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Irina18 [472]
3 years ago
6

The graph of a sinusoidal function has a maximum point at (0,10) and then intersects its midline at (pi/4,4). Write the formula

of the function, where x is entered in radians. f(x)=
Mathematics
1 answer:
docker41 [41]3 years ago
5 0

Answer: y = 6 cos (2x) + 4

<u>Step-by-step explanation:</u>

A cosine function is expressed as: y = A cos (Bx - C) + D   where

  • amplitude (A) is the distance from the midline to the max/min.
  • B = 2π/P  where P is the period
  • C/B is the phase shift
  • D is the center line (aka midline)

A = Max - Midline

   = 10 - 4

   = 6

The max to the midpoint is π/4

⇒ 1/4 P = π/4

⇒ P = π

B = 2π/P    

  = 2π/π

  = 2

C = 0 because there is no phase shift

D = 4 (given)

Input A = 6, B = 2, C = 0, and D = 4 into the cosine function:

y = 2 cos (2x - 0) + 4

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3 years ago
Determine a series of transformations that would map polygon ABCDE onto polygon A’B’C’D’E
zalisa [80]

Answer:

Reflected across x-axis followed by a dilation with a scale factor of 2 about the origin.

Step-by-step explanation:

It's clear from the graph,

Polygon ABCDE is reflected across x-axis then dilated so that it overlaps polygon A'B'C'D'E'

Let's choose a point A having coordinates (-2, -1)

By reflecting point A across x-axis,

Rule to be followed for the reflection,

(x, y) → (x, -y)

By this rule, coordinates of the image point A will be,

A(-2, -1) → A"(-2, 1)

Now point A"(-2, 1) has been dilated by a scale factor = k to form an image points A'(-4, 2).

Rule for the dilation of a point about the origin is,

A"(x, y) → A'(kx, ky)

A"(-2, 1) → A'(-2k, k)

Since, coordinates of point A' are (-4, -2),

Therefore, -2k = -4

k = 2

k = 2

Hence, polygon ABCDE was reflected across x-axis followed by a dilation with a scale factor of 2 about the origin to form polygon A'B'C'D'E'.

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Please solve 7(b=2) = 49
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Here is your answer
Please mark it brainliest

7 0
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OverLord2011 [107]

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Below

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What is the missing reason in Step 7? Triangle angle sum theorem quadrilateral angle sum theorem definition of complementary con
Daniel [21]

Answer:

Hello your question is incomplete attached below is the complete question

Given: wxyz is a parallelogram, zx ≅ wy prove: wxyz is a rectangle what is the missing reason in step 7? a. triangle angle sum theorem. b. quadrilateral angle sum theorem. c. definition of complementary. d. consecutive ∠s in a ▱ are supplementary. 1. wxyz is a ▱; zx ≅ wy 1. given 2. zy ≅ wx 2. opp. sides of ▱ are ≅ 3. yx ≅ yx 3. reflexive 4. △zyx ≅ △wxy 4. sss ≅ thm. 5. ∠zyx ≅ ∠wxy 5. cpctc 6. m∠zyx ≅ m∠wxy 6. def. of ≅ 7. m∠zyx + m∠wxy = 180° 7. ? 8. m∠zyx + m∠zyx = 180° 8. substitution 9. 2(m∠zyx) = 180° 9. simplification 10. m∠zyx = 90° 10. div. prop. of equality 11. wxyz is a rectangle 11. rectangle ∠ thm.

answer: consecutive angles of any parallelogram are supplementary

Step-by-step explanation:

The missing reason in step 7 is : consecutive angles of any parallelogram are supplementary i.e. m∠ZYX + m∠WXY  = 180°

<u>Reason </u>:  ZY || WX also  XY is the transversal line hence ∠wyx and ∠wxy are the consecutive angles on lines ZY and WX therefore m∠ZYX + m∠WXY = 180°  ( sum of consecutive angles )

4 0
3 years ago
Read 2 more answers
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