g is a trigonometric function of the form g(x)=a sin (bx+c)+d.
The function intersects its midline at (-1 , 6) and has a minimum point at (-3.5 , 3)
Find a formula for g (x). Give an exact expression.
Answers
Answer:
Formula for g(x) is [tex]g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6[/tex]
Step-by-step explanation:
Given - g is a trigonometric function of the form g(x)=a sin (bx+c)+d. The function intersects its midline at (-1 , 6) and has a minimum point at (-3.5 , 3)
To find - Find a formula for g (x). Give an exact expression.
Proof -
Given that,
g(x)=a sin (bx+c)+d
We know that, Midline is present in between maximum and minimum
Here given that, minimum is present is 3 and midline is present at 6
So, Maximum occurs at 9.
Now,
We know that,
Standard form of sine function is - g(x) = Asin(B(x-C)) + D
Where
A = Amplitude
and Amplitude = (Maximum - minimum) / 2
= (9 - 3)/ 2
= 6/2 = 3
⇒A = 3
Now,
Period = [tex]\frac{2\pi }{B}[/tex]
⇒B = (2π) / Period
= (2π) / 10
= π/5
⇒B = π/5
Now,
Phase Shift : C = -1 ( i.e. 1 to the left)
Vertical Shift : D = 6
So,
We get
g(x) = Asin(B(x-C)) + D
= [tex]3 sin(\frac{\pi }{5}(x -(- 1))) + 6[/tex]
⇒[tex]g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6[/tex]
∴ we get
Formula for g(x) is [tex]g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6[/tex]
Related Questions
A game of chance has a spinner with five equal sized sections. The results of 625 spins are shown below.
For which color is the experimental probability closest to the theoretical probability? Use the drop down menus to explain your answer.
(Brown,Orange,Yellow,Green,Purple) The experimental probability is (22.72%, 18.88%, 21.92%, 19.52%) and the theoretical probability is (10%, 25%, 20%)
For which color is the difference between the theoretical probability and experimental probability greatest? Use the drop down menus to explain your answer.
Brown,Green,Yellow,Orange,Purple) The experimental probability is (16.96%, 22.72, 18.88%, 21.92%) and the theoretical probability is (25%, 10%, 20%).
Answers
Answer:
https://e-eduanswers.com/mathematics/question176807332
Step-by-step explanation:
picture is included ! i need help guys please
Answers
Answer: y=-3x+2
Step-by-step explanation: quik maf
Answer:
y = -3x + 2
Step-by-step explanation:
Slope = Change in y / Change in x
Slope = -3/1
Slope = -3
Y-intercept = when x = 0, y = 2, therefore y-intercept = 2
Hence, equation:
y = -3x + 2
Hope this helps!
new one i need help with this one
Answers
Answer:
10
Step-by-step explanation:
Correct me if I’m wrong it’s been a while but I think u add 3 + 3 + 2+ 2
Answer:
It is 10
Step-by-step explanation:
In order to do perimeter you need to add each corners value, in this case a to B is one side and A to D is another, in order to get from A to B you have to walk 3 units, so their is our first part, now for the second you need to walk from point a to point D which if you do it will be 4 units.
Now we have 2 numbers, 4 and 3, We still have the other side but it will be the same, so you will do 4+4 and 3+3, in this case it will be 8+6 so the answer should be 14. I might be wrong.
hello please help i’ll give brainliest
Answers
Answer:
Living
Step-by-step explanation:
Recently, Caroline purchased a BBQ grill to use this summer. The cost of the grill was $390 and sales tax
in her city is 7.4%. What is the amount of sales tax that Caroline will pay for the grill? Sales tax =
What is the total cost of the grill, including sales tax? Total cost of the grill =
Answers
hi
Sales taxes = 390 *0.074 = 28.86
Total cost : 390+28.86 = 418.86
Julio says if you subtract 15 from my number and multiply the difference by -2 the result is -36 what's julio's number
Answers
What are the first three terms of the sequence defined by the recursive function an = an-1-(an-2-4), when a5 =-2 and a6 = 0?
-14, 14,- 4
6, 10,8
-2 0,2
2, 8, 10
Answers
Answer:
6, 10 and 8
Step-by-step explanation:
Given the recursive function an = an-1-(an-2 - 4), when a5 =-2 and a6 = 0?
a6 = a5 - (a4 - 4)
0 = -2 - (14 - 4)
2 = - (a4 - 4)
-2 = a4 - 4
a4 = -2 + 4
a4 = 2
a5 = a4 - (a3 - 4)
-2 = 2 - (a3 - 4)
-2-2 = - (a3 - 4)
-4 = -(a3 - 4)
4 = a3 - 4
a3 = 4+4
a3 = 8
Also
a4 = a3 - (a2 - 4)
2 = 8 - (a2 - 4)
2-8 = - (a2 - 4)
-6 = -(a2 - 4)
6 = a2 - 4
a2 = 6+4
a2 = 10
a3 = a2 - (a1 - 4)
8 = 10 - (a1 - 4)
8-10 = - (a1 - 4)
-2 = -(a1 - 4)
2 = a1 - 4
a1 = 2+4
a1 = 6
Hence the first 3 terms are 6, 10 and 8
Answer:
C. 6, 10, 8
Step-by-step explanation:
i took the test
Susan makes $22 per hour in a clerical position. If she works 30 hours per week, what is her gross
weekly income?
$2,640
$500
$600
$660
Answers
Help me please I don’t understand eee
Answers
yeah please help me I’ll give brainliest if correct
Answers
Answer:
p=20
6p=120
Step-by-step explanation:
Answer:
A: 6p = 120
Solution:
6 / p = 120 / 6
p = 20
dont forget to five-star and heart! ;)
AADE and AABC are similar. Which best explains why the slope of the line between
points A and D is the same as the slope between points A and B?
The triangles are similar, so the sides are proportional:
AE = AC and DE = BC. Therefore, De = BC, so the slope of
AD is the same as the slope of AB.
Points A, D and B are on the hypotenuses of similar triangles.
Therefore, AD = AB, so the slope of AD is the same as the
slope of AB
The triangles are similar, so the sides are proportional:
DE = BC. Therefore, the slope of AD is the same as the slope
of AB
AE C
The triangles are similar, so the sides have equal lengths.
Therefore, AD = DB, so the slope of AD is the same as the
slope of AB
Answers
Answer:
(c) The triangles are similar, so the sides are proportional: DE = BC. Therefore, the slope of AD is the same as the slope of AB
Step-by-step explanation:
Given
See attachment for proper format of question
Required
Why is the slope between A and D the same
From the question, we understand that:
[tex]\triangle ADE[/tex] and [tex]\triangle ABC[/tex] are similar
This implies that similar sides are proportional.
i.e.
[tex]AD \to AB[/tex]
[tex]AE \to AC[/tex]
[tex]DE \to BC[/tex]
Slope (m) is calculated as:
[tex]m = \frac{Rise}{Run}[/tex]
So, the slope of [tex]\triangle ADE[/tex] is:
[tex]m = \frac{DE}{AE}[/tex]
Slope of [tex]\triangle ABC[/tex] is:
[tex]m = \frac{BC}{AC}[/tex]
Since the triangles are similar, then:
[tex]m = m[/tex]
i.e.
[tex]\frac{DE}{AE} = \frac{BC}{AC}[/tex]
Hence, (c) is true
please help ill give brainlist!
Answers
Answer:
[tex]y = 12 \tan(30 \degree ) \\ y = 6.92[/tex]
[tex]x = \frac{12}{ \cos(30 \degree) } \\ x = 13.8[/tex]
[tex] \small{ \star{ \underline{ \blue{becker}}}}[/tex]
she had a shoe box full of 5 cents 6 cents and 7 cents what totals could she make and what totals were impossible
Answers
Can someone please help me with math.
Answers
I think it’s A
A single card is drawn from a standard 52 card deck.
Work out the probability of choosing "a spade"
Answers
Answer: [tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
A standard 52 card deck includes spades, clubs, hearts, and diamonds.
13 card of each category is present
So, there are 13 spades present in the deck
Probability is the ratio of favorable to the total outcomes.
[tex]\therefore P=\dfrac{13}{52}\\\\\Rightarrow P=\dfrac{1}{4}[/tex]
Find the remaining volume of the cube with the cone removed.
Answers
D
Step-by-Step explanation:
The eqution of the diagonal of a parallelogram is 3y=5x +k. The two opposite vertices of a parallelogram are the points (1,-2), (-2,1).Find the value of k
Answers
Answer:
[tex]k = 1[/tex]
Step-by-step explanation:
Given
[tex]3y = 5x + k[/tex]
Opposite points: [tex](1,-2)[/tex] and [tex](-2,1)[/tex]
Required
Find k
First, calculate the midpoint of the opposite points.
[tex](x,y) = 0.5(x_1 + x_2,y_1 + y_2)[/tex]
This gives:
[tex](x,y) = 0.5(1 -2,-2 + 1)[/tex]
[tex](x,y) = 0.5(-1,-1)[/tex]
Open bracket
[tex](x,y) = (-0.5,-0.5)[/tex]
The equation [tex]3y = 5x + k[/tex] becomes:
[tex]3 * -0.5 = 5 * -0.5 + k[/tex]
[tex]-1.5 = -2.5 + k[/tex]
Solve for k
[tex]k = 2.5-1.5[/tex]
[tex]k = 1[/tex]
Solve the equation:
3x - 5 = -26
Answers
Answer:
x = -7
Explanation:
Move the constant to the right-hand side and change its sign:
3x = -26 + 5
Calculate the sum:
3x = -21
Divide both side of the equations by 3:
Therefore, the answer will be x = -7
Answer:
[tex]3x - 5 = - 26 \\ \\ = > 3x = - 26 + 5 \\ \\ = > 3x = - 21 \\ \\ = > x = - \cancel\frac{ - 21}{3} \\ \\ = > x = - 7[/tex]
Hope This Helps You ❤️A right triangular prism and its net are shown below.
(All lengths are in centimeters.)
Answers
Answer:
A=4
B=8
C=6
D=10
SA=208
Surface area=bh+(s1+s2+s3)H
=6×8+(4+6+10)(8)
=208
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the value of y?
Answers
y + 35 = ( y ) + ( y - 31 )
y + 35 = 2y - 31
Add both sides 31
y + 35 + 31 = 2y - 31 + 31
y + 66 = 2y
Subtract both sides y
y - y + 66 = 2y - y
y = 66
£730 is divided between June, Sushil & Fiona so that June gets twice as much as Sushil, and Sushil gets three times as much as Fiona. How much does Sushil get?
Answers
Answer:
Sushil gets $219.
Step-by-step explanation:
With the information provided, you can write the following equations:
It says that £730 is divided between June, Sushil & Fiona, which can be expressed as:
x+y+z=730 (1), where:
x is the amount June gets
y is the amount Sushil gets
z is the amount Fiona gets
Also, the statement indicates that June gets twice as much as Sushil which means that the amount June gets is equal to two for the amount Sushil gets:
x=2y (2)
Besides, you know that Sushil gets three times as much as Fiona which means that the amount Sushil gets is equal to 3 for the amount Fiona gets:
y=3z (3)
Now, you can replace (3) in (1) and (2) and you will have 2 new equations:
x=2(3z)
x=6z (4)
x+3z+z=730
x+4z=730 (5)
You have the following equations:
x=6z (4)
x+4z=730(5)
Next, you can replace (4) in (5) and solve for z:
6z+4z=730
10z=730
z=730/10
z=73
Now, you can replace the value of z in (3):
y=3z
y=3(73)
y=219
Finally, you can replace the value of y in (2):
x=2y
x=2(219)
x=438
According to this, the answer is that Sushil gets $219.
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be shorter than 63 inches tall, to the nearest thousandth?
Answers
The probability that a randomly selected student from the all-boys school will be shorter than 63 inches tall is approximately 0.9%.
To find the probability that a randomly selected student will be shorter than 63 inches tall, we need to use the standard normal distribution table or a statistical calculator.
Calculate the z-score for the value of 63 inches using the formula:
z = (X - μ) / σ
where X is the value (63 inches), μ is the mean (70 inches), and σ is the standard deviation (3 inches).
z = (63 - 70) / 3
z = -7 / 3
z = -2.3333
Now, we look up the area to the left of the z-score -2.3333 in the standard normal distribution table.
Using a standard normal distribution table, the cumulative probability for z = -2.33 (rounded to two decimal places) is approximately 0.009.
So, the probability that a randomly selected student will be shorter than 63 inches tall is approximately 0.009 or 0.9% (rounded to the nearest thousandth).
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ4
find the volume of the cone above in terms of pi
Answers
good luck :))))
Josh is a car salesman. He gets an annual salary of $45,000 plus a commission, C, of $250 for every car he sells. Which equation represents Josh's total annual salary, S?
A. S=45,000+250C
B.S=45,000−250C
C. S=45,000C+250
D. S=45,000C−250
Answers
As for 250, it goes to every car he sells, making it the slope
S = y + mc (y = y intercept, m = slope)
Plug in the values to see
Solution: A. 45,000 + 250C
Erin opened a savings account that earns 3% simple interest. If she deposts $2,750 and doesnt make any additional deposits or withdrawals how much money will be in her account at the end of 6 years?
Answers
Answer:
3245$ (im assuming the interest is yearly)
Step-by-step explanation:
using the is/of method
3% x
___ ___ cross mult and divide. = 82.5 interest x 6 years of it
100 2750
2750 + 495
4. Find both solutions by (
:): x^2 + 6x + 5 = 0
Answers
Answer:
x1 = -5 and x-2 = -1
Step-by-step explanation:
hope this helps
Answer:
x = - 1, - 5
Step-by-step explanation:
Pls help and find the area
Answers
Answer:
I don’t know the area but here’s a hint to help you (hint: length x with x height)
Step-by-step explanation:
what is 30 tens in hundreds
Answers
Answer:
300
Step-by-step explanation:
each ten is worth 10 so 10x30+ 300
plz mark brainliest
Name 4 fractions that are between 1/5 and 1/7
Answers
Answer:
21/240, 22/140, 23/140, 24/140
Step-by-step explanation:
7 and 5 have a common multiple of 140 and
140/7=20 20/140
140/5=28 28/140
21-27 are all numbers b/w 20 and 28
Answer:
21/140, 22/140, 23/140, 24/140
7 and 5 = common multiple of 140.
140/7 = 20 , 20/140
140/5 = 28, 28/140
21, 22, 23, 24, 25, 26, and 27 are the numbers between 20 and 28.
R=( − 2 , 2 ) , ( 2 , − 2 ) , ( − 4 , 4 ) , ( 4 , − 4 ) is r a function?
Answers
Answer:
Step-by-step explanation:
The four inputs (x-coordinates) are {-2, 2, -4, 4}. No input appears more than once. Therefore this seet of points represents a function.