Modeling with sinusoidal functions
Hiro is riding a carousel that is next to a wall.
His horizontal distance C(t) (in m) away from the wall as a function of time t (in seconds) can be modeled by a
sinusoidal expression of the form a · cos(b. t) + d.
Att = 0, when he starts, he is closest to the wall, a distance of 2 m away. After 77 seconds he reaches his mid-
way point from the wall, which is 7 m away.
Find C(t).
t should be in radians.
C(t)

Answer:

2/7

Step-by-step explanation:

Answer:

Please check the explanation.

Step-by-step explanation:

Thus, the domain of the first relation is: {-2, -1, 0, 2}

Thus, the range of the first relation is: {-4, -2, 2}

Given the second relation

x        y

-4      -2

-2       1

1         4  

4         4

Thus,

The domain of the second relation is: {-4, -2, 1, 4}

Thus,

The range of the second relation is: {-2, 1, 4, 4}

Answer: -20n^2 - 39n - 15

Step-by-step explanation:

first, we remove the parenthesis (multiply everything out).

-20n^2 - 24n - 15 - 15n

then, we simply collect like terms.

-20n^2 - 39n - 15

Answer:

-20n^2-39n-15

Step-by-step explanation:

Given: -4n(5n+6)-5(3+3n)

Use the distributive property: -20n^2-24n-15-15n

Combine like terms: -20n^2-39n-15

Your simplified expression is -20n^2-39n-15

Answer:

-32/45

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

Answer:

1.) slope = 2

2.) slope = [tex]-2\frac{2}{3}[/tex]

3.) slope = [tex]\frac{2}{3}[/tex]

4.) slope = [tex]\frac{1}{4}[/tex]

5.) slope = [tex]1\frac{8}{9}[/tex]

6.) slope = -2

7.) slope = -3

Step-by-step explanation:

In order to find the slope we have to divide they "y" value (the number of units by which the piece of antler goes up) by the "x" value the number of units by which the piece of antler goes to the side). Notice the if the antler moves to the left as it foes up then the "x" value is negative.

Now as I said before we know this......

Let "m" be the slope, then....

[tex]m = \frac{y}{x}[/tex]

So now we just have to plug in the y and x values for each antler and we will get the slopes for each one of them.

1.)

[tex]m = \frac{y}{x}[/tex]

[tex]m= \frac{4}{2}[/tex]

[tex]m = 2[/tex]

2.)

[tex]m = \frac{y}{x}[/tex]

[tex]m = \frac{4}{-1.5}[/tex]

[tex]m = -2\frac{2}{3}[/tex]

3.)

[tex]m = \frac{y}{x}[/tex]

[tex]m = \frac{2}{3}[/tex]

4.)

[tex]m = \frac{y}{x}[/tex]

[tex]m = \frac{1}{4}[/tex]

5.)

[tex]m = \frac{y}{x}[/tex]

[tex]m = \frac{8.5}{4.5}[/tex]

[tex]m = 1\frac{8}{9}[/tex]

6.)

[tex]m = \frac{y}{x}[/tex]

[tex]m = \frac{2}{-1}[/tex]

[tex]m= -2[/tex]

7.)

[tex]m = \frac{y}{x}[/tex]

[tex]m = \frac{3}{-1}[/tex]

[tex]m = -3[/tex]

Answer:

4,1

Step-by-step explanation:

x+y=5 2x-y=7

x=5-y 2(5-y)-y=7

10-2y-y=7

10-3y=7

10-7=3y

3=3y

1=y

substitutes y=1 in x+y=5

x+1=5

x=5-1

x=4

(4,1)

check:

x+y=5

4+1=5

Answer:

[tex]f(-10)=186[/tex]

Step-by-step explanation:

We can use substitution to find the value of [tex]f(-10)[/tex].

[tex]f(x) = 2x^2+x-4[/tex]

[tex]f(-10) = 2(-10)^2-10-4[/tex]

[tex]=200-10-4[/tex]

[tex]=186[/tex]

∴ [tex]f(-10) =186[/tex]

Hope this helps :)

Answer:

The value of f(-10) is equal to 186.

Step-by-step explanation:

We are given the function:

[tex]f(x) = 2x^2 + x - 4[/tex]

We are told to find the value of:

[tex]f(-10)[/tex]

If we pay close attention, we can see a transition between:

[tex]f(x) \rightarrow f(-10)[/tex]

We have turned x into -10, making x = -10.

Therefore, we can change the value of x in the entire function to -10.

[tex]f(-10)=2(-10)^2+(-10) - 4\\\\f(-10) = 200 - 10 - 4\\\\f(-10) = 186[/tex]

Therefore, f(-10) = 186.

Answer:

Geometric sequence

.Step-by-step explanation:

Geometric sequences are defined by an initial value and a common ratio . If a sequence does not have a common ratio or a common difference, it is neither an arithmetic nor a geometric sequence. You should still try to figure out the pattern and come up with a formula that describes it.

Answer: Neither

Step-by-step explanation:

Answer: 3 grams

Step-by-step explanation: Each distribution of food must be equal so divide food by amount of cats which is 3 to get 3

Mathmatically 9/3 = 3 grams

Answer:

10 flour

Step-by-step explanation:

          1:2

         5:x     all you have to do is multiply by 2, sense the ratio is 1:2, flour will always be 2 times greater than sugar. so the answer is 5 x 2 =10

Answer:

Pacific Ocean at a grand 63 million square miles

Step-by-step explanation:

Answer:

pacific ocean

Step-by-step explanation:

it is the largest ocean in the world

Answer:

30

Step-by-step explanation:

5=5,10,15,20,25,(30),35

6=6,12,18,24,(30),36

30 is the first number that can be used to divide both numbers

Answer:

30

Step-by-step explanation:

5* 6 =30 and no number less than 30 works :)

Answer:

each section will be .7 inches long

Step-by-step explanation:

8.4/ 12

The answer is 69

(ariana grande) teehee can u stay up all night me to the daylight 34 35!!!!

Answer:

50

Step-by-step explanation:

Already done this

Answer:

50

Step-by-step explanation:

i just simplified the expression

Answer:

Im so sorry, I dont know the answer and accidentally clicked on it. It wont let me get out of this... SO SORRY!

Step-by-step explanation:

none

Answer:

The answer will be 40.397.

Step-by-step explanation:

Since the equation of your best fit line is y= 0.404x - 0.003 and they want you to calculate how high the line will be when x=100, plug in 100 in x which will be y= 0.404(100) - 0.003 and you'll get an answer of 40.397.

Answer:

40.397

Step-by-step explanation:

0.404(100)-0.003=40.397

Just plug in the X value for X in the equation and solve. it gives you your answer.

Hope this helps.

Answer:

slope: (1 ,-3)

y-intercept: -1

y = -3/1 -1

Step-by-step explanation:

hope it helps!

Answer:

5/14

Step-by-step explanation:

To work this out, we simply need to divide 1 3/4 miles by 4 9/10 miles.

1 3/4 ÷ 4 9/10

Start by converting both terms to improper fractions:

(4/4 + 3/4) ÷ (40/10 + 9/10)

= 7/4 ÷ 49/10

To divide, we simply multiply by the reciprocal of the second fraction:

7/4 * 10/49

= 70 / 196

Now we can take out common factors of the 70 / 196

70 / 196

= (5 * 2 * 7) / (14 * 2 * 7)

= 5 / 14

So the straight section of the track is five fourteenths of the entire length.

Answer:

y=-2x+6

Step-by-step explanation:

Answer:

C, third quadrant

Step-by-step explanation:

Answer:

amm

Step-by-step explanation:

Answer:

The relation represented by diagram 4 is NOT a function.

Step-by-step explanation:

To tell if a relation is not a function, pay attention to the x-intercepts. If there is more than one y-intercept with the same x-intercept, then it is not a function, because a function can only have one output (y-value) for each input (x-value).

According to the fourth diagram, the domains include 1, 2, and 3 while the range includes A, B, and C. Also, the ordered pairs would go as follows according to the arrows:

(1, A), (2, A), (2, B), (3, C)

While the y-values, A and B, are different, they share the same input, 2. Therefore, the relation represented by the 4th diagram is NOT a function.

Hope this helps!