Answer: F(x) = 2*sin(x/10 +(3/2)*pi) + 5
Step-by-step explanation:
The information that we have is that:
We have a minimum at (0, 3)
the midline is at (5*pi, 5)
This is a sinusoidal function, so we can write one generic one as:
F(x) = A*sin(c*x + p) + B.
where A and B are constants, c is the frequency and p is a phase
First, the minimum of the sine function is when sin(x) = -1, and this happens at (3/2)*pi
We know that this minimum is at x = 0.
sin(c*0 + p) = -1
Then p = 3/2*pi.
So our function is:
F(x) = A*sin(c*x +(3/2)*pi) + B.
Now, we know that F(0) = 3, so:
3 = A*sin(c*0 +(3/2)*pi) + B = -A + B.
now we can use the other hint, the midpoint of the sine function is when sin(x) = 0, and this happens at x = 0 and x = pi, particularlly as we here have a phase of 3/2*pi, we should find x = 2*pi.
then:
c*5*pi + (3/2)*pi = 2*pi
c*5 + 3/2 = 2
c*5 = 2 - 3/2 = 1/2
C = 1/2*5 = 1/10
So our function is
F(x) = A*sin(x/10 +(3/2)*pi) + B
and we know that when x = 5*pi, F(5*pi) = 5, so:
5 = F(x) = A*sin(5*pi/10 +(3/2)*pi) + B
5 = B
and we aready knew that:
- A + B = 3
-A + 5 = 3
A = 5 - 3 = 2
So our equation is:
F(x) = 2*sin(x/10 +(3/2)*pi) + 5
Answer:
the correct answer is
[tex]f(x) = - 2 \cos( \frac{1}{10}x ) + 5[/tex]
In Mrs. Nathan's class, there are 16 boys and 20 girls. What is the ratio of girls to boys in Mrs. Nathan's class?
Answer:
5:4
Step-by-step explanation:
In Mrs. Nathan's class, the ratio of girls to boys is 5:4.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, In Mrs. Nathan's class, there are 16 boys and 20 girls.
the ratio of girls to boys = 20/16
the ratio of girls to boys = 5/4
Therefore, the ratio of girls to boys in Mrs. Nathan's class is 5: 4.
Learn more about ratios here:
https://brainly.com/question/13419413
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If C is the midpoint of AB and AB = 20, what is AC?
Answer:
AC = 10
Step-by-step explanation:
AC+ BC =AB
If C is the midpoint then AC = BC
AC + AC = 20
2 AC = 20
Divide by 2
2AC /2 = 20/2
AC = 10
Answer:
AC=10
Step-by-step explanation:
If a-------c-------b and AB=20 and C is the midpoint, then half of 20 would be 10.
Given: ∠1 =∠ 4 ∠ B = ∠D Prove: AD = CB Which of the following triangle congruence theorems would be used in this proof? A. SAS B. ASA C. AAS
Answer:
Step-by-step explanation:
<2=180-(1+B)
<3=180-(4+D)
trg ACB=trgACD(<2=<3, AC =AC, <1=<4
ASA
find the area of the shape
37.68 is the area of the Pac-Man
In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and -2 for every incorrect answer and 0 for not supplying any answer. If Yash scored 94 marks in a test, what are the possibilities of his marking correct or wrong answer
Answer:
1. 47 correct, 0 wrong and 3 unanswered
2. 48 correct, 1 wrong and 1 unanswered
Step-by-step explanation:
Given;
Total number of questions = 50
For correct answers = 2
For wrong answers = -2
Unanswered questions = 0
Yash scored 94 marks
Let c, w and u represent the number of correct, wrong and unanswered questions
2×c - 2 × w + 0×u = 94
2c -2w = 94 .....1
And;
c + w + u = 50 .....2
We have 2 equations and 3 unknowns
By observing the problem, we can see two possible solutions;
Case 1: Assuming he did not miss (get wrong) any answer;
He needs to score 47 answers right;
47 × 2 = 94
Then;
c = 47 w = 0 and u = 50 - (47+0) = 3
47 correct, 0 wrong and 3 unanswered
Case 2: Assuming he got one answer wrong;
He would need to score one more answer right compared to the first case;
(47+1) × 2 - 1 × 2 = 96 - 2 = 94
c = 47+1 = 48
w = 1
u = 50 - (48+1) = 1
So he need to score 48 correct answers, 1 wrong answer and 1 unanswered.
OA ⊥ OC start overline, O, A, end overline, \perp, start overline, O, C, end overline \qquad m \angle BOC = 6x - 6^\circm∠BOC=6x−6 ∘ m, angle, B, O, C, equals, 6, x, minus, 6, degrees \qquad m \angle AOB = 5x + 8^\circm∠AOB=5x+8 ∘ m, angle, A, O, B, equals, 5, x, plus, 8, degrees Find m\angle BOCm∠BOCm, angle, B, O, C:
Answer:
42 degrees.
Step-by-step explanation:
[tex]\angle BOC+\angle AOB=90^\circ $(Complementary Angles)\\6x - 6^\circ+5x + 8^\circ=90^\circ\\6x+5x-6^\circ+ 8^\circ=90^\circ\\11x+ 2^\circ=90^\circ\\11x=90^\circ-2^\circ\\11x=88^\circ\\$Divide both sides by 11\\x=8^\circ\\$Therefore:\\m\angle BOC=6x - 6^\circ\\=6(8) - 6^\circ\\=48-6\\=42^\circ[/tex]
The measure of angle BOC is 42 degrees.
Answer:
BOC = 42º
Step-by-step explanation:
Angle BOC is equal to 42 degrees, due to these steps -
1. Create the equation which will result to be -
6x - 6 + 5x + 8 = 90
2. Simplify by adding variables and numbers together -
11x + 2 = 90
3. Subtract 2 from both sides to get -
11x = 88
4. Divide by 11 on both sides to get-
x = 8
5. Substitute x in angle BOC as 8 to get this equation -
6(8) - 6
6. Solve
48 - 6 =
42º
Your final answer for angle BOC is 42º!
What is the sum of this arithmetic series?
Answer:
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Step-by-step explanation:
Explanation
Let a , a+d , a+2 d , ..........a+(n-1)d +....... is an arithmetic sequence
The sum of the sequence is called arithmetic series
The [tex]n^{th}[/tex] term of the sequence
[tex]t_{n} = a + (n-1) d[/tex]
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Here 'a' is the first term of the sequence
and 'd' be the difference between two values
sum of first term
put n=1 ⇒ [tex]S_{1} = a[/tex]
Put n =2 ⇒ [tex]S_{2} = \frac{2}{2} (2 a + (2-1)d)[/tex]
[tex]S_{2} = 2 a + d[/tex]
......and so on
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
In the triangle below, what is the length of the side opposite the 60° angle?
Answer:
C. 3√3
Step-by-step explanation:
Remember your 30-60-90 triangle rules.
They give you 3 as a side in the 30-60-90. That side length 3 will be your x. The side opposite of it is x√3. Simply plug in 3 as it is x and you should get 3√3 as your answer.
Answer:
C
Step-by-step explanation:
In all 30 60 90 triangles, the side opposite the 60 degree angle will be the short leg times [tex]\sqrt{3}[/tex]
So, the length of that side in this triangle will be 3[tex]\sqrt{3}[/tex]
HELPPPPPP ITS ABOUT EQUATIONSSSS HELPPPPP
Explanation needed
Answer:
C. the average total cost for the first month of a gym membership
Step-by-step explanation:
x=1 is for month 1,
the value of y includes 1-month fee and one off payment, so this is the average total for the first month of membership
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
A circle is centered at Q(1,-5) and has a radius of 5. Where does the point Y(4,-1) lie?
Answer:
Point Y (4, -1) lies on the circle.
Step-by-step explanation:
Distance = √[(x2-x1)² + (y2 - y1)²] = √[(4-1)² + (-1-(-5))²] = √[3² + 4²]= √25 = 5
Point Y (4, -1) lies on the circle, because the distance from the center to this point equals radius of the circle.
Answer:
On the circle
Step-by-step explanation:
Please answer this math question !! Thank u !! 20 POINTS AND BRAINLIEST!!
Answer:
infinite solutions
Step-by-step explanation:
Given the 2 equations
y = 6x - 3 → (1)
12x - 2y - 6 = 0 → (2)
Substitute y = 6x - 3 into (2)
12x - 2(6x - 3) - 6 = 0 ← distribute and simplify left side
12x - 12x + 6 - 6 = 0
0 = 0
This solution 0 = 0 indicates that any value of x is a solution
Thus there are an infinite number of solutions to the system
I need help ASAP please help me I’ll give brainliest
Answer:
Volume = 1,017.4m^3 .
Step-by-step explanation:
[tex]V = \frac{1}{3} pir^{2}h \\h (height) = 12m\\r (radius ) = 9m\\PI = 3.14\\V =\frac{1}{3} * 3.14 *9^{2} *12\\\\V = 1,017.36\\V = 1,017.4m^{3} .[/tex]
If x=1+√2, evaluate x³+1/x³.
Answer:
18
Step-by-step explanation:
So we start solving like:
x+1x=3
(x+1x)3=33
x3+3.x2.1x+3.x.1x2+1x3=27
(x3+1x3)+3.x2.1x+3.x.1x2=27
x3+1x3+(3x+3x)=27
x3+1x3+3(x+1x)=27
x3+1x3+3×3=27
x3+1x3+9=27
x3+1x3=18
Therefore the answer is 18
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is 112 degrees. Exterior angle to angle B is 2 x degrees and the exterior angle to angle C is (2 x + 12) degrees.
Answer:
70°
Step-by-step explanation:
∠A =112°,
Exterior angle to angle B is 2x, therefore ∠B = 180 -2x (angle on straight line)
Exterior angle to angle C is 2x + 12, therefore ∠C = 180 -(2x +12) (angle on straight line) = 180 - 12 -2x = 168 - 2x
∠A + ∠B + ∠C = 180 (sum o angles in a triangle)
112 + 180 - 2x + 168 - 2x = 180
460 - 4x = 180
4x = 460 - 180 = 280
x = 280/4 = 70
x = 70°
Answer:
70º
Step-by-step explanation:
i took the test
what is the equation of a circle with center (5, -8) and diameter 4?
Answer:
is 8 porque s mi nose maje
Any one can help me please please I need help please each one 3 step explanation
Answer:
a) Area of wall to be painted = 114 sq ft
b) Number of cans required = 2×5 = 10
c) Total cost of paint = $338.43
Step-by-step explanation:
Part a)We are asked to find the area of wall that needs to be painted.
we need to subtract the area of window from the area of wall.
We know that area of a rectangular shape is given by
Area = Width×Length
Area of whole wall = 8×15 = 120 sq ft
Area of window = 2×3 = 6 sq ft
Area of wall to be painted = 120 - 6 = 114 sq ft
Part b)1 can of paint will cover 25 sq ft of area.
So to cover the area of wall to be painted,
114/25 = 4.56
since number of cans cannot be in fraction so we would need 5 cans
Since two coats of paints are needed so
Number of cans required = 2×5 = 10
Part c)1 can of paint costs $29.95
We have total 10 cans
$29.95×10 = $299.5
There is also a 13% tax so the total cost is
$299.5×0.13 = $38.93
Total cost of paint = $299.5 + $38.93
Total cost of paint = $338.43
Teresa is 25 years old, and she makes $30,000 per year. If Teresa were to die,
how much would the beneficiaries of her life insurance policy receive if they
can get by on 75% of her income?
Answer:
They would receive $22,500 which is 75% of her income
Step-by-step explanation:
Here, we want to know how much the beneficiaries of a life insurance scheme would receive if their principal die.
From the question, we are told that they have the right to claim 75% of her income
From the question also, we were told that what she earns per annum is $30,000
Now, since they have the right to claim 75%, the amount they can claim out of the said income will be;
75/100 * $30,000 = $22,500
Answer:225,000
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) Dara invests $800 at 12.5% per annum compound
interest compounded half- yearly .What in his amount of
interest at the end of the first year?
answer: $1,012.50
Step-by-step explanation:
12.5 ÷ 100 = 0.125
0.125 × 800 = 100
800 + 100= 900 ( half-yearly interest)
0.125 × 900 = 112.5
900 + 112.5 = $1,012.50 ( end of first year interest)
the weights, in pounds, of the upper class men offensive line players for a college are shown below:
322, 290, 321, 326, 330, 315, 311, 292, 290
What is the average, or mean, weight of the upper-class men offensive players? provide your answer with 3 sig figs.
1) 311 pounds
2) 315 pounds
3) 290 pounds
4) 318 pounds
Answer:
311 pounds
Step-by-step explanation:
Here, we are to calculate the average weight of the upper-class men offensive players
To calculate this, we need to sum up all the weights and divide by their count
Mathematically, that would be;
Average weight = (322+290+321+326+330+315+311+292+290)/9 = 2,797/9 = 310.77778
Now this written in 3 significant figures would be 311 pounds
Answer:
311
Step-by-step explanation:
You add all of the numbers first (2797)
Then you divide by how many numbers there were (9)
You get 310.7778
Then you round with 3 sig figs.
That is 311
Hope this helps:D
If f(x) = x2 + 1 and g(x) = 3x+1, find f(2) + g(3).
Answer:
ES IGUAL A 15
Step-by-step explanation:
Laura and Andy are trying out for a part in a school play. There is a total of 9 students trying out for the same part. If the students are chosen at random to audition, what is the probability that Laura will go first and Andy second?
The probability that Laura will go first and Andy second is 1/210
Ratio of three angles of a triangle is 1 : 2 : 3. Find the angles.
Answer:
30⁰ , 60⁰ , 90⁰
Step-by-step explanation:
Let the angles x , 2x , 3x
By angle sum property:
x + 2x + 3x = 180⁰
6x = 180⁰
x = 30⁰
Angles are : 30⁰ , 60⁰ , 90⁰
Answer:
30°, 60°, 90°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the parts of the ratio, 1 + 2 + 3 = 6 parts
Divide to find the value of one part of the ratio
180° ÷ 6 = 30° ← value of 1 part of the ratio, thus
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Thus angles are 30°, 60° and 90°
Identify the Domain and Range of the graph below:
Answer:
Domain: ∞
Range: y ≥ -4
Step-by-step explanation:
The domain of any quadratic function is always infinite or ∞. The range ends where the minimum value is or the maximum value depending on which way the parabola is facing- upward or downward.
Jenny is going to tile her kitchen floor. She has taken out all the furniture and appliances. Below is the floor
plan of her kitchen.
2.5m
1.5m
14m
Jenny wants to know if she has got enough money to buy the tiles.
The tiles are sold in packs, which cover 3m
Jenny has a discount card which gives her 25% off any marked price at the DIY shop.
The tiles are marked at £14.40
Jenny has £100 to spend on the tiles.
How much extra does Jenny need to buy the tiles?
Give your answer in pence.
Answer:
Jenny needs £8 extra to buy the tiles.
Step-by-step explanation:
Jenny's kitchen floor is in the form of trapezoid.
Area of a trapezoid = [tex]\frac{1}{2}(b_1+b_2)h[/tex]
[tex]=\frac{1}{2}(2.5+1.5)14[/tex]
= 28 meter²
One pack of tiles covers the area = 3 meter²
She needs the number of packs of tiles = [tex]\frac{\text{total area }}{\text{area covered by one pack of tile}}[/tex]
[tex]=\frac{28}{3}[/tex]
= 9.33
Therefore, she has to purchase 10 packs of tiles.
Since the price of one pack of tiles = £14.40
Price of 10 packs of tiles = 14.40 × 10
= £144
Price after using discount card of 25% = 144 -(25% of 144)
= 144 - (0.25 × 144)
= 144 - 36
= £108
Jenny has £100, so she needs £8 extra to buy the tiles.
Find the distance between points (5,1) and (3,4) to the nearest tenth
Answer:
3.6 units (nearest tenth)
Step-by-step explanation:
distance formula
= [tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
Thus, distance between the 2 points
= √[(5 - 3)² + (1 - 4)²]
= √[ 2²+ ( - 3)²]
= √13
= 3.6 units (nearest tenth)
can some one help me this please
Please answer CORRECTLY !!!!!! Will mark BRAINLIEST !!!!!!!!!
Answer:
Is this correct
The store's rectangular floor is 42 meters long and 39 M wide how many square meters of flooring do they need use estimation access to the reasonableness of your answer
Answer: They need to use 1,638 square meters of flooring.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given, and apply the next formula:
Area of a rectangle: length x width
Replacing with the values given and solving for the area (A):
A = 42 x 39 = 1,638 m2
They need to use 1,638 square meters of flooring.
Feel free to ask for more if needed or if you did not understand something.
I hope you can see but can somebody please help me with this?
Answer:
c find the value
Step-by-step explanation:
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