1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Masteriza [31]
3 years ago
11

Given the cosine equation y = 2cos(4x) - 1, What is the midline?

Mathematics
1 answer:
pogonyaev3 years ago
6 0

Answer:

y = 2 \cos(4x)  - 1 \\ when \: y = 0 \\  \cos(4x)  =  \frac{1}{2}  \\ 4x = 60 \\ x = 15 \\ when \: x = 0 \\ y = 2 - 1 = 1 \\ intercepts =  > (15, \: 0) \: and \: (0, \: 1) \\ midpoints : ( \frac{15 + 0}{2} , \:  \frac{0 + 1}{2} ) \\  = (7.5, \: 0.5) \\ gradient =  \frac{1 - 0}{0 - 15}  \\  =  -  \frac{1}{15}  \\ y = mx + c \\ at \: (7.5, \: 0.5) \\ 0.5 =  -  \frac{1}{15}  \times 7.5 + c \\ 0.5 =  - 0.5 + c \\ c = 1 \\  \therefore \: y =  -  \frac{1}{15} x + 1 \\  =  > 15y =  - x + 15

You might be interested in
A projectile is fired with muzzle speed 250 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe
qaws [65]

The projectile's horizontal and vertical positions at time t are given by

x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ\,t

y=30\,\mathrm m+\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ\,t-\dfrac g2t^2

where g=9.8\dfrac{\rm m}{\mathrm s^2}. Solve y=0 for the time t it takes for the projectile to reach the ground:

30+\dfrac{250}{\sqrt2}t-4.9t^2=0\implies t\approx36.2458\,\mathrm s

In this time, the projectile will have traveled horizontally a distance of

x=\dfrac{250\frac{\rm m}{\rm s}}{\sqrt2}(36.2458\,\mathrm s)\approx6400\,\mathrm m

The projectile's horizontal and vertical velocities are given by

v_x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ

v_y=\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ-gt

At the time the projectile hits the ground, its velocity vector has horizontal component approx. 176.77 m/s and vertical component approx. -178.43 m/s, which corresponds to a speed of about \sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}.

7 0
3 years ago
If (1)=3 and f(n)=f(n-1)-1 then find the value of f(6)
katrin [286]

Answer:

f(1) = 3

f(n) = f(n-1) - 1

Otherwise,

f(n) = f(1) - (n-1)

=> f(6) = 3 - 5 = -2

Hope this helps!

:)

8 0
3 years ago
The length of a rectangle is twice its width, while the
hoa [83]

Answer: Length = 12 units

Width = 6 units

Step-by-step explanation:

Let the width of the rectangle be represented by x.

Since the length of a rectangle is twice its width, thus means that the length will be: = 2x

Perimeter of a rectangle = 2(l + w)

where,

L = length

W = width

Therefore,

Perimeter = 2(l + b)

36 = 2(2x + x)

36 = 2(3x)

36 = 6x

x = 36/6

x = 6

Width = 6 units

Length = 2 × Width = 2 × 6 = 12 units

7 0
3 years ago
Solve the inequality -1/2x -3 ≤ -2.5
IgorLugansk [536]

Answer:

x ≥-1

Step-by-step explanation:

-1/2x -3 ≤ -2.5

Add 3 to each side

-1/2x -3+3 ≤ -2.5+3

-1/2x ≤ .5

Multiply each side by -2, remembering to flip the inequality

-2 * -1/2x ≥ 1/2 * -2

x ≥-1

7 0
3 years ago
What is the unknown term in sequence ? 28.6 , 26.1, 23.6 ,__,18.6
4vir4ik [10]

<u>21.1</u>

Each number is 2.5 less than the previous one.

7 0
3 years ago
Read 2 more answers
Other questions:
  • Which graph represents the function?
    11·1 answer
  • What is Algebra?<br>What is a equation?​
    5·1 answer
  • 100 points
    9·2 answers
  • PLEASE ANSWERRRRRRRRRR
    9·1 answer
  • Uncle Ian spent $59 at a book store. He bought science fiction and mystery novels. The science fiction novels cost $7 apiece and
    6·1 answer
  • PLEASE HELP QUICK<br> Factor out the GCF of 14x4 + 21x2 + 28x
    14·1 answer
  • a trail is 5 miles long. carlos walks 2/3 of the trail and runs the rest. how many miles does carlos walk?
    14·1 answer
  • Pam borrowed $0.45 from her friend Tina for five days to buy candy bars. Represent the amount that pam borrowed as the product o
    5·1 answer
  • One more dilation problem <br> Write the rule to describe each transformation??
    7·2 answers
  • The fully simplified form of 2ab÷(8a) is:
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!