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
Sergeu [11.5K]
3 years ago
14

A sinusoidal function whose period is 1/2 , maximum value is 10, and minimum value is −4 has a y-intercept of 3.

Mathematics
1 answer:
zmey [24]3 years ago
4 0

f(x) = 7 sin (4πx) + 3. The function f(x) = 7 sin (4πx) + 3 describe a sinusoidal function whose period is 1/2, maximum value 10, minimum value -4, and it has a y-intercept of 3.

A sinudoidal function whose period is 1/2, maximum value is 10, minimum value is -4, and it has a y-intercept of 3. Let's write to the form f(x) = A sin (ωx +φ) + k, where A is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, φ the initial phase (horizontal shift), and k is y-intercept (vertical shift).

Calculating the amplitude:

A = |max - min/2|

A = |10 - (-4)/2| = 14/2

A = 7

calculating the ω:

The period of a sinusoidal is T = 1/f --------> f = 1 / T

ω = 2πf -------> ω = 2π ( 1/T) with T = 1/2

ω = 2π (1/(1/2) = 2π (2)

ω = 4π

The y-intercept k = 3

Writing the equation function with A = 7, ω = 4π, k = 3, φ = 0.

f(x) = A f(x) = A sin (ωx +φ) + k ----------> f(x) = 7 sin (4πx) + 3.

You might be interested in
I need help with questions #7 and #8 plz
katen-ka-za [31]

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

c^2 = a^2 + b^2 - 2ab \cos C

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

18^2 = 12^2 + 16^2 - 2(12)(16) \cos C

324 = 144 + 256 - 384 \cos C

-384 \cos C = -76

\cos C = 0.2

C = \cos^{-1} 0.2

C = 78.6^\circ

Now we use the law of sines to find angle A.

Law of Sines

\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

We know c and C. We can solve for a.

\dfrac{a}{\sin A} = \dfrac{c}{\sin C}

\dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ}

Cross multiply.

18 \sin A = 12 \sin 78.6^\circ

\sin A = \dfrac{12 \sin 78.6^\circ}{18}

\sin A = 0.6535

A = \sin^{-1} 0.6535

A = 40.8^\circ

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

a^2 = b^2 + c^2 - 2bc \cos A

b^2 = a^2 + c^2 - 2ac \cos B

c^2 = a^2 + b^2 - 2ab \cos C

Find angle A:

a^2 = b^2 + c^2 - 2bc \cos A

8^2 = 18^2 + 12^2 - 2(18)(12) \cos A

64 = 468 - 432 \cos A

\cos A = 0.9352

A = 20.7^\circ

Find angle B:

b^2 = a^2 + c^2 - 2ac \cos B

18^2 = 8^2 + 12^2 - 2(8)(12) \cos B

324 = 208 - 192 \cos A

\cos B = -0.6042

B = 127.2^\circ

Find angle C:

c^2 = a^2 + b^2 - 2ab \cos C

12^2 = 8^2 + 18^2 - 2(8)(18) \cos B

144 = 388 - 288 \cos A

\cos C = 0.8472

C = 32.1^\circ

8 0
3 years ago
17 times 14 times 123
LUCKY_DIMON [66]

Answer:

29274

Step-by-step explanation:

Because 17*14=238 and 238*123=29274

8 0
3 years ago
Read 2 more answers
Help me with this question please?
UNO [17]
\bf 3^{n+2}-3^n=8\cdot 3^n\implies \boxed{3^n\cdot 3^2}-3^n=8\cdot 3^n&#10;\\\\\\&#10;\stackrel{common~factor}{3^n}(3^2-1)=8\cdot 3^n\implies 3^2-1=\cfrac{8\cdot \underline{3^n}}{\underline{3^n}}\implies 3^2-1=8&#10;\\\\\\&#10;9-1=8\implies 8=8
6 0
3 years ago
Shelby is decorating a rectangular ballroom ceiling with garland. Beginning in a corner, Shelby strings garland along length of
Liono4ka [1.6K]

Answer:

since the room is rectangular and has 4 sides

2 sides have the same length

18*2= 36m

80*2=160m

then add the sums...

the answer is 196 meters

Step-by-step explanation:

3 0
3 years ago
How many centimeters are in 5.2 inches? [1 inch = 2.5 cm]
Molodets [167]
This would be about 13 cm
6 0
4 years ago
Read 2 more answers
Other questions:
  • Find the surface area of the cube shown below 2 1/2
    5·1 answer
  • Alex invested $400 in a CD that pays 3% simple interest, calculated semiannually. How much money will Alex earn in 2 years? A. $
    10·1 answer
  • Combine the term : 5n-n
    12·1 answer
  • PLEEEAAAASE HELLP!!!Tina is making a cylindrical sandbox that has a radius of 2 feet. She bought 18.84 cubic feet of sand for th
    10·2 answers
  • Can y’all help me please hurry!!
    13·1 answer
  • What is the solution to the system of equations y=-3×-2 5×+2y=15
    7·2 answers
  • An aircraft carrier left Diego Garcia one
    9·1 answer
  • Amanda is on the swim team. Each week she swims a total of 6000 meters. How many kilometers does she swim each week ?
    13·1 answer
  • (Find m∠IGH) m∠IGH =
    10·1 answer
  • If
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!