i need help with this question

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).)

The number of gallons of fuel required for 200 miles will be 6.7 gallons. The correct option is C.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that Becky is planning a two 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon.

The total miles covered in two trips will be,

100 + 100 = 200 miles

The amount of fuel will be calculated as:-

Fuel = 200 /  30

Fuel = 6.7 gallons

Therefore, the fuel quantity will be 6.7 gallons.

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Answer:

a) (2x+3) (x+4)

b) (5x-3) (x-1)

c) (-2x-3) (x-3)

d) 3(x-1) (3x-8)

e) -2(3x+5) (x-2)

f)  h(4x-3) (3x-4)

g) -(x-3) (x+7)

h) (3x-2) (x+3)

i)  2(2x+1) (x-2)

j) (3h+2) (h-7)

Step-by-step explanation:

your welcome :)

Answer:

a)

(x+4)(2x+3)

b)

(x-2)(5x-3)

c)

(-x+3)(2x-3)

d)

3(x-1)(3x-8)

e)

2(-x+2)(3x+5)

f)

h(3x-4)(4x-3)

g)

(x+7)(-x+3)

h)

(x+3)(3x-2)

i)

2(x-2)(2x+1)

j)

(h-7)(3h+2)

Hope this helps!

Answer:

6.67%

Step-by-step explanation:

5 / 75 = 0.066667

(0.066667)(100) = 6.67%

Answer:

Step-by-step explanation:

Example 1: Changing the whole number 5 into a fraction.

Take the whole number (5), add a line below it (/), then add a 1 to the denominator.

5 = 5/1

Example 2: Changing the whole number 5 into a fraction.

Take the whole number (5), multiply it by 2 add a line below it (/), then add a 2 to the denominator.

5 = (5*2)/2 = 10/2

***This can be reduced to 5/1***

Example 3: Changing the whole number 5 into a fraction.

Take the whole number (5), multiply it by 3 add a line below it (/), then add a 3 to the denominator.

5 = (5*3)/3 = 15/3

***This can also be reduced to 5/1***

If you follow the pattern, you will realize all whole numbers are fractions already.

They are fractions with a denominator of 1. This fraction can be manipulated with all of the same standard rules you would traditionally use with fractions, even when the denominator isn’t shown.

A fraction is simply a way to describe portions of a whole. The denominator simply tells you how many pieces to break the whole into. When the denominator is 1, you are breaking the whole into one piece (or not breaking it apart at all.

I hope this helps.

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!

Answer:

X-intercept at (1/2 ,0)

domain of (0, infinity)

Vertical asymptote of x = 0

Step-by-step explanation:

Plato I got it right on the test

Answer:

6/8 and 12/16

Step-by-step explanation:

Important: 3/4 looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3/4. To find an equivalent fraction to 3/4 , or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By multiplying the original fraction by 2, we get:

3x2/3x2=6/8

List of Equivalent Fractions of 3/4:

3/4, 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36, 30/40, 33/44, 36/48, 39/52, 42/56, 45/60, 48/64, 51/68, 54/72, 57/76, 60/80 ...

11 miles far does the boat travel

Step-by-step explanation:

hope it helps

The total distance travelled will be 22 miles and the bearing will be 60.89° .

It is given that a boat travels from port town to north for 7.4 miles and then east for 3.6 miles and stops at destination.

We have to find out the total distance travelled and bearing from stopped position.

What are bearings ?

A bearing is the angle in degrees measured clockwise from north i.e., 30° from north.

As per the question ;

Boat travels from port town to north for 7.4 miles and then east for 3.6 miles and it then stops at destination.

So ;

a)

Total distance travelled from port town to destination is ;

= 7.4 miles + 3.6 miles

= 11 miles

And

If boat's captain turns back to town , then total distance will be ;

= 11 + 11

= 22 miles

b)

We know that ;

cos θ = B/H

The bearing would be ;

cos θ = [tex]\frac{3.6}{7.4}[/tex]

cos θ = 0.486

θ = [tex]cos^{-1}[/tex] (0.486)

θ = 60.89°

Thus , the total distance travelled will be 22 miles and the bearing will be 60.89° .

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Answer:

101.6cm²

Step-by-step explanation:

1 inch = 2.54cm

that means:

40in² × 2.54 = 101.6cm²

Answer:

Step-by-step explanation:

J

B = 3J

T = J + 5

J + 3J + J + 5 = 60

5J = 55

J = $11

B = $33

T = $16

The amount earned by Jim, Bill and Tom is equal to [tex]\boldsymbol{\$ 11},\boldsymbol{\$ 33},\boldsymbol{\$ 16}[/tex].

Let .

The amount earned by Jim be [tex]\boldsymbol{x}[/tex].

Amount earned by Bill [tex]=\boldsymbol{3x}[/tex]

Amount earned by Tom [tex]=\boldsymbol{x+5}[/tex]

Total amount earned by all [tex]=\boldsymbol{\$ 60}[/tex][tex]x+3x+x+5=60\\5x=55\\x=11[/tex]

So,

Amount earned by Jim [tex]=\boldsymbol{\$ 11}[/tex]

Amount earned by Bill [tex]=3(11)[/tex] [tex]=\boldsymbol{\$ 33}[/tex]

Amount earned by Tom [tex]=11+5[/tex] [tex]=\boldsymbol{\$ 16}[/tex]

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Answer:

First mechanic 10 hours, Second is 15 hours

Step-by-step explanation:

x + y = 25, so y = 25 - x

75x + 45y = 1425

Substitute in the first equation

75x + 45(25 - x) = 1425

75x + 1125 - 45x = 1425

30x = 300

x = 10

Therefore, y = 15

Answer:

they both worked

8 hours

Answer:

d

Step-by-step explanation:

distribute two through the parentheses

=4x-2

move the constant to the right side and change its sign

=4x=8+2

=4x=10

divide both sides by 4

x=5/2

Answer:

The answer is number 3.

Step-by-step explanation:

-15 - 8 = -23

12 + 11 = 23

When you subtract -23 from 23 you have a sum of 0

Therefore the answer is 0

Answer:

neither of them are

Step-by-step explanation:

Answer:

Real Numbers are numerical values that can represent distance on a line. An example of it being one is 15 and an example of it NOT being one is ∞.

If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.

Given the following data:

To determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.

Note: The diagonal side of the rectangular pool represents the hypotenuse.

Mathematically, Pythagorean's theorem is given by the formula:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

Substituting the given parameters into the formula, we have;

[tex]Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}[/tex]

Hypotenuse = 10 meters.

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Answer:

C (1,0)

Step-by-step explanation:

Answer:

C. (1,0)

Step-by-step explanation:

When you go 3 to the left, you end up at (0, -2). When you go up 2, you get (1,0).

9−8.4=6

0.6≠6

False

I don't know...

Answer:

0.6 his answer is false.

Step-by-step explanation:

...

Answer:

Answer:

28+66+86=180

180=180

Step-by-step explanation:

Since there is a triangle and the 3 measures from the angles we can find the value of x using the hint given that the sum of the interior angles must be 180°

Write the equation

\begin{gathered}x+(2x+10)+(3x+2)=180\\\end{gathered}

x+(2x+10)+(3x+2)=180

Simplify left side of the equation

\begin{gathered}6x+12=180\\\end{gathered}

6x+12=180

Solve equation for x

\begin{gathered}6x=180-12\\6x=168\\x=28\end{gathered}

6x=180−12

6x=168

x=28

Replace x into the 3 angles and find their respectives values

\begin{gathered}A=x\\A=28\\\\B=2x+10\\B=2*28+10\\B=56+10\\B=66\\\\C=3x+2\\C=84+2\\C=86\end{gathered}

A=x

A=28

B=2x+10

B=2∗28+10

B=56+10

B=66

C=3x+2

C=84+2

C=86

Check if the answers are correct

\begin{gathered}28+66+86=180\\180=180\end{gathered}

28+66+86=180

180=180

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Answer:1. How can you tell by looking at each graph that a proportional relationship exists between the quantities?

relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

2. Find the constant of proportionality for each graph. Write your answer as y = kx.

y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.

Step-by-step explanation:

Answer:

20 which is twenty

Step-by-step explanation:

searched it up on chrome

Answer:

9 because there the same length

Answer:

the measure of the seg CD is 9

Step-by-step explanation:

It is 9 because the shape is a parallelogram. One of the properties of a parall is that opposite sides are congruent which makes side BA equals side CD

Answer:

18÷3=6

Step-by-step explanation:

18 trumpets have to be DIVIDED into 3 rows so you would divide 18 by three to get 6 trumpets in each row.

Answer: It,ll increase

Step-by-step explanation:

Answer:

Add all of the numbers together then multipy them by 25

Step-by-step explanation:

35X25=875

Answer:

Its the first one

Step-by-step explanation:

4x4=16 8x2=16 so its the first

These three lines should say:

4 rows with 16 boxes in each row

8 rows with 8 boxes in each row

16 rows with 4 boxes in each row

Answer:

r = 1

Step-by-step explanation:

Use the distributive property to multiply −6 by −3+5r.

18−30r=−5−7r

Add 7r to both sides.

18−30r+7r=−5

Add −30r and 7r to get −23r.

18−23r=−5

Subtract 18 from both sides.

−23r=−5−18

Subtract 18 from −5 to get −23.

−23r=−23

Divide both sides by −23.

r=−23/−23​

Divide −23 by −23 to get 1.

r=1