Answer:
g(x) = 3*sin((-15/4)*pi*x + (-15/4)*pi) + 6
Step-by-step explanation:
The function has the form:
g(x) = a*sin(b*x + c) + d
We know that:
The midline is at (-1, 6)
The midline is the value of g(x) when the sin(x) part is equal to zero
Then the midline is y = 6 = d
g(x) = a*sin(b*x + c) + 6
And from this we also know that:
sin(b*-1 + c) = 0,
We also know that the minimum is at (-3.5, 3)
The minimum is the y-value when the sin(x) part is equal to -1
Then
sin(b*-3.5 + c) = -1
And:
g(-3.5) = 3 = a*(-1) + 6
3 = -a + 6
a = -3 + 6 = 3
The equation is something like:
g(x) = 3*sin(b*x + c) + 6
To find the values of b and c, we need to use the two remaining equations:
sin(b*-3.5 + c) = -1
sin(b*-1 + c) = 0
We also know that:
Sin(0 ) = 0
sin( (3/2)*pi) = -1
where pi = 3.14
Then we can just write:
b*-1 + c = 0
b*-3.5 + c = (3/2)*pi
From the first one, we get:
-b + c = 0
c = b
Replacing that on the other equation we get:
c*-3.5 + c = (3/2)*pi
c*(-3.5 + 1) = (3/2)*pi
c*(-2.5) = (3/2)*pi
c = (3/2)*pi/(-2.5)
and:
-2.5 = -5/2
c = (3/2)*(-5/2)*pi = (-15/4)*pi
Then the equation becomes:
g(x) = 3*sin((-15/4)*pi*x + (-15/4)*pi) + 6
The trigonometric function equation becomes [tex]g(x)=3 sin(-1.88x-1.88)+6[/tex]
The function has the form:
[tex]g(x)=a sin(bx+c)+d[/tex]
The midline is at (-1, 6)
So, the midline is y = 6 = d
[tex]g(x)=a sin(bx+c)+6[/tex]
We know that the midline is the value of g(x) when the sin(x) part is equal to zero
Given that The function intersects its midline at (-1,6) and has a minimum point at (-3.5,3).
[tex]sin(-1*b + c) = 0,[/tex]
The minimum is the y-value when the sin(x) part is equal to -1
[tex]sin(-3.5*b + c) = -1[/tex]
Since, [tex]g(-3.5) = 3 = a*(-1) + 6[/tex]
[tex]a = -3 + 6 = 3[/tex]
Now equation become,
[tex]g(x) = 3*sin(b*x + c) + 6[/tex]
To find the values of b and c, we need to use the two remaining equations:
[tex]sin(-3.5b + c) = -1=sin( (3/2)* \pi)\\\\ -3.5b + c = (3/2)* \pi[/tex]
[tex]sin(-1b + c) = 0=sin(0)\\\\-b+c=0\\\\b=c[/tex]
Substituting b = c in above equation and [tex]\pi=3.14[/tex]
We get,
[tex]-3.5c + c = (3/2)*\pi\\\\-2.5c=4.71\\\\c=-1.88[/tex]
also [tex]b=-1.88[/tex]
Therefore, equation becomes [tex]g(x)=3 sin(-1.88x-1.88)+6[/tex]
Learn more:
https://brainly.com/question/13729598
Select the correct text in the passage.
In this excerpt from A Christmas Carol by Charles Dickens, which sentence indicates that Scrooge formed relationships primarily for selfish
reasons?
"I don't mind going if a lunch is provided," observed the gentleman with the excrescence on his nose. "But I must be fed, if I make one."
Another laugh.
"Well, I am the most disinterested among you, after all," said the first speaker, "for I never wear black gloves, and I never eat lunch. But I'll offer
to go, if anybody else will. When I come to think of it, I'm not at all sure that I wasn't his most particular friend; for we used to stop and speak
whenever we met. Bye, byel
Speakers and listeners strolled away, and mixed with other groups. Scrooge knew the men, and looked towards the Spirit for an explanation.
The Phantom glided on into a street. Its finger pointed to two persons meeting. Scrooge listened again, thinking that the explanation might lie
here.
He knew these men, also, perfectly. They were men of business: very wealthy, and of great importance. He had made a point always of standing
well in their esteem: in a business point of view, that is strictly in a business point of view.
Answer: it's the last
Step-by-step explanation:
HELP! Which yd symbol is correct? I’m not sure which!!!
Answer:
yd^3
Step-by-step explanation:
Answer:
120yd^2
Step-by-step explanation:
A=BH
A= 15×8
A=120
symbol = yd^2
final answer= 120yd^2.
Please help due in 15 min!!!!
Answer: True
Step-by-step explanation:
2 with the exponent of 1/2 is 1.41. SQRT for 2 is also the same.
2 with the exponent of -1 is 0.5. Fraction of 1/2 is the same.
please answer fast and quickly
Answer:
Blue
stay safe healthy and happy...Hello there I hope you are having an great day :) If you select a marble without looking which colour are you less likely to pick, All together there is 10 marbles.
Orange : 2/10
Black : 2/10
Green : 5/10
Blue: 1/10
The less Colour is Blue as there is only 1 Marble so it probably the less likely to be picked.
Hopefully that helps you :)
Help I need help!!! please!!!
[tex]a.(x - 4)(x - 9) = x {}^{2} - 9x - 4x - 36 = x {}^{2} - 3x - 36[/tex]
Mr lance designed a class banner shaped like a the polygon shown. What is the name of the polygon?
Answer:
hexagon
Step-by-step explanation:
i g
Question 6: Write an equation for the parabola with vertex (2, 5) and focus (-1, 5).
A. (x - 2)^2 = -12(y - 5)
B. (x - 2)^2 = -3(y - 5)
C. (y - 5)^2 = -12(x - 2)
D. (y - 5)^2 = -3(x - 2)
Need help with this question please!!
Answer:
11.1
Step-by-step explanation:
Use the Pythagorean theorem to find the unknown side.
[tex]a^{2} +b^{2} =c^{2} \\AB^{2} +BC^{2} =AC^{2} \\AB^{2} +19^{2} =22^{2} \\\\AB^{2}=22^{2}-19^{2\\AB=\sqrt{123} \\AB=11.1[/tex]
What is mZPQR in radians?
Answer:
7pi/20 radians
Step-by-step explanation:
63 pi
------ x---------- = 63pi/180
1 180
63pi/180 simplified is 7pi/20 radians.
When the rate is Rs 210 per piece, a certain sum of money can buy 16 pieces of
Tshirts. If the rate increases to Rs. 280 per piece, how many pieces of T-shirts
can be bought with the sum?
Answer:
12 pieces of T-shirts can be bought with the sum.Step-by-step explanation:
Given that:
The rate is Rs 210 per piece, a certain sum of money can buy 16 pieces of T-shirts.To Find:
If the rate increases to Rs. 280 per piece, how many pieces of T-shirts can be bought with the sum?Let us assume:
x pieces of T-shirts can be bought with the sum.Finding the number of T-shirts bought:
According to the question.
Rate × Pieces of T-shirts = Rate × Pieces of T-shirts
⟶ 210 × 16 = 280 × x
⟶ 3360 = 280x
⟶ x = 3360/28
⟶ x = 12
Hence,
If the rate increases to Rs. 280 per piece, 12 pieces of T-shirts can be bought with the sum.Abby and Bill share a 20-ounce bucket of clay. By the end of the week, Abby has used
1/10
of the bucket, and Bill has used
2/5
of the bucket of clay. How many ounces are left in the bucket?
Answer:
A little brain/willpower.....Im sure you can figure it out!!!
What is the length of KL?
A 24
B 37
C 33
D 12
find equation so EASY PLZ HELPPP URGENT WILL GIVE BRAINESD MARK 11+ POINTS
Answer:
y= -4x+4
Step-by-step explanation:
there you go!!!
Answer:
m= -4 would be the equation
Step-by-step explanation:
If the radius of a sphere is 6cm, then it’s volume is____
A. 288pi cm^3
B. 576pi cm^3
C. 72pi cm^3
D. 36pi cm^3
Answer:
[tex]A. \: 288\pi( {cm}^{3} )[/tex]
Step-by-step explanation:
Hint:
Formula = [tex] \frac{4}{3} \pi {r}^{3} [/tex]Radius = 6 cmSimplify:
[tex] \frac{4}{3} \pi (radius {)}^{3} [/tex][tex] \frac{4}{3} \pi \times {6}^{3} [/tex][tex] \frac{4\pi}{3} \times 216[/tex][tex]4\pi = \frac{216}{3} [/tex][tex]4\pi \times 72[/tex]
[tex]288\pi( {cm}^{2} )[/tex]
Hope it is helpful....You want to fill up a jar with lemonade.
Is this the characteristic of total surface area or volume?
PLEASEEEEEEEE HELPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
1
14
The answer is one over fourteen because there are 8 white eggs (remember the 10 brown eggs), and half of them (the white ones) are cracked, so four. And, if you randomly grab an egg, there is 1/14 of a chance you could grab a cracked, white, egg.
Find the area of the figure.
4 in.
-6 in.
6 in.
10 in.
Answer:
68 in
Step-by-step explanation:
Find area of the rectangle - 6 x 10 = 60
Find area of the triangle (Formula - 1/2(base)(height)) - 1/2(4)(6) = 8
Add them - 60 + 8 = 68
What is the slope of the equation: y = -3x + 7
Step-by-step explanation:
tan‐¹ –3 I guess
Correct me if I am wrong
Answer:
-3
Step-by-step explanation:
in y=mx+b, m is the slope. There for -3 is the slope.
HELP ME PLEASE IHDGYSKHJN
Answer:
b.39
Step-by-step explanation:
312 divided by 8 is 39
Answer:
312 divided by 8 = 39, B is your answer
Step-by-step explanation:
You need to spread the books equally amongst the 8 shelves there are. Which means you divide.
Multiple Select: Multiply and match each of the following
expressions.
A. (x − p) (x + p)
B. (x – 5) (x + 7)
C.(x + p) (x + p)
A.isz? - 2px – pº A.isx? – p2 B.isz? + 2x – 35
B.isx? - 20 – 35 Cisx2 + 2px +p?
Answer:
A. (x − p) (x + p) = x² - p²
B. (x – 5) (x + 7) = x² + 2x - 35
C. (x + p) (x + p) = x² + 2px + p²
Step-by-step explanation:
To find - Multiply and match each of the following expressions.
A. (x − p) (x + p)
B. (x – 5) (x + 7)
C.(x + p) (x + p)
Proof -
A.)
The expression is - (x − p) (x + p)
Now,
(x − p) (x + p) = x(x + p) - p(x + p)
= x(x) + x(p) - p(x) - p(p)
= x² + xp - px - p²
= x² - p²
⇒(x − p) (x + p) = x² - p²
B.)
The expression is - (x – 5) (x + 7)
Now,
(x − 5) (x + 7) = x(x + 7) - 5(x + 7)
= x(x) + x(7) - 5(x) - 5(7)
= x² + 7x - 5x - 35
= x² + 2x - 35
⇒(x − 5) (x + 7) = x² + 2x - 35
C.)
The expression is - (x + p) (x + p)
Now,
(x + p) (x + p) = x(x + p) + p(x + p)
= x(x) + x(p) + p(x) + p(p)
= x² + xp + px + p²
= x² + 2px + p²
⇒(x + p) (x + p) = x² + 2px + p²
Help please how do I find x and y
Answer:
Option 3
Step-by-step explanation:
tan33°=x/7
x=4.5
4.5^2+7^2=y^2
20.25+49=y^2
y=√69.25
y=8.3
A standard American deck of cards contains 52 cards in four “suits”:
♣ clubs
♦ diamonds
♥ hearts
♠ spades
Each card also has a “rank”. There are 13 ranks: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), A(ace). Every suit-rank combination occurs in the deck, so a typical card might be called “the 7 of clubs” or “the queen of hearts”. Suppose we shuffle a deck (meaning that we put the cards in random order), then we draw a card
off the top. What is the probability that this card has an even number on it? (Jacks, queens, kings, and aces do not have numbers on them.)
I need the answer quickly pls
Answer:
5/13
Step-by-step explanation:
We can first start by finding the number of even numbers in one suit and then multiply by 4. The even numbers are:
2, 4, 6, 8, 10
There are 5, and since there are 4 suits, there is a total of 20 even cards.
Probability is equal to the amount of desirable outcomes over the total number of outcomes. The desirable outcomes are when we pull out an even number, and as we calculated earlier, there are 20 of those. There are 52 total cards, so that is the number of total outcomes. We get the expression:
20 / 52 which simplifies to 5/13
1. Find six rational numbers between 2/7 and 5/2
Answer:
5/14
6/14
7/14
8/14
9/14
10/14
Step-by-step explanation:
We need to find the six rational numbers between 2/7 and 5/2. Firstly convert the fractions into like fractions.
LCM of 7 & 2 = 14=> 2/7 = 2×2/7×2 = 4/14
=> 5/2 = 5 ×7/2×7 = 35/14
Therefore the six rational numbers are
5/146/147/148/149/1410/14Henry is planning to attend a public university after he graduates from high school in 3 years. He is devising a plan to save money each month to help with the expenses of attending the university. The cost of attending the public university for one-year is $26,500. His family has promised to contribute $13,450 each year he is in school. What is the minimum amount of money Henry must contribute to his savings per month for the next 3 years to have enough money to pay for his first year of tuition?
a
$501.32
b
$362.50
c
$294.38
d
$482.35
pls answer due in a few
Answer:
Step-by-step explanation:
2x² + 7x + 3 = 0
a = 2 , b = 7 , c = 3
D = b² - 4ac = 7² - 4(2)(3) = 49 - 24 = 25 = 5²
Given equation has 2 real solutions (C)
super urgent will give u 5 rating and thansk if u answer
A jar contains 12 oatmeal cookies, 13 sugar cookies and 5 chocolate chip cookies. The percent of cookies that are oatmeal is ?
Answer:
40%
Step-by-step explanation:
I added all the cookie numbers together to get 30 then I found the percentage of 12 in 30 which is equal to 40 percent
please answer accurately with a full explanation and please don't do short answers thank u, and if u spam this question u will be reported. please answer with a proper answer, not a short one thank u so much
Answer:
When buying a backpack you want to pick the one with the greatest volume. Backpack A has the highest volume (5200) which means that it's the backpack that will allow me to fit the most stuff.
Step-by-step explanation:
This questions i just asking which bag has the greatest volume
the formula for that is just l*w*h
calculate the volume for each backpack:
a: 26*20*10=5200
b: 32*16*8=4096
c: 28*14*12= 4704
We can see that backpack A has the greatest volume, so we should pick it.
This is what I have so far I just need the last step
Answer:
-2
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
-6/3=-2
Plz help will mark brainliest
Answer:
the correct answers are A B C E
Write the equation of the line that goes through the point (-2, 8) with a slope of 1/2
Answer:
The answer is Y = 1/2x + 9
Step-by-step explanation:
The general equation with a slope and intercept is:
y=mx+b
We are given a slope of 1/2, which represents the "M" part of the equation.
So we have:
Y = 1/2x + b
We do not know what "b" is, so the equation is not complete.
We plug in "-2" for X and "8" for Y:
8 = 1/2 (-2) + b
b = 9
So, the full equation is: Y = 1/2x + 9