The equation of the function is y = 10 * sin(x/2pi) + 5.
What is the sinusoidal function?
The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.
The graph of a sinusoidal function can be represented by the equation:
y = A * sin(B(x - C)) + D
where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.
From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.
The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.
The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.
So the frequency is 1/2π.
The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.
The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.
So the equation of the function is:
y = 10 * sin(1/2pi (x - 0)) + 5
y = 10 * sin(x/2pi) + 5
where x is entered in radians.
Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.
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A girl borrowed R128000 from a bank to buy a piece of land. If the land charge 15% p. A, compounded half yearly, what will he have to pay after 1½ year? Alo find fhe compound interet
Girl have to pay total R159014 to bank and compound interest is R31014.
A girl borrow R128000 from a bank to buy a piece of land.
Land charge is 15% Per Annum and time is 1 [tex]\frac{1}{2}[/tex] year.
Compounding with half yearly.
So land charge will be (15/2) % per half yearly and time will be 2 x 1 [tex]\frac{1}{2}[/tex] = 3 half years.
Total amount ( A ) =P (1+R/100)^T
P = initial principal = 128000
R = (15/2) %
T = 3 half yearly
A =P[tex](1+\frac{R}{100} )^{T}[/tex]
A=128000[tex](1+\frac{15}{2*100} )^{3}[/tex]
A=128000[tex](\frac{43}{40} )^{3}[/tex]
A=159014
Total interest amount = 159014 – 128000 = 31014
Therefore , total payable amount is R159014 and interest amount is R31014.
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Re-write the quadratic function below in Standard Form
y= 9(x - 1)(x + 7)
The value of quadratic function is,
⇒ y = 9x² + 54x - 63
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ y = 9 (x - 1) (x + 7)
Now, We can find the quadratic equation as;
⇒ y = 9 (x - 1) (x + 7)
⇒ y = 9 (x² + 7x - x - 7)
⇒ y = 9 (x² + 6x - 7)
⇒ y = 9x² + 54x - 63
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Find a1
a2 = 7, а5 = 7/27
A group of numbers in a particular order are called a sequence. For instance: a1, a2, a3, a4,..., an,... The first term is designated as a1, the second term as a2, and the nth term as an.
In math, what does an a1 mean?The sequence's first term is a1 = 1, making it the first term. I = 2 and a2 = 2 if I = 2. I = 3, hence a3 = 3 if I = 3.
The definition of an arithmetic sequence's nth term is: The equation a = a1 + (n - 1)d determines the nth term of an arithmetic sequence with a1 as its first term and d as its common difference.
A group of numbers in a particular order are called a sequence. For instance: a1, a2, a3, a4,..., an,... The first term is designated as a1, the second term as a2, and the nth term as an.
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The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.
The expression [tex]x^{3} +3x^{2}[/tex] represents the volume of the prism, in cubic units.
We have given that the,
The height of a right rectangular prism is 3 units greater than the length of the base.
The edge length of the square base is x units.
The volume of a rectangular prism = width*length*height
V=w*l*h ......(1)
We have given that the
h=3 greater than the length of the base
and the length of the base is x
Hence, h=x+3
length of base = x
width = x
Substituting values l h and w into the formula (1) we get,
V=w*l*h
= [tex](x)*(x)*(x+3)[/tex]
= [tex]x^{2}*(x+3)[/tex]
=[tex]x^{3}+3x^{2}[/tex]
Therefore the expression
[tex]x^{3}+3x^{2}[/tex] represents the volume of the prism, in cubic units.
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Miriam spent $80 on a concert ticket and 2
snacks. A movie ticket costs $65. How
much was spent on each snack (they cost
the same amount)
The equation represents the cost of snacks. Then the cost of each snack will be $7.5.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Miriam spent $80 on a concert ticket and 2 snacks. A movie ticket costs $65.
Let 'x' be the cost of each snack. Then the equation is given as,
65 + 2x = 80
Simplify the equation, then we have
65 + 2x = 80
2x = 80 - 65
2x = 15
x = 15 / 2
x = $7.5
The equation represents the cost of snacks. Then the cost of each snack will be $7.5.
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In the figure below, C is between A and D, and B is the midpoint of AC. If BC=3 and AD=13, find CD.
The length of CD is 7 units.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
From the figure it is given that C is between A and D.
B is the midpoint of AC
BC=3 and AD=13, we have to find CD.
As B is the midpoint of AC, then BC=AB
BC=AB=3
AC=AB+BC=6
Now to find CD=AD-AC
CD=13-6
CD=7
Hence, the length of CD is 7 units.
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3. Last week Thema ran 2 fewer than 4m miles.
This week she ran 0.5 miles more than last
week. Write an expression for the total number
of miles Thema ran in the two weeks. Then
combine like terms.
The expression for the total miles Thema ran in two weeks will be 8m-3.5 miles.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
As given last week Thema ran=4m-2 miles
this week thema ran=4m-2+0.5 miles
Hence,
expression for the total number of miles Thema ran in the two weeks will be 4m-2+4m-1.5
=8m-3.5 miles
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Factorise a³ + b³ + c³ please i need this immediately
Answer:
a³(b-c) + b³(c-a) + c³(a-b) = (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)
This is a factorized form of the polynomial, as you can see it factorizes as a combination of difference of squares and difference of cubes.
here is one way to factorize the polynomial a³(b-c) + b³(c-a) + c³(a-b) step by step:
First, we can factor out a³ from the first term, b³ from the second term, and c³ from the third term:
a³(b-c) + b³(c-a) + c³(a-b) = a³(b-c) + b³(c-a) + c³(a-b)
Next, we can factor out (b-c) from the first and second terms, and (c-a) from the second and third terms:
a³(b-c) + b³(c-a) + c³(a-b) = (b-c)(a³ + b³) + (c-a)(b³ + c³)
We can factor out (a-b) from the first and third terms, and then we can use difference of cubes to factorise out:
(b-c)(a³ + b³) + (c-a)(b³ + c³) = (b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²)
Now we can combine like terms, and we get:
(b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²) = (a-b)(b-c)(c-a)(a + b + c)(a² + b² + c² - ab - bc - ca)
The factorized form of the polynomial is (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)
This is a general formula for the factorization of a polynomial of the form a³(b-c) + b³(c-a) + c³(a-b)
By using difference of cubes we can factorise the above polynomial, hope it helps.
y = 4/11x + 1
f(5) =
f'(5) =
Answer:
f(5) = 31/11
f'(5) = 4/11
Step-by-step explanation:
y = 4/11x + 1
f(x) = 4x/11 + 1 ==> y = f(x)
f(5) = 4(5)/11 + 1 ==> substitute 5 for x
f(5) = 20/11 + 1 ==> simplify
f(5) = 20/11 + 11/11 ==> make common denominators to simplify easier
f(5) = (20+11)/11
f(5) = 31/11
f'(x) = 4/11
Hence, f'(5) = 4/11 since every value of x will make the derivative 4/11.
Please helppppp meeeeee !!!!!!
Answer:
There are 7 ounces of applesauce in each of Newton's containers.
Step-by-step explanation:
72.5/2.5= 29
29-8=21
21/3=7
Answer: it is 7 in each container .
Step-by-step explanation: becuase if she has 2.5 times more than her what you want to do is divide 72.5 by 2.5 and get 29 the he ate 8 ounces now take away 8 from 29 and you will get 21 and then divide 21 by 3 and you will get 7.... Easy math hope this helps
What are the 4 acute angles?.
Four acute angles are given by : Angle with measure 12 degrees, angle with measure 45 degrees , angle with measure 89 degrees and angle with measure 1 degree.
As given in the question,
Four angles representing acute angles are as follow :
Acute angles : Acute angles are geometrical figure, angles which has measure greater than zero degree and less than 90 degree.
Examples of acute angles are given by :
a. 12 degree : 12 degree is less than 90 degree and greater than 0 degree.
b. 45 degree : 45 degree is more than 0 and smaller than 90 degree.
c. 89 degree : 1 degree less than 90 and 89 more than 0.
d. 1 degree : 0 < 1 < 90.
Therefore, four acute angles are of measure 12 degree, 45 degree, 89 degree and 1 degree.
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Is 2x 3y =- 6 in standard form?.
Yes, 2x + 3y = -6 is in standard form.
The standard form of a linear equation is an equation where the variables are written with a coefficient of 1 or -1, and the constant term (the term with no variables) is written on the right side of the equation. The equation is also written in the form of Ax + By = C, where
x and y are variablesA, B, and C are constants.In equation 2x + 3y = -6, the variables x and y are written with coefficients of 2 and 3 respectively, and the constant term -6 is on the right side of the equation. This satisfies the criteria for standard form as described above.
Key points:
In summary, 2x + 3y = -6 is in standard form because it satisfies the following key points:
The variables are written with a coefficient of 1 or -1.The constant term is written on the right side of the equation.The equation is written in the form of Ax + By = CThe coefficients of the variables are positive or negative but not zero.Learn more about linear equations here:
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
Answer:
the answer is 56.58%
Step-by-step explanation:
The first step is to divide 43 by 76 to get the answer in decimal form:
43 ÷ 76 ≈ 0.5658
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.5658 × 100 = 56.58%
Answer the question below. Be sure to show all of your work.
Naomi earned $45 after babysitting for 5 hours one afternoon. Another day, she babysat for
8 hours and earned $72. Write two equations (one in point-slope and one in slope-intercept)
that represents the number of hours she babysits, x, and the amount of money she earns, y.
Leticia babysat 5 hours on Saturday.
How to calculate?First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. Leticia watched the children for four hours on Friday and for an undetermined period of time on Saturday.
earned $72, Therefore:
8 ( 4 + x ) = 72
( 4 + x ) = 72 / 8
4 + x = 9
x = 9 - 4
x = 5
Leticia babysat 5 hours on Saturday
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The base of a right triangle is 48cm and its hypotenuse is 50cm. What will be the areas of the triangle? class 9
The area of a triangle can be found using the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 48cm and the hypotenuse is 50cm. Since this is a right triangle, we can use the Pythagorean theorem to find the length of the height. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So,
c^2 = a^2 + b^2
50^2 = 48^2 + b^2
2500 = 2304 + b^2
b^2 = 2500 - 2304
b = √(2500 - 2304)
b = √(196)
b = 14
So, the height of the triangle is 14cm.
Area = (1/2) * 48 * 14 = 336cm^2
Can someone explain how to solve this please?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionSolution is in the attached photo, do take note when you square a square root, you will get the original expression. (Power 2 x Power Half = Power 1).
what is 16 over 16 as a whole number
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
16/16
16 ÷ 16 = 1
So your answer is 1
HAVE A GREAT DAY!
16<21<25, so 21−−√ is between
Answer:
This meant to be a question?
Step-by-step explanation:
What type of term 2x 3y is?.
The concept is Binomial distribution, an integer that can be obtained by evaluating a polynomial containing two terms The answer is, a linear equation in two variables.
In probability theory and statistics, a binomial distribution with parameters n and p is a discrete probability distribution of the number of successes in a sequence of n independent experiments, each of which asks a yes-no question and each has its own assessment of the Boolean result: passed or failed.
Data:
A polynomial of form 2x + 3y
The polynomial above is the sum of 2x and 3y.
In the expression, the polynomial is the sum of two terms, each of which is a monomial
Again, we know that a binomial is a polynomial that is the sum of two terms, each of which is a monomial, so the given polynomial is a binomial
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Sebatian i having a tea party at home for which he ha invited ome of hi friend. If 8 bottle
of mango juice cot AED 16 , then how much hould he pend for 15 uch bottle?
15 bottles of Mango juice cost AED 30
Will this solve this question by the unitary method
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What would he pay for 15 bottles of mango juice if 8 bottles cost AED 16?
so,
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
8 bottle=AED16 So I bottle of mango juice costs AED 2.
2x15=30
So,15 bottles of Mango juice cost AED 30
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The expression
is equivalent to what answer in the picture
Answer:
-4w^6
Step-by-step explanation:
12/-3 = -4
w^9/w^3 = w^6
y^3/y^3 = 1
Answer: -4w^6
Answer:
option 1 = - 4w⁶
Step-by-step explanation:
attached the solution, hope that helps...
What is the inverse of an exponential function?.
The inverse of an exponential function is the natural logarithm function. More specifically, if f(x) = a^x, where a is a positive constant and x is a real number, then the inverse function, denoted as f^-1(x), is given by f^-1(x) = log_a(x).
An inverse function is a function that "undoes" the effect of another function. In other words, if we have two functions, f and g, such that g(f(x)) = x for all x in the domain of f, and f(g(x)) = x for all x in the domain of g, then f and g are inverses of each other.
In the case of exponential functions, f(x) = a^x where a is a positive constant and x is a real number, the inverse function is the natural logarithm function, g(x) = log_a(x).
The natural logarithm function "undoes" the effect of the exponential function by taking the logarithm of the output of the exponential function with base 'a' and returns the input value.
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What is the multiplicative inverse of 7 /- 9?.
The multiplicative inverse of -7/9 is -9/7
The multiplicative inverse of a number is basically the reciprocal of the number Multiplicative inverse of a is 1/a where a≠ 0
The standard form to represent the multiplicative inverse is as follows:
a * (1/a) = 1
when a number is multiplied by its multiplicative inverse then the result is 1.
The multiplicative inverse is the Reciprocal of a fractional number where the number and denominator are simply interchanged.
Hence multiplicative inverse of 7/9 is
1/(7/-9) = -9/7
The multiplicative inverse of -7/9 is- 9/7.
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What is the sum of the polynomials x2 9 +- 3x2 11x 4?.
The sum of the polynomials (-x² + 9) and (-3x² - 11x + 4) is -4x² - 11x - 5.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
What is the sum of the polynomials (-x² + 9) and (-3x² - 11x + 4)?
What is the sum of the polynomials m'n 3 +( M N 4?.
The sum of the polynomials (m + n + 3) + (m + n + 4) is 2m+2n+7
Sum of given polynomials (m+n+3) +(m+n+4)
Firstly, open the parenthesis we will get m+n+3+m+n+4
After simplification, we will get 2m+2n+7
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
What is the sum of the polynomials (m + n + 3) + (m + n + 4)?
Elena is 59 inches. Some people are taller than Elena
The height of Andre, given the height of Elena is 63 inches tall.
The height of Lin is 65 .5 inches tall.
The height of Noah is 59 + d inchs tall.
How tall are the people?The height of the other people given which include Andre, Lin, and Noah, are all dependent on the height of Elena.
Andre is 4 inches taller than Elena so the height is:
= 59 + 4
= 63 inches
The height of Lin is:
= 59 + 6 .5
= 65 .5 inches
The height of Noah is:
= 59 + d inches
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What is the value of k for which the system of equations KX 2y 5 and 3x Y 1 has no solution?.
So, the system of equations kx + 2y = 5 and 3x + y = 1 has no solution when k - 6 ≠ k, which means k ≠ 6.
A system of equations has no solution when there are no values that can be assigned to the variables that make all equations true. This means that the equations are inconsistent.
In this case, the system of equations is kx + 2y = 5 and 3x + y = 1. To check whether the system has a solution or not, we can use different methods such as substitution, elimination, or graphing.
One of the methods that can be used to check for consistency is by finding the determinant of the system and comparing it with the determinant of the coefficient matrix. The determinant of the system is the determinant of the matrix formed by the coefficients of the variables and the constant terms.
The determinant of the system is |k 2| |3 1| = k1 - 23 = k - 6
The determinant of the coefficient matrix is |k 2| = k*1 = k
To have no solution, the determinant of the system must be non-zero but different from the determinant of the coefficient matrix.
Therefore, the system of equations kx + 2y = 5 and 3x + y = 1 has no solution when k - 6 ≠ k, which means k ≠ 6.
In other words, the system of equations kx + 2y = 5 and 3x + y = 1 has no solution when k is different from 6.
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What is the trigonometric ratio of sin θ?.
The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
In arithmetic, the trigonometric functions (also known as circular features, perspective features, or goniometric functions) are actual features that relate an angle of a proper-angled triangle to ratios of side lengths. they may be extensively utilized in all sciences which might be associated with geometry, such as navigation, strong mechanics, celestial mechanics, geodesy, and lots of others. they are a few of the handiest periodic features, and as such are also extensively used for analyzing periodic phenomena through Fourier analysis.
The trigonometric functions most extensively used in cutting-edge mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. each of these six trigonometric capabilities has a corresponding inverse function and an analog most of the hyperbolic features.
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The point of intersection of the perpendicular bisectors of the sides of a triangle is called a. circumecentre
b. incentre
c. congruent
d. concurrent
The point of intersection of the perpendicular bisectors of the sides of a triangle is called circumcenter
What are perpendicular bisectors?Lines that cut through the middle of each side of a triangle's perpendicular bisector are perpendicular to the provided side. The circumcenter (Durell 1928), which is also the center of the triangle's circumcircle, is where the triangle's three perpendicular bisectors (Casey 1888, p. 9) meet.Measuring a line segment that needs to be bisected will help you discover a perpendicular bisector. The midway of the measured length can then be determined by dividing it by two. From this center, extend a line at a 90-degree angle.The circumcenter is where the perpendicular bisectors of a triangle's sides meet. It is located in the middle of a triangle's perimeter. The center of a polygon's circle is known as the circumcenter. The polygon's circumcenter, also known as the center of that circle, is the circle that passes through all of the polygon's vertices. Cyclic polygons are the collective name for the circumcircle polygons.To learn more about perpendicular bisectors refer to:
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What is the ratio of the 3 sides of a 45 − 45 − 90 triangle?.
The ratios of the sides of a 45-45-90 triangle are 1:1:[tex]\sqrt{2}[/tex].
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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