Mathematics College

for each problem find the instantaneous rate of change of the function at the given value ...Thank you and God Bless

Answers

Answer 1

Answer:

The instantaneous rate of change of the function at the given value is -2.

[tex]f^{\prime}(0)=-2[/tex]

Explanation:

The instantaneous rate of change of the function at point x=a can be written as;

[tex]f^{\prime}(a)=\frac{df(a)}{dx}[/tex]

For the given function;

[tex]y=2x^2-2x+2[/tex]

Then the derivative of the function is;

[tex]f^{\prime}(x)=y^{\prime}=4x-2[/tex]

substituting x=0, we have;

[tex]\begin{gathered} f^{\prime}(0)=4(0)-2 \\ f^{\prime}(0)=-2 \end{gathered}[/tex]

Therefore, the instantaneous rate of change of the function at the given value is -2.

[tex]f^{\prime}(0)=-2[/tex]

Related Questions

9. After 25 minutes, an object accelerated from O km/hr to 50 km/hr south. What was the acceleration of the object? 2 km/hr south 2 km/hr/hr south 2 km/hr/s south 2 km/hr/min south

Answers

Acceleration is the rate of change of velocity.

Acceleration = change in velocity/change in time

Acceleration = (50 - 0)/(25 - 0)

Acceleration = 2 km/min South

5 Guess my rule: X Y 1 9 IN min OUT

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1) Looking at that table, we can pick the points

(1,9) (3,23)

2) Note that every time x increases by 2 units y increases by 14

3) Considering this a linear function we can find the rule by plugging in

23-9/3-1=14/2 = 7

9=7(1)+b

9=7 +b

2 =b

So we can write the rule as y =7x+2

Jenny is designing a pen for a cow in the shape of a right triangle. Because of space limitation on the farm, the first side of the pen should measure 10 feet and form a right angle with the second side, which should be 14 feet long. How many feet of fencing does Jenny need to make the whole pen? Round to the nearest tenth.

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Answer:

Step-by-step explanation:

14 x 10 is 140.

Since a triangle is just half a square, we multiply the two sides we have and then divide it.

140 ÷ 10 = 70.

Answer = 70.

P.S If it is correct, pls give Brainliest, thanks!

Please answer correctly and explain how you got it please don't have but it would help.

Answers

Answer: Linear

Step-by-step explanation:

Each time [tex]x[/tex] increases by [tex]1[/tex], [tex]y[/tex] decreases by [tex]8[/tex]. Since the value of y changes at a constant rate, the relationship is linear.

1. What is the domain of the graph?84-8O{x | -3 SXS3)all real numbers{x | xs-3 or x 2 3}y 1-3 sy s 3)

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From the graph below, the domain is

[tex]x\colon\text{ x }\leq\text{ -3 or x }\ge\text{ 3}[/tex]

six times the sum of four and a number is 7. what is the number?

Answers

Step-by-step explanation:

6×(4 + x) = 7

24 + 6x = 7

6x = -17

x = -17/6 = -2.833333333... = -2 5/6

The cost for Albert to play 2 games of laser tag is $18. Based on this relationship, which equation can be used to determine the total cost, y, in dollars, for Albert to play any number of games, x, of laser tag?

Answers

The equation that can be used to determine the total cost, y, in dollars for Albert to play any number of games, x, is Y = 18x/2 or 9x.

What is an equation?

An equation is a mathematical statement expressing the equality that two values or expressions share.

Equations are generally represented using the equation sign (=).

The cost of 2 games of laser tag = $18

The cost of 1 game of laser tag = $9 ($18/2)

The cost of x laser tag games = $9x or 18x/2

Thus, we can represent the equation of the total cost as y = 9x.

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Suppose that R and S are points on the number line.
If RS 6 and R lies at -18, where could S be located?

Answers

Answer: Either -12 or -24

==========================================================

Explanation:

Draw a vertical number line. Plot point R at -18 which is 18 units below 0.

Then move up 6 units to arrive at -12 which is one potential location of point S. The distance from R = -18 to R = -12 is RS = 6 units.

Now go back to point R = -18. This time move down 6 units to arrive at -24 as the other possible location of S.

See the diagram below.

Two buses leave Dallas at the same time traveling in opposite directions. One bus travels at 59 mph and the other at 54 mph. How soon will they be 791 miles apart?

Answers

Let t be the time, in hours, elapsed till the buses are 791 miles apart, then we can set the following equation:

[tex]59mph\cdot t+54\text{mph}\cdot t=791\text{ miles.}[/tex]

Solving the above equation for t we get:

[tex]\begin{gathered} 113\text{ mph}\cdot t=791miles, \\ t=\frac{791}{113}\text{hours,} \\ t=7\text{ hours.} \end{gathered}[/tex]

Answer: 7 hours.

help
A) What is true about each multiple of 3 other than that it is a multiple of 3?

B) What is true about each number with a factor of 7 other than that it is a factor of 7?

Answers

Every other multiple of 3 is even.

The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7

The digits in multiples of 3 add up to a multiple of 3 (36 = 3 + 6, 111 = 1 + 1 + 1, etc.) All EVEN multiples of 3 are also a multiple of 6 (the even multiples of 3 are the 6 “count by's”).

The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7. To find out which one is a factor of 7, we should divide each of them by 7. 1/7 will be a decimal number and 7/7 = 1, which is a whole number. Thus, 7 will be a multiple of 7 and also a factor of 7.

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components.

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In 2Use the formula t=kthat gives the time for a population, with a growth rate k, to double, to answer the following que0.0031The growth model A = 6 e describes the population, A, of a country in millions, t years after 2003.a. What is the country's growth rate?

Answers

We have an exponential function for the population A(t) and we have to find the growth rate.

[tex]A=6e^{0.003t}[/tex]

This can be expressed as:

[tex]\frac{A(t+1)-A(t)}{A(t)}=\frac{A(t+1)}{A(t)}-1[/tex]

For the exponential formula we get:

[tex]\begin{gathered} \frac{A(t+1)}{A(t)}-1 \\ \frac{6e^{0.003(t+1)}}{6e^{0.003t}}-1 \\ e^{0.003(t+1-t)}-1 \\ e^{0.003\cdot1}-1 \\ 1.003-1 \\ k=0.003 \end{gathered}[/tex]

The growth rate is 0.003 or 0.3%.

We can calculate the time needed to double the population dividing ln(2) by the growth rate:

[tex]t=\frac{\ln (2)}{k}\approx\frac{0.693}{0.003}\approx231[/tex]

Answer:

a) The growth rate is 0.003 or 0.3%

b) The number of years to duplicate the population is 231 years.

Which expression is equivalent to the given expression? \frac{\left(ab^{2}\right)^{3}}{b^{5}}

Answers

The expression which is equivalent to the given expression; (ab²)³/b⁵ as given in the task content is; a³b.

Which expression is equivalent to the given expression; (ab²)³/b⁵ as in the task content?

It follows from the task content that the expression which is equivalent to; (ab²)³/b⁵ be determined.

Hence, since the given expression is; (ab²)³/b⁵.

By first applying the power of power law of indices; we have;

(ab²)³/b⁵ = a³b⁶/b⁵.

Also, by applying the quotient of powers rule of indices; we have;

a³ b^(6 - 5)

= a³b¹

= a³b

Ultimately, the expression which is equivalent to; (ab²)³/b⁵ as required in the task content is; a³b.

Answers

the fraction is info

I only need the answer
THANK YOU!!

Answers

The value of C is 7.68 units and the value of angle A and B is 23° and 66° respectively.

As we can see,

This is a right angled triangle.

We can use Pythagoras theorem to find the value of third side,

It says, Square of hypotenuse side H is equal to square of Base side B plus square of Perpendicular side.

H² = P² + B².

The value of perpendicular here is 3.

The value of base here is 7.

Putting the values,

H² = (7)²+(3)²

H² = 49 + 9

H² = 58

H = √58

H = 7.68

Now, using trigonometric ratios,

For angle B,

Sin(B) = Perpendicular/Hypotenuse = P/H

Sin(B) = 7/7.68

Sin(B) = 0.91

Sin(66°) = 0.91

The value of B in degree is 66°.

For angle A,

Sin(A) = Perpendicular/Hypotenuse = P/H

Sin(A) = 3/7.68

Sin(A) = 0.39

Sin(23°) = 0.39

The value of A in degree is 23°.

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Solve for x.
(8x - 34)
(5x + 2)°%

Answers

8x - 34 and 5x + 2 are corresponding angles and, by the Corresponding Angles Theorem, are congruent.

8x - 34 = 5x + 2
8x - 34 + 34 = 5x = 2 + 34
8x = 5x + 36
8x - 5x = 5x + 36 - 5x
3x = 36
3x/3 = 36/3
x = 12

what is the equation of.the line+that+passes through (2,8) and has a slope of 3/2?

Answers

The line that passes through the point (2, 8) and has a slope of 3/2 is given by the equation y = (3/2)x + 10

What is equation of line passing through the point (x,y)?

(Y - Y1) = m(X - X1) is an equation for a line that passes through the point (x1, y1) and has a slope of m.

The line passing through points (2, 8) and having a slope of 3/2 is now a given.

Consequently, (x1,y1) equals (2, 8) and m = 3/2.

As a result, the line's equation is (y - y1) = m(x - x1).

When you combine (x1,y1) and m, you get (y - 8) = (3/2) (x - 2)

When we expand them, we obtain (y - 8) = (3/2) (x - 2)

y = (3/2)x + 5

Consequently, the equation y = (3/2)x + 5 describes the line that passes through the points (2, 8) and has a slope of 3/2.

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What is the length of a rope if the mass of a rope is 4.25

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Using a regression calculator, the line of best fit for the given set of data is:

[tex]y=0.34121x+0.168088[/tex]

where y = mass of the rope and x = length of the rope.

To estimate the length of the rope if its mass is 4.25 kilograms, let's replace "y" in the equation above with 4.25, and then solve for x.

[tex]4.25=0.34121x+0.168088[/tex]

Subtract 0.168088 on both sides of the equation.

[tex]4.25-0.168088=0.34121x+0.168088-0.168088[/tex][tex]4.081912=0.34121x[/tex]

Then, divide both sides of the equation by 0.34121.

[tex]\frac{4.081912}{0.34121}=\frac{0.34121x}{0.34121}[/tex][tex]\begin{gathered} 11.963049=x \\ 11.96\approx x \end{gathered}[/tex]

Therefore, the length of the rope having a mass of 4.25 kilograms is approximately 11.96 meters.

A tank has 120 gallons of water and is being drained at a rate of 1/2
gallon each second. Another tank has 100 gallons of water and is being drained at a rate of 1/4
gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?

Answers

It will take 80 seconds for both tank 1 and tank 2 to have the same amount of water

Water in the tank 1 = 120 gallons

Drainage rate of tank 1 = 1/2 gallon each second

Water in tank 2 = 100 gallons

Drainage rate of tank 2 = 1/4 gallon each second

Let x represent the number of seconds it will take for both tanks to have the same amount of water

Formulating the equation we get the following:

Water in tank 1 - Drainage rate of tank 1*x = Water in tank 2 - Drainage rate of tank 2*x

120 - 1/2x = 100 - 1/4x

20 = 1/2x - 1/4x

20 = 1/4x

x = 80

So, it will take 80 seconds

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Kubin Company’s relevant range of production is 18,000 to 22,000 units. When it produces and
sells 20,000 units, its average costs per unit are as follows:
Required:
1. Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 20,000 units?
b. What is the total indirect manufacturing cost incurred to make 20,000 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 20,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the
Manufacturing Department?
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume
that the company spent $50,000 of its total fixed selling expense on advertising and the
remainder of the total fixed selling expense comprised the fixed portion of the company’s
sales representatives’ compensation.
a. When the company sells 20,000 units, what is the total direct selling expense that can be
readily traced to individual sales representatives?
b. When the company sells 20,000 units, what is the total indirect selling expense that
cannot be readily traced to individual sales representatives?
4. Are Kubin’s administrative expenses always going to be treated as indirect costs in its internal
management reports?

Answers

For 18000 units the calculated sum is $150,000.

The following are the company's production and period costs:

The product costs $ 350,000 for 20,000 units.

20,000 units = $150,000 in cost period

The product costs $ 385,000 for 22,000 units.

18,000 units each period = $ 135,000

The corporation incurs two major costs while creating an item: production costs and period costs.

Production costs are expenses directly connected to the manufacturing process. These expenses include labor, raw materials, and overhead.

While period costs are expenses incurred for the company's activities such as administrative and selling/sales charges,1. The cost of making 20,000 units is

Existing unit manufacturing costs are as follows:

Direct labor costs $7.00. Manufacturing variable overhead of $4.00 Fixed manufacturing overhead of $1.50 $ 5.00

Total product cost per unit = $7.00 + $4.00 + $1.50 + 5.00 = $17.5

So, for 20,000 units, the calculation is: 20,000 x $17.5 = $350,000

The time required to produce 20,000 units is

Each unit's cost period is as follows:

$ 3.50 in fixed selling expenses, $ 2.50 in fixed administration expenses, and $ 1.00 in variable administrative expenses.

Total period cost per unit = $ 3.5+ $ 2.5+ $ 1.00+ $ 0.5 = $ 7.5

So, for 20,000 units, the calculation is: 20,000 x $ 7.5 = $150,000

The cost of making 22,000 units is

Existing manufacturing costs per unit: $ 17.5

So, for 20,000 pieces, the cost is 22,000 x $17.5 = $ 385,000

The total period cost / unit for generating 18,000 units is $ 7.5.

So, for 18,000 units, the calculation is: 18,000 x $ 7.5 = $ 135,000

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Please explain the steps you would take to solve this derivative (gr 12 calc)

Answers

First step, derivative of the constant:

[tex]f^{\prime}(x)=\frac{1}{2}\frac{d(e^{-3x^2+tan(3x+5)})}{dx}[/tex]

Second step, the chain rule:

[tex]\begin{gathered} =\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{d(-3x^2+tan(3x+5))}{dx} \\ =\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{(-6x+sec^2(3x+5)*3)}{} \end{gathered}[/tex]

Where we applied that the derivative of tangent is the secant^2.

Hence the answer is:

[tex]\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{(-6x+3sec^2(3x+5))}{}[/tex]

Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day Explain your reasoning. Answer is $178 explain your answer thank you! 40 points if answered correctly!!

Answers

Answer:

$194.69

Step-by-step explanation:

The best way to predict the amount of tips is using this formula:

[tex]100(\frac{Tips(total)}{Customers(total)} )[/tex]

This finds the average tip per customer with all of the data, and multiplies it by 100 to get the predicted amount of tips for 100 customers.

Plugging in the data from the table gives you this equation:

[tex]100(\frac{1174}{603} )[/tex]

This equals $194.69.

Find the mean, mode, and range Mean_______ show all workRange_______show all workExplain how you find thisMode_________

Answers

To answer this question, it is a good practice to order the data in ascending order as follows:

[tex]9,\: 10,\: 10,\: 10,\: 10,\: 11,\: 11,\: 11,\: 11,\: 11,\: 11,\: 12,\: 12,\: 12,\: 12,\: 12,\: 13,\: 13,\: 13,\: 14,\: 14,\: 15,\: 15,\: 15,\: 15,\: 15,\: 15,16,17,17[/tex]

We need to check for the total number of data. In this case, we have 30 observations.

Finding the mean

To find the mean, we need to find the sum of all the observations and then divide this result by the total of observations (30). Then, we have:

[tex]\frac{9+\: 10+\: 10+10+\: 10+\: 11+\: 11+\: 11+\: 11+\: 11+\: 11+\: 12+\: 12+\: 12+\: 12+\: 12+\: 13+\: 13+\: 13+\: 14+\: 14+15+\: 15+\: 15+15+15+_{}15+16+17+17}{30}[/tex]

Then, the value for the mean is:

[tex]\text{mean}=\frac{382}{30}=12.73333333\ldots[/tex]Finding the range

The range is the result of subtracting the greatest number and the lowest number in the data:

[tex]\text{Range}=17-9=8[/tex]Finding the mode

The mode is the observation that is repeated the most (appears the most).

We can see that we have two values that appear six times in the list: 11 and 15.

Therefore, we can see that there is not a unique element, so there is no mode.

In summary, we have:

• Mean = 12.73333...

• Range = 8

• Mode = None.

cos(theta) = - 3/4 and is in the 3rd quadrant, find the following:

Answers

Answer:

[tex]\begin{gathered} sin(\theta)=\frac{-\sqrt{7}}{4} \\ cos(\theta)=-\frac{3}{4} \\ tan(\theta)=\frac{\sqrt{7}}{3} \\ csc(\theta)=-\frac{4}{\sqrt{7}} \\ sec(\theta)=-\frac{4}{3} \\ cot(\theta)=\frac{3}{\sqrt{7}} \end{gathered}[/tex]

Step-by-step explanation:

If theta is in the third quadrant, draw the diagram to easily identify the other trigonometric relations:

Solve for the missing leg of the triangle, using the Pythagorean theorem:

[tex]\begin{gathered} \text{ adjacent}^2+\text{ opposite}^2=\text{ hypotenuse}^2 \\ -3^2+\text{ opposite}^2=4^2 \\ \text{ opposite=}\sqrt{16-9} \\ \text{ opposite=}\sqrt{7} \end{gathered}[/tex]

Therefore, for the trigonometric relationships:

[tex]\begin{gathered} \text{ sin\lparen}\theta)=\frac{opposite}{hypotenuse} \\ \text{ cos\lparen}\theta)=\frac{adjacent}{hypotenuse} \\ tan(\theta)=\frac{opposite}{adjacent} \\ csc(\theta)=\frac{hypotenuse}{opposite} \\ sec(\theta)=\frac{hypotenuse}{adjacent} \\ cot(\theta)=\frac{adjacent}{opposite} \end{gathered}[/tex]

Now, substitute and solve for the relations:

what is 4x-2=3(x-3)

Answers

4x -2 = 3(x-3)

4x - 2 = 3x - 9

bring like terms together

4x-3x = -9 +2

x = -7

eekkea dasd. dkksalaq'w

Answers

? You’re ok ?? I hope so

Answer: ooja kopa weqe

Daniyar paid his April FlashCard bill in full. His May bill shows an average daily balance of $270.31 and a monthly periodic rate of 1.65%. What is the finance charge on Daniyar's May statement?

Answers

The finance charge on Daniyar's May statement is $4.45.

What is finance charge?

The cost of consumer credit expressed as a dollar amount is the financing charge. It includes any fee imposed by the creditor as an incident to or a requirement of the credit extension that is directly or indirectly payable by the customer. It excludes any fee that would be paid in an equivalent cash transaction.

The finance charge is equal to the product of the average daily balance and the monthly periodic rate.

So,

$270.31 x 1.65%

= $270.31 x 0.0165

= $4.45

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which anwser shows the best approximation of [tex] \sqrt{42 } + \sqrt{63} [/tex]1. 10.22. 14.43. 14.84. 13.8

Answers

[tex]\begin{gathered} \text{ }\sqrt[]{42}\text{ + }\sqrt[]{63} \\ =\sqrt[]{42}\text{ = 6.4807} \\ \sqrt[]{63}=7.9373 \\ \sqrt[]{42}\text{ + }\sqrt[]{63}\text{ = 6.4807 + }7.9373 \\ =14.4180 \\ To\text{ 1 decimal place, we have 14.4} \\ \text{ The answer is 14.4} \end{gathered}[/tex]

how much money must be loaned to receive 15,000 if the money is loaned for 5 years at 12% interest

Answers

Step-by-step explanation:

i don't know if this is right

Rewrite the following expression as a single logarithm: 2log(x+3) + 3log(x - 7) - Slog(x - 2) + 2log(x) 3 log (x+3)(x-7) 12(3-2) 5 A. 5 log (x + 3)?(x - 2) (1-7712 B. 3 (1 +31°160 – 7) log O c. (x-2)-5-1 p2(x+3)*(1-73 log OD. (r-2) 5

Answers

Let's look at some logarithm properties,

[tex]\begin{gathered} p\log _b(M)=\log _b(M^p) \\ \log _b(\frac{M}{N})=\log _bM-\log _bN \\ \log _b(MN)=\log _bM+\log _bN \end{gathered}[/tex]

We will use this properties to simplify and write the expression as a single logarithm.

The steps are shown below:

[tex]\begin{gathered} 2\log (x+3)+3\log (x-7)-5\log (x-2)+2\log (x) \\ =\log (x+3)^2+\log (x-7)^3-\log (x-2)^5+\log (x)^2 \\ =\log (\frac{(x+3)^2(x-7)^3(x)^2}{(x-2)^5}) \end{gathered}[/tex]

The expression, as a single logarithm, is,

[tex]\log (\frac{(x+3)^2(x-7)^3(x)^2}{(x-2)^5})[/tex]

From the answer choices, the correct answer is D.

Answer

PLEASE HURRY ASAP PLEASE HURRY

The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?

Answers

The stock witness an total average decrease in stock of $80 in the 8 weeks

How to determine the total average decrease in the stock

The given parameters are:

Average decrease per week = 10 dollars

Also, we have the number of weeks to be

Number of Weeks = 8 weeks

So, the total average decrease in the stock is calculated using the following equation

Total = Average decrease per week x Number of weeks

Substitute the known values in the above equation

So, we have the following equation

Total = 10 x 8

Evaluate the products in the above equation

So, we have the following equation

Total = 80

Hence, the total average decrease in the stock is $80