3^{n-1}+1)}{3^{n-1}+1}\\\\=9\\[/tex]

Answer: 15 cups

Step-by-step explanation:

Answer:

Step-by-step explanation:

400*e^(.09*3)

$523.97

answer is b

Answer: Option B

$523.97

Explanation:

= 400×e^(0.09×3)

= $523.97

Must click thanks and mark brainliest

Answer:

it is 1/4

Step-by-step explanation:

20/60=10/30=1/3

Answer:

20/60=1/3

Step-by-step explanation:

20/60

HCF=20,

20*1=20, 20*3=60

1/3

or,

Remove the zeros,

2/6

Divide by 2 on both,

1/3

or divide by any common factor on both and keep dividing until u cant no more

20/60=1/3

Step-by-step explanation:

Just till the number 9 upside down to make it 6 then

6+11+13=30

The sum of three odd numbers can never be even. so I did it in that way.

I HOPE THIS WILL HELP U

STAY SAFE, STAY HAPPY

Answer:

then what's the question???..

Answer:

7

Step-by-step explanation:

Answer:

= 4

Step-by-step explanation:

first lets find the value of x in 3x+2=5/9

3x+2=5/9

3x = [tex]\frac{5}{9}[/tex] -2

3x = [tex]\frac{3}{9}[/tex]

3x = [tex]\frac{1}{2}[/tex]

x = [tex]\frac{1}{2 * 3\\ }[/tex]

x = [tex]\frac{1}{6}[/tex]

[tex]\frac{1}{6}[/tex] can also be written as [tex]6^{-1}[/tex]

−3x+8

-3 ([tex]\frac{1}{6}[/tex]) +8

[tex]\frac{-3}{6}[/tex] +8

= 4

X <0 means x would be negative.

For x/y, a negative divided by a positive would give a negative answer.

A negative multiplied by a positive would result in a negative.

The answer would be B. Negative

[tex]\\ \sf\longmapsto 0.9(7x+14)=1.5-(x+2)[/tex]

[tex]\\ \sf\longmapsto 6.3x+12.6=1.5-x-2[/tex]

[tex]\\ \sf\longmapsto 63x+12.6=-x-0.5[/tex]

[tex]\\ \sf\longmapsto 63x+x=-0.5-12.6[/tex]

[tex]\\ \sf\longmapsto 64x=-13.1[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-13.1}{64}[/tex]

[tex]\\ \sf\longmapsto x=0.2[/tex]

que es eso ._ .wooooooooo .

Answer:

3(x + 8)

Step-by-step explanation:

"The product of three and the sum of a number and eight".

First, note that:

1) Product means multiply.

2) Sum means addition.

With that in mind, also note the order of operations. The order of operations is defined as PEMDAS, or:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

Also, let "a number" be denoted as the variable, x.

~

Firstly, "the sum of a number and eight": x + 8

Next, "The product of...": 3 *

Putting the two parts together will generate: 3(x + 8)

3(x + 8) is your answer.

~

9514 1404 393

Answer:

  14 minutes

Step-by-step explanation:

Let t represent the time it took Suki to pick out her pumpkin. The given relation is ...

  10t -13 = 127 . . . . . equation for minutes to carve

  10t = 140 . . . . . . . . add 13

  t = 14 . . . . . . . . . . divide by 10

It took Suki 14 minutes to pick out her pumpkin.

Answer:

x = 48

Step-by-step explanation:

Pythagorean thm:

a² + b² = c²

Given:

a = x

b = 36

c = 60

Work:

a² + b² = c²

x² + 36² = 60²

x² + 1296 = 3600

x² = 3600 - 1296

x² = 2304

√x² = √2304

x = 48

The rocket will be at the height of 450metres at 13.16secs and 6.84secs

Given the expression modeled by the height S(t)=-5t^2+100t where

t is the time taken by the rocket to take off

s is the height traveled by rocket

In order to find the height of the rocket 7 seconds after it takes off, we will substitute t = 7 into the equation

S(7) = -5(7)²+100(7)

S(7) = -5(49)+700

S(7) = -245+700

S(7) = 455metres

Hence the height of the rocket 7 seconds after it takes off is 455metres

Given that S = 450m, we can also get the time taken by the rocket at this height.

Recall that S(t)= -5t²+100t

450 = -5t²+100t

Rearrange

-5t²+100t - 450 = 0

5t²-100t + 450 = 0

Divide through by 5

t²-20t + 90 = 0

On factorizing above equation;

t= 10+√10 or t=10−√10

t = 10+3.1623 or 10 - 3.1623

t = 13.16 and 6.84secs

Hence the rocket will be at the height of 450metres at 13.16secs and 6.84secs

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Answer:

Step-by-step explanation:

A right triangle has one right angle and two acute angles.

A and B are the acute angles.

A+B =  90°

One acute angle is 45 less than twice the other acute angle.

A = 2B-45°

(2B-45°) + B = 90°

3B = 135°

B = 45°

A = 45°

[tex]\\ \sf\longmapsto \dfrac{AK}{DK}=\dfrac{CK}{BK}[/tex]

[tex]\\ \sf\longmapsto \dfrac{14}{12}=\dfrac{4x+1}{3x+3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{4x+1}{3x+3}[/tex]

[tex]\\ \sf\longmapsto 7(3x+3)=6(4x+1)[/tex]

[tex]\\ \sf\longmapsto 21x+21=24x+6[/tex]

[tex]\\ \sf\longmapsto 24x-21x=21-6[/tex]

[tex]\\ \sf\longmapsto 3x=15[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{15}{3}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

C. 44.98

Step-by-step explanation:

Hi there!

We are given the right triangle ABC, m<B=12°, and CB =44

We want to find the length of AB

We can use trigonometry to do it

Let's find the ratio in reference to angle B, as that angle is given.

In reference to angle B the opposite angle is AC, the adjacent side is CB, and the hypotenuse is AB

Now let's recall the 3 most commonly used functions:

[tex]sine=\frac{opposite}{hypoptenuse}[/tex]

[tex]cosine=\frac{adjacent}{hypotenuse}[/tex]

[tex]tangent=\frac{opposite}{adjacent}[/tex]

Let's find the cosine of angle B, as it uses CB and AB, which are the given side and the side we need to find

In that case,

cos(12)=[tex]\frac{CB}{AB}[/tex]

cos(12)=[tex]\frac{44}{AB}[/tex]

Multiply both sides by AB

[tex]AB[/tex]*cos(12)=44

Divide both sides by cos(12)

AB=[tex]\frac{44}{cos(12)}[/tex]

Now plug [tex]\frac{44}{cos(12)}[/tex] into your calculator. Make sure your calculator is on degree mode

AB≈44.98

So the answer is C

Hope this helps!

Answer: b) Surveys

When a person does not have enough time he must should take the faster and effective route in this case carlos does not have time for individual interviews or phone calls. Focus group is not used to get feedback it is to discuss about data before a item is launched. Therefore it should be survey because it is used to collect feedback from large amount of people.

Must click thanks and mark brainliest

Your answer is in the attachment.

Answer:

H0 : The variables are independent

H1 : The variables are not independent

Step-by-step explanation:

In a Chisquare test ; The null hypothesis is used to lay claim that the variables are independent, that is no relationship exists between the categorical variables in the population while the alternative hypothesis negates the null thus claiming that the variables aren't independent.

The null hypothesis, H0 : The variables are independent, A = B = C

The alternative hypothesis ; H1 : The variables are not independent, A ≠ B ≠ C

Answer:

Bonsoir,

f'(-5)=-4/3

f'(-1) =3/4

Step-by-step explanation:

f'(-5) = ?

2 points : (-6,9) and (-3,5)

f'(-5)=(9-5)/(-6-(-3))=-4/3

f'(-1) = ?

2 points : (-3,5) and (1,8)

f'(-1)=(5-8)/(-3-1)=3/4

The lines are perpendicular

The derivative at the points -5 and -1 are:

f’(-5)  = -4/3

f’(-1) = 3/4

The slope of the tangent line to the graph of a function at a point is called the derivative of the function at that point.

We consider the line on which where the x coordinate -5 lies.

It is the line with points (-3, 5) and (-6, 9).

Slope of the line =  [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{9-5}{-6+3} = \frac{-4}{3}[/tex]

f'(-5) = -4/3

We consider the line on which where the x coordinate -1 lies.

It is the line with points (-3, 5) and (1, 8).

Slope of the line =  [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{8-5}{1+3} = \frac{3}{4}[/tex]

f'(-1) = 3/4

Learn more about derivative at a point here

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#SPJ2

For this problem, you can see that a ratio exists between A, B, and C. Now you'll just have to find the constant k that satisfies this ratio using the proportional relationship formula.

After that, you can plug in the constant k to find the missing C value.

If they run 3 miles west then 8 miles north, it forms a right triangle. So just use the Pythagorean Theorum.

A^2+B^=C^2

3^2+8^3=C^2

9+64=C^2

Square root 73=C or 8.54=C (Miles)

The runner is 8.54 miles from her starting point if she plans to run straight back.

From the question, a runner jogs 3 miles west and then jogs 8 miles north.

An illustrative diagram for the journey is shown in the attachment below.

In the diagram, S is the starting point. That is, the runner jogs 3 miles west to a place R and then 8 miles north to a place E.

The cardinal points (North, East, West and South) are indicated beside the diagram.

Now, to calculate how far she is from her starting point if she plans to run straight back, we will determine the length of /ES/ in the diagram.

The diagram is a right-angled triangle and /ES/ can be determined using the Pythagorean theorem.

The Pythagorean theorem states that, in a right-angled triangle, the square of the longest side ( that is hypotenuse) equals sum of the squares of the other two sides.

In the diagram, hypotenuse = /ES/

∴ /ES/² = /SR/² + /RE/²

/SR/ = 3 miles

/RE/ =8 miles

/ES/² = 3² + 8²

/ES/² = 9 + 64

/ES/² = 73

/ES/ = [tex]\sqrt{73}[/tex]

/ES/ = 8.54 miles

Hence, the runner is 8.54 miles from her starting point if she plans to run straight back.

Learn more here: https://brainly.com/question/20327506