Answer is h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π ) - [tex]\frac{1}{2}[/tex]
∵The maximum point (- 2π. 3 )
minimum point (- π / 2 , - 4)
and h(x) = a cos (b x + c)+ d
∴ a + d = 3 d = - 1/ 2
⇒
-a + d = -4 a = 7 / 2
{solve the equation}
and -2πb + c = 0 b = 2 / 3
⇒
- ( π/ 2) b + c = λ c = 4 / 3 π
∴ h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π) - [tex]\frac{1}{2}[/tex]
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant
here detail explanation:
Sine Function
Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:
Sin a =Opposite/Hypotenuse = CB/CA
Cos Function
Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.
Cos a = Adjacent/Hypotenuse = AB/CA
Tan Function
The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.
Tan a = Opposite/Adjacent = CB/BA
Also, in terms of sine and cos, tan can be represented as:
Tan a = sin a/cos a
Secant, Cosecant and Cotangent Functions
Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:
Sec a = 1/(cos a) = Hypotenuse/Adjacent = CA/AB
Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB
cot a = 1/(tan a) = Adjacent/Opposite = BA/CB
Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.
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Refer to the number line. find the coordinate of point c that is 78 of the distance from m to j.
The coordinate of point c is such that point c is 7/8 of m to j is [ 7/8(x₂ - x₁), 7/8(y₂ - y₁) ].
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
For example (5,3) here 5 will be for the x and 3 will be for the y.
Another example is (9,0) here 9 is for x and 0 is for y.
Let's say the coordinate of m → (x₁,y₁)
j → (x₂ ,y₂)
Now since point c is proportion with 7/8
So,
It will be 7/8 times of difference between of x and y coordinate of points m and j
So,
x = 7/8(x₂ - x₁) and y = 7/8(y₂ - y₁)
Hence "The coordinate of point c is such that point c is 7/8 of m to j is [ 7/8(x₂ - x₁), 7/8(y₂ - y₁) ]".
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each problem, create a table
Write an equation, in slope-intercept form, to model each situation.
1. You rent a bicycle for $20 plus $2 per hour.
Y=2x120
Answer:
You have a fixed cost ($20) and a variable cost ($2*number of hours you rent the bike)
Cost = Variable Cost + Fixed Cost
Let y = your Cost and x = the number of hours you rent the bike. The fixed cost is $20.
y = ($2 per hour)*(x hours) + $20
y = 2x + 20
Which new angle is created by extending one side of a triangle?
a remote interior angle
an adjacent interior angle
an exterior angle
a complementary angle
The created by extending one side of a triangle is called: C. an exterior angle.
What is an Exterior Angle of a Triangle?An exterior angle of a triangle is an angle that is formed by extending any of the sides of a triangle. The angle formed, which is called the exterior angle, has a measure that is equal to the sum of the opposite interior angles of the triangle.
Therefore, the angle shown in the image given that is created by extending one side of a triangle is called: C. an exterior angle.
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Write two expressions that represent the volume of the cube, one with exponents and one without.
There are two squares with the same side lengths scaled copies of one another explain your reasoning
A square is a rectangle with equal lengths on each side. The two squares with the same length side will be lengths scaled copies of one another.
A rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).
As it is known that two squares are always similar to each other which is because all the angles of a square are always 90°. Therefore, any two squares are always similar to each other.
Now, as it is given that the two square have the same length sides. Therefore, the two squares with the same length side will be lengths scaled copies of one another. This is because all the sides are equal and all the angles are equal.
Hence, the two squares with the same length side will be lengths scaled copies of one another.
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Write the rational number 36/5 as a decimal
Answer:
36/5 as a decimal is 7.2
Step-by-step explanation:
In the fraction 36/5, 36 is the numerator and 5 is the denominator, the fraction bar means "divided by". Therefore, the fraction 36/5 is same as "36 divided by 5" or "36 ÷ 5".
When we calculated 36 divided by 5, we found that 36/5 in decimal form is:
36 ÷ 5 = 7.2
Therefore, the decimal form of 36/5 is 7.2
Consider this set of numbers: 1, 1, 2, 2, 3, 3, 4, 7, 7, 7, 8, 9. the _____ of the set is 7.
Answer:
mode
Step-by-step explanation:
The mode of the set is 7, as 7 is the number that occurs the most frequently.
How many units from zero is 0 on the number line? What is the opposite of 0?
Answer:
The absolute value of a number is the distance between the number and zero on a number line. Every number and it opposite are the same distance from zero on the number line.
6/X + 9 if x = 3
pls help me
answer:
6/x + 9 = 11
explanation:
6 div. 3= 2
2+9=11
Simplify $(-3x^2 y)(5x^4 y^3).$
Answer: [tex]-15x^6y^4[/tex]
Step-by-step explanation:
(-3x^2 y)(5x^4 y^3)=
-3x^2 *5x^4 *y*y^3=
-3*5*x^2 *x^4 *y^4=
-15*x^(2+4) *y^4=[tex]-15x^6y^4[/tex]
candice is a building manager for the crowley enterprise office building
one of her responsibilities is cleaning the office building's 200-gallon
aquarium. for cleaning, she must remove the fish from the aquarium
and drain the water. the water drains at a constant rate of 10 gallons
per minute.
The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.
The independent variable, as indicated in the name is not influenced by other variables but can predetermine its own self.
So, the independent variable is the water in the 200 gallon aquarium
Now, the dependent variable is the tested variable and is depends on the independent variable, which is the time it takes to drain the 200 gallon aquarium.
Hence, independent variable is volume of water in the aquarium and dependent variable is time it will take to drain the aquarium.
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Find the remainder for this calculation.
161 4
40 Remainder 1
hope this helps :)
Use the graph to determine
A) The function’s domain
B) The function’s range
C) The X-intercepts
D) Y-intercepts
E) The missing function values indicated by question marks below
Answer:its C
Step-by-step explanation:
they x will intercept when you do it right
What is the value of the "?" in the figure below
Answer:
I think it is none of the choices.
Step-by-step explanation:
what is 11 9/8 as a mixed number in the simplest form
Answer:
97/8
Step-by-step explanation:
first we multiply 11 x 8 to get 88
then we add the numerator (number on top,9) so we add 88+9 to get 97
now we can write our answer
97/8
it cannot be simplified any more than this.
i hope this helped and if you have any questions just ask!
hi please help me ii need this one right now
Answer:the graph is not linear
Step-by-step explanation:
Unit 2 Logic and Proof Homework 1 Inductive reasoning
Answer:
The answers for this question is given below in the explanation section, kindly refer.
Step-by-step explanation:
Find the next 5 terms:
1) 28 < 33, 38, 43, 48, 53 => In every next term 5 is added.
2) 64 < 32, 16, 8, 4, 2 => In every next step the term is divided by 2.
3) 64 < 125, 216, 343, 512, 729 => In every next step it is a cube of next number.
4) 13 < 17, 19, 23, 29, 31 => In every next term it is the next prime number.
5) V < VI, VII, VIII, IX, X => In every next term it is the next roman numeral.
6) 8 < 13, 21, 34, 56, 90 => In every next term it is the sum of previous two terms.
7) => In every next term the arrows rotate clockwise in direction.
T/F:
8) False => 17+19 = 36, which is not a prime number.
9) True
10) True
11) True
12) True
13) True
14) False => ostrich, penguin, etc.
15) True
16) False => (a + b)² = a² + b² + 2ab
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The following addition problem is not correct if the numbers are interpreted as base 10. In what number base is the problem correct? 66 87 85 48
The base is 24.
Let the base be b. we know that b>8
If we added everything, it would look something like this:
66 + 87 + 85 + 48
=132
Adding up the one's digit gives us 26, so we have 26 mod b=2
The only options for b are b = 12 or 24.
If b = 12, the sum of the one's digit would be [tex]22_{12}[/tex] so we could carry the 2 to the tens column. Adding everything up would give us [tex]24_{12}[/tex] the answer is [tex]242_{12}[/tex]
That means the base is 24.
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The probability of a particular event occurring is 0.27.
What is the probability that the event will NOT occur?
The Probability of not occurring of that event is 0.73.
Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Flipping a coin is the best illustration for understanding probability:
Heads or tails are the two possible results.
What is the likelihood that the coin will land on heads? P(H) = can be used to determine this. P(H)=? P, H, the equals sign, the left and right parenthesis, and the question mark. It's possible that you already know 50%, or half and half, is the likelihood. How do we figure it out, though?
Probability of an event = (number of possible outcomes) / (total number of outcomes)
we know , total probability is always 1
Total probability = pro. of event occur + prob. of event not occur
1 = 0.27 + event not occur
probability of event not occur is 0.73
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can someone solve this please, thank you
Answer:
110
Step-by-step explanation:
13x - 20 + 7x = 180
20x -20 = 180
20x = 200
x = 10
13(10) - 20
=110
Ronald wants to rent a car to take a trip and has a budget of $60. there is a fixed rental fee of $25 and a daily fee of $5. write an inequality that would be used to solve for the maximum number of days for which ronald can rent the car on his budget. 25 5x ≤ 60 25 5x ≥ 60 25x 5 ≤ 60 25x 5 ≥ 60
Answer:
60>x>25
Step-by-step explanation:
There are three dials on a combination lock.
Each dial can be set to one of the numbers 1, 2, 3, 4, 5, 6
The three digit number 536 is one way the dials can
be set as shown in the diagram.
a) Work out the number of different three digit numbers
that can be set for the combination lock.
Answer: 136, 625,532,413
Step-by-step explanation:
the number of triangles is 1/3 the number of sides
Answer:
y=(1/3) or y=1/3x
Step-by-step explanation:
Without the parenthesis, your equation can be interpreted as Y = one over 3x
The equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
Let's denote the number of sides of a polygon as "s" and the number of triangles that can be formed within the polygon as "t."
The equation for the number of triangles being 1/3 the number of sides is:
t = (1/3) × s
This equation states that the number of triangles (t) is equal to one-third of the number of sides (s) in a given polygon.
Hence, the equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
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Complete question:
Write an equation for the number of triangles is 1/3 the number of sides.
Identify a counterexample for the following statement:
"If a number is a perfect square, then it can't end with a 1."
Answer:
81
Step-by-step explanation:
81 is a perfect square, and also ends with 1.
Write the decimal equivalent for each rational number. Use a bar over any repeating digits 3/11
Answer:
see below
Step-by-step explanation:
1/11=0.0909....
3/11=0.090909...*3 or 0.27272727...
Which expression is equivalent to (2^-1)^3
The solution is [tex]\frac{1}{8}[/tex] .
To understand this problem we need to know the concept of surds and indices, powers and exponents.
If we write [tex]x^{2}[/tex] it means that x must be multiplied by itself two times.
But if we write [tex]x^{-2}[/tex] it means [tex]\frac{1}{x^{2} }[/tex].
Which means if an number has negative power then it must be written in the inverse format to make it positive.
Given here is [tex](2^{-1})^{3}[/tex]
⇒[tex](\frac{1}{2}) ^{3}[/tex]
⇒[tex]\frac{1}{8}[/tex] is the required solution of the problem.
This can also be solved in other ways by multiplying the powers and then inverting the fraction to make it positive.
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Name the angle in as many different ways as possible.
Answer:
WXZ, ZXW, 1
Step-by-step explanation:
Examine the distribution of the target variable. what is the proportion of individuals who purchased organic products?
The proportion of individuals who purchased organic products is 24.77%.
The target variable is the variable whose values are modeled and predicted by other variables. A predictor variable is a variable whose values will be used to predict the value of the target variable
The target variable (also called the dependent variable) used in the analysis for this tutorial is a categorical variable that differentiates clinicians in the study that indicated that they would be Highly Likely to Use Product X from those that had a Low Likelihood to Use the new product
Organic food is grown without the use of synthetic chemicals, such as human-made pesticides and fertilizers, and does not contain genetically modified organisms (GMOs). Organic foods include fresh produce, meats, and dairy products as well as processed foods such as crackers, drinks, and frozen meals.
According to the plot the distribution of target variable is as follows
0’s: 167181’s
5505
The proportion of individuals who purchased organic products are: 5505/22223
= 0.2477
=24.77%
That is around 24.77% people have purchased organic products.
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Find each product.
29. (r-1)(7r+2)
31. x²(3x-2)(5x+1)
37. (m-n+k)(m+2n-3k)
43. (2m+3)(2m-3)
45. (4x²-5y)(4x²+5y)
Answer:
29. 7r^2-5r-2
31. 15x^4-7x^3-2x^2
37. -3k^2-2km+5kn+m^2+mn-2n^2
43. 4m^2-9
5. 16x^4 - 25y^2
Step-by-step explanation:
To solve these you expand the polynomial and use the FOIL method.
How+long+will+it+take+for+$2900+to+grow+to+$25,600+at+an+interest+rate+of+10.4%+if+the+interest+is+compounded+quarterly?+round+the+number+of+years+to+the+nearest+hundredth.+group+of+answer+choices
The number of years to the nearest hundredth is t = 21 years and 3 months.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
It is given that:
A = $25,600
P = $29,00
r = 10.4 = 0.104
n = 4
[tex]\rm 25600 = 2900(1+\dfrac{0.104}{4})^{4t}[/tex]
After solving:
t = 21.212 years
Or
t = 21 years and 3 months
Thus, the number of years to the nearest hundredth is t = 21 years and 3 months.
The complete question is:
How long will it take for $2900 to grow to $25,600 at an interest rate of 10.4% if the interest is compounded quarterly round the number of years to the nearest hundredth?
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