Evaluate the difference quotient for the given function.

f(t) = g(t) h(t) , where g(t) = cos(t) and h(t) =sin(t)

Answers

Answer 1

Assuming you mean f(t) = g(t) × h(t), notice that

f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)

Then the difference quotient of f is

[tex]\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}[/tex]

Recall the angle sum identity for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

Then we can write the difference quotient as

[tex]\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}[/tex]

or

[tex]\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}[/tex]

(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)


Related Questions

Pls help I’m failing do it on paper and put it in the answer box

Answers

Step-by-step explanation:

there is no mathematical problem to solve.

just follow the instructions as given.

this is an exercise for you to get a feeling about what is what. it is imperative that you do it.

there is really nothing to solve.

remember, that a positive slope means the line goes up (from left to right), and a negative slope means the line goes down (again from left to right).

and I am sure you know what vertical and horizontal means.

A nut mixture of peanuts and macadamia nuts at a small fair is $1.00 per pound of peanuts and $3.26 per pound of macadamia nuts. Over the
entire day, 131 pounds of the nut mixture were sold for $248.52. If p is the number peanuts and n is the number of macadamia nuts, then the
system of equations that models this scenario is:

p+n=131
P+3.26n = 248.52

ANSWER CHOICES:

(Please help it would mean everything to me. I’d give brainliest <3)

Answers

Answer:

D

Step-by-step explanation:

You can infer to the solution of this problem by looking at the choices. Hope this helped :)

7x+27x+2 from -5x^2-2x
ADDING AND SUBTRACTING POLYNOMIALS

Answers

Answer:

7x+27x=34x

34x+2-(-5×^2)-2x

34x+2+5x^2-2x

34x+2x=36x

36x+2+5x^2

Find the value of x.
x=__ (simplify your answer. Type an exact answer isn’t radicals as needed.)

Answers

[tex] {5}^{2} + {x}^{2} = {8}^{2} [/tex]

[tex]25 + {x}^{2} = 64[/tex]

Subtract both sides 25

[tex]25 - 25 + {x}^{2} = 64 - 25[/tex]

[tex] {x}^{2} = 39[/tex]

Thus :

[tex]x = \sqrt{39} [/tex]

[tex]x = 6.245[/tex]

suppose You earn Birr 10,000.00 per month and pay 20% tax and spend 60% of it. Again the recipient of the money spent by you pays 20% tax and spends 60% of it. If this process continues without end, find the total amount that wil be paid for the tax​

Answers

Answer:

  Birr 5000

Step-by-step explanation:

You will pay 10,000×20% = 2000 in tax. Recipients of your spending will pay ...

  0.60×10,000×20% = 1200

Recipients of the spending at the next level will pay a tax of ...

  0.60×0.60×10,000×20% = 720

That is, the tax amounts have an initial value (a1) of 2000 and a common ratio (r) of 0.60. Their total is given by the formula ...

  sum = a1/(1 -r)

  sum = 2000/(1 -0.6) = 5000

Birr 5000 will be the total amount paid for tax in this process.

Please help me... I really need it.

Answers

Answer:

If you are writing a seesya let me help you

Step-by-step explanation:

Make sure to hilight key info

Also use grammarly to correct past tense and sentences

Make sure to make sense

In one month Karissa earned $600 at her part-time job, and $50 was withheld for federal income tax. Suppose she earns $900 next month. How much will be withheld for federal income tax?

Answers

Don't get me wrong, I am not exactly sure but I believe it is supposed to be 75$.

The value of a share of stock on the stock market decreased by 14%. If it used to be worth $102.64, what is it worth now? Round to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

The share of stock is $88.33 worth now which is the value of a share of stock on the stock market decreased by 14%.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

The value of a share of stock on the stock market decreased by 14%. If it used to be worth $102.64 which is given in the question.

We have to determine the evaluation of 15% of 60.

⇒ 14% of $102.64

15%  is expressed as 15/100 in fractional form

⇒ (14/100)(102.64)

15/100  is expressed as 0.15 in decimal form

⇒ (0.14)(102.64)

Apply the multiplication operation, and we get

⇒ 14.31

Therefore, 14% of $102.64 would be $14.31.

The share of stock is worth now: $102.64 - $14.31 = $88.33.

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can help my little bro

Answers

Answer:

$0.03

Step-by-step explanation:

chips: 7.84/16=0.49

pretzels: 12.48/24=0.52

0.52=0.49=0.03

The term laissez-faire refers to an economic system that is characterized by

A. public ownership of the basic means of production

B. equal distribution of goods and services to all citizens

C. little governmental involvement in business and financial matters

D. government planning for production of consumer goods

Answers

Answer:

Answer: C.

Step-by-step explanation:

the term laissez faire refers to the economic policy of letting owners of industry and business set working conditions without interference

What is the equation of the line that passes through the point (-6,8) and has an undefined slope?​

Answers

Answer:

x = -6

Step-by-step explanation:

Slope is rise over run (change in y divided by change in x), and to have an undefined slope change in x must be zero. The line x = -6 is a vertical line that passes through the point (-6,8).

what is 12-(-3)-2(4)

Answers

Answer:

7

Step-by-step explanation:

12-(-3)-2(4)

12-(-3)-8

15-8=7

12- (-3) - 2(4) = 12 + 3 - 8 = 7
Ok done. Thank to me :>

what is the area and perimeter of the figure with the given vertices? (7,8) , (-5, -8) , (7,-8) , (-5,8)?

Answers

Answer:

perimeter: 56 unitsarea: 192 square units

Step-by-step explanation:

We assume you're interested in the convex polygon, so the given vertices are not listed in order around the figure.

The figure is 12 units by 16 units, so has a perimeter of ...

  P = 2(L +W)

  P = 2(16 +12) = 56 . . . . units

and an area of ...

  A = LW

  A = (16)(12) = 192 . . . . square units

12 - 33/4 equal in fraction form?

Answers

The answer is 3 3/4
Happy Holidays!

Answer:

The answer is 3  3/4 I think

Step-by-step explanation:

Given that
[tex] log_{4}(y - 1) + log_{4}( \frac{x}{2} ) = z \: \: and \: log_{2}(y + 2) + log_{2}(x) = z - 1 \: show \: that \: {y}^{2} = 1 + {8}^{z} \: and \: find \: the \: values \: of \: y \: and \: x [/tex]
when z = 1

Answers

Answer:

Gracias por los puntos

Bye :v

Which is a composite number? A.97 B.89 C.95 D.13

PLEASE I REALLY NEED THE CORRECT ANSWER RIGHT NOW!!!!​

Answers

Answer: C. 95 is a composite number.

Step-by-step explanation:

You can look at the ones place of each number to see if any end in 0, 2, 5, or any other digit that indicates that the number is not prime. Since 95 ends in a 5, it can be divided by 5, making it have more factors than 1 and itself. Therefore, 95 is the composite number of the list of numbers.

Answer:95

Step-by-step explanation:composite numbers are numbers that have more factors than 1 and itself, factors are numbers you can multiply to get a number. 95 is a composite number since 1,95, AND 5 are all factors of 95 making it a composite number

What is the solution to this equation? 1⁵+5²/25⁰-5¹=

Answers

Answer:

It is 21 first guy is no doubt correct.

Step-by-step explanation:

The expression results to 21.

What are Exponents and power?

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

1⁵+5²/25⁰-5¹

So, 1⁵ = 1

5² = 25

25⁰ = 1

5¹ = 5

Now, 1⁵+5²/25⁰-5¹

= 1+ 25 / 1 - 5

= 1 + 20

= 21

Hence, the expression results to 21.

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6/7 divided by 12/14 please show the work

Answers

Answer:

1

Step-by-step explanation:

When dividing one fraction by another, the best way to solve it is to multiply by the reciprocal. The reciprocal just flipping the fraction over. So you would leave the 6/7 and the multiply by 14/12( because you are multiplying by the reciprocal). When you do that, you then can just multiply the top and the bottom to form one fraction. The numerator is 6*14 = 84, and the denominator is 7*14 = 84. So you are left with 84/84 which anything over itself is equal to one.

Hope this helps!

hope this help u and good luck

Logan has an automatic hummingbird feeder in his backyard. He fills it to its capacity, 10 fluid ounces. Each day, it releases 1 fluid ounce of nectar.


Write an equation that shows how the number of fluid ounces of nectar remaining, y, depends on the number of days since Logan filled it, x.

Answers

Answer:

-1x+10

Step-by-step explanation:

The equation that shows how the number of fluid ounces of nectar remaining (y) depends on the number of days since Logan filled it (x) is:

y = 10 - x.

The relationship between the number of fluid ounces of nectar remaining (y) and the number of days since Logan filled the hummingbird feeder (x) can be represented using a linear equation.

Initially, when Logan fills the hummingbird feeder to its capacity of 10 fluid ounces, the nectar remaining is 10 fluid ounces.

As each day passes, 1 fluid ounce of nectar is released.

Therefore, the equation that shows how the number of fluid ounces of nectar remaining (y) depends on the number of days since Logan filled it (x) is:  y = 10 - x.

Here's an explanation of each component of the equation:

y: This represents the number of fluid ounces of nectar remaining.

As the days pass, this value will decrease as nectar is released.

10: This is the initial amount of nectar in the feeder when Logan fills it to its capacity of 10 fluid ounces.

x: This represents the number of days that have passed since Logan filled the feeder.

Each day, the amount of nectar decreases by 1 fluid ounce, hence the subtraction of "x."

This equation forms a linear relationship where the nectar remaining decreases by 1 fluid ounce for each day that passes.

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A ball is thrown from an initial height of 3 feet with an initial upward velocity of 37 fts. The ball's height h (in feet) after 1 seconds is given by the following.
h= 3+37t-16t^2
Find all values of t for which the ball's height is 23 feet.

Answers

Answer:

t=(37+root89)/32,(37-root89)/32

Step-by-step explanation:

Solve the equation:

23=3+37t-16t^2

what is 3.98.7 * 29.76+

Answers

Answer:

- 7% of 3.98...

... is equivalent to multiplying them:

- 7% × 3.98 ≈ - 0.28

(Rounded to a maximum of 2 decimals)

Step-by-step explanation:

I need help with problem.

Answers

I believe it is reflection across y=-2

Answer:

Reflection across the x-axis

Step-by-step explanation:

Rule of thumb: If the figure is diagonal, it is x-axis, but if it is horizontal, it is the y-axis.

What is 9 + 10 I do not know

Answers

Answer:

21, jk its 19 if you really dont know

Step-by-step explanation:

Answer:

9 + 10 = 19

just add it

hope it helps

Functions fg and hare shown on the graph. Y 10- 8 6 h 4- 2- x 10 -6 -4 - 2 2. 4 6 8 -10 -8 10 2- 4 -6 00 8- -10 Which of these functions have a domain of all real numbers? ОА. function fonly OB. functions f, g, and h oc functions fand gonly . OD functions g and h only​

Answers

the answer is b. functions f,g and h

All the function graphed have domain of all real numbers.

What is Function?

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

The domain of a function is defined by the graph's x-values (input values).

Similarly, Range is defined by the set of y-values (output values) in the function's graph.

Now, From the graph attached,

Domain of function 'f' : {x | x ∈ R}

Domain of function 'g' : {x | x ∈ R}

Domain of function 'h' : {x | x ∈ R}

Learn more about Function here:

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Tracey paid $150 for an item that was originally priced at $510. What percent of the original price did Tracey pay?

Answers

Answer:

29.4118%

Step-by-step explanation

510 * x = 150

x = .2941176

multiply by 100 to get percent

29.4118

What is the correct factorization of x^2 - 2x - 15?
HURRRYYYY PLS
A. 4
B. 5
C.8
D.12

Answers

Answer:

option b

Step-by-step explanation:

[tex] {x}^{2} - 2x - 15[/tex]

[tex] {x}^{2} - 5x + 3x - 15 = 0[/tex]

[tex] x(x - 5) + 3(x - 5) = 0[/tex]

[tex](x - 5)(x + 3) = 0[/tex]

x = -3 (Not possible)

x = 5

So, x = 5

Allison was comparing the price of salmon at two stores. At SuperGrocery B, 0.5 pounds of salmon costs $2.77. The table below represents the total cost, in dollars and cents, yy, that it costs for xx pounds of salmon at SuperGrocery A.

Answers

Answer:

15.48

Step-by-step explanation:

When we divide 6.45 by 10, we get 0.645 so, we know that is the rate per 0.1 pound. We multiply 6.45 by 2 to get 12.9 and add 0.645 four times since it is 2.4 pounds and get 15.48.

Answer:15.48

Step-by-step explanation:

15.48

i need help with this question

Answers

Answer:

check online for more information

HELP PLSSS

Use the commutative
property to make an
equivalent
expression.
4+m=?

A. 4-m
B. m+4

Answers

Answer:

B. m+4

Step-by-step explanation:

You are just writing the same equation but backwards so that the numbers still stay the same as well as the answer.

Answer: A

Step-by-step explanation:

Which unit rate is equivalent to 12 miles per gallon? 24 miles 2 gallons 2 gallons 24 miles 36 miles 4 gallons 4 gallons 36 miles​

Answers

Answer:

24/2

Step-by-step explanation:

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