The value of cos t from the unit circle is cos t = 0.94868
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
The terminal side of angle θ intersects the unit circle in the first quadrant at ( 3√10/10,√10/10 )
So , the equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Substituting the values of x and y in the equation , we get
x = 3√10 / 10
x = 3/√10
And , y = √10/10
y = 1/√10
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
So , the value of cos θ = ( 3/√10 ) and sin θ = ( 1/√10 )
On simplifying the equation , we get
cos t = ( 3/√10 )
cost t = 0.94868
Hence , the value of cos t = 0.94868
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Please help
Given the function f(x) = -3x^3 +3x^2+ 3x + 3, which of the following is true?
-It is positive
-It is a cubic function
-The domain is all real numbers.
-It has at most 2 solutions
-it is a polynomial function
Answer: Given the function f(x) = -3x^3 +3x^2+ 3x + 3, the following is true:
-It is not necessarily positive or negative as the value of f(x) depends on the value of x.
-It is a cubic function as it contains an x^3 term.
-The domain is all real numbers as there are no restrictions on the input x.
-It has at most 3 solutions as it is a cubic function and cubic functions can have at most 3 real roots.
-It is a polynomial function as it is a finite sum of terms involving non-negative integer powers of x.
Step-by-step explanation:
Match the following terms with the correct definitions
Answer: The space inside a figure -- Area
The sum of all sides in a figure -- Perimeter
The distance vertically in a triangle -- Height
The distance horizontally in a triangle -- Base
Find the value of the variable m and YZ if Y is between X and Z, XY=9m−3 , YZ=6m+1 , and XZ=13m+6 .
The value of variable m is 4.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We have to find value of m
As Y is between X and Z it is taken as the midpoint.
The values of XY, YZ and XZ are given as below.
XY=9m−3 , YZ=6m+1 , and XZ=13m+6 .
We need to find the value of the variable m.
If we add xy and yx we get xz.
So by the equation xy+yz=xz we get the value m.
9m-3+6m+1=13m+6
Add the like terms
15m-2=13m+6
15m-13m=2+6
2m=8
Divide both sides by 2
m=4
Hence, the value of variable m is 4.
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I have attached the screen shot of the problem
Answer:
(7x+3)
Step-by-step explanation:
7. Use coordinate geometry to find the perimeter and area of a polygon.
Part I: The coordinate grid below displays the stakes and wickets of the croquet
course. Sonja warmed up by putting her ball down at wicket 2. She then hit it through
wicket 9, then wicket 8, then wicket 5, then wicket 3, and finally back to wicket 2. On
the coordinate grid, draw the path of Sonja's ball. (5 points)
feet
y
70
60
50
40
30
20
(15,43)
9
(16,18)
(37,65)
8
●
(40,42)
Stake B
(70,72)
171
(66,68)
(62,64)
●3
(63.19)
On solving the provided question, we can say that Make a table with the x,y coordinates of each vertex.
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
Make a table with the x,y coordinates of each vertex.
Vertical left side of the table A ,B,C D.. A again (From top to bottom)
Horizontal top of the table : x,y( From left to right)
Start at any vertex and go around the polygon in either direction.
Add the starting vertex again at the end.
Combine the first two rows by:
Multiplying the first row x by the second row y
Multiplying the first row y by the second row x
Subtract the second product form the first.
Repeat this for rows 2 and 3, then rows 3 and 4 and so on.
Add these results, make it positive if required, and divide by two.
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Find the slope of the line.
Write answer as an integer or a reduced fraction.
Do NOT use 1 as a denominator!
A line running through the points (2, 0) and (0, 4) has a slope of -2.
Finding the slope of a lineThe slope of a line is defined as the change in y-axis of the line to the x-axis. Mathematically, it is expressed as:
Slope = Δy/Δx
Using the coordinate points (2, 0) and (0, 4) to determine the required slope:
Slope = 4-0/0-2
Slope= 4/-2
Slope = -2
Hence the slope of the line passing through the point (2, 0) and (0, 4) is -2
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if a/b - d = 2c/b, find the value of c when a = 3, b = 4 and d = 5
Answer: 23
Step-by-step explanation:
first we put the values a=3,b=4 and d=-5. in a/b-d=2c/b equation which is given in the question. so,it gives us 3/4+5=2c/4,3+20=2c/4×4,3+20=c.so,the value of c is 23
Answer:
[tex]\huge\boxed{\sf c = -17/2}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle \frac{a}{b} - d=\frac{2c}{b}[/tex]
Where, a = 3, b = 4, d = 5
[tex]\displaystyle \frac{3}{4} - 5 =\frac{2c}{4} \\\\Take \ LCM\\\\\frac{3-(5 \times 4)}{4} = \frac{c}{2} \\\\\frac{3-20}{4} = \frac{c}{2} \\\\\frac{-17}{4} = \frac{c}{2} \\\\Cross \ Multiply\\\\-17 \times 2 = 4 \times c\\\\-34 = 4c\\\\Divide \ both \ sides\ by \ 4\\\\-34/4 = c\\\\c = -17/2\\\\\rule[225]{225}{2}[/tex]
A plant is already 41 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after m months is given by the following.
H=41 + m
What is the plant's height after 22 months?
Answer:902
Step-by-step explanation:
41×22=902
One quart is approximately equal to 0.95 liter. To convert quarts to liters, which operation should you use? Why?
A. addition; there is about 0.95 liter in 1 quart. Add when converting smaller units to larger units.
B. Division; there is about 0.95 liter in 1 quart. Divide when converting smaller units to larger units.
C. Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.
D. Subtraction; there is about 0.95 liter in 1 quart. Subtract when converting larger units to smaller units.
The operation you would use is multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units. (option C).
What is multiplication?Multiplication is the operation that is used to determine the product of two or more numbers. The sign that is used to denote multiplication is ×. Multiplication is one of the operations in maths. Other operations in mathematics ae addition, division and subtraction.
1 quart = 0.95 liters
In order to convert 100 quart to liters, multiply 100 by 0.95
0.95 x 100 = 95 liters
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Salma is going to an amusement park. The price of admission into the park is $10, and once she is inside the park, she will have to pay $5 for every ride she rides on. How much money would Salma have to pay in total if she goes on 6 rides? How much would she have to pay if she goes on r rides?
The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r
What is a solution to a linear equation?A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value.
Given here: Admission price=$10 and ride fee= $5
Now if Salma goes for 6 rides than we have
Total fee= 10+5×6
=$40
And if Salma decides to go for r rides than we can express the total cost as some function of the number of rides r
T(r)=10+5r
Hence, The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r
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Santiago wants to walk at least 500 miles before the end of this year. He has already walked 437'miles, and there are 36 days left in the year. Which inequality can be used to find x , the number of miles he should walk each day to meet his goal?
The required inequality is 437 + 36x ≥ 500, where x is the number of miles he should walk each day to meet his goal.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Given,
His trip length was 437 miles, and he had 36 days left.
If x is the number of miles covered each day, then the remaining miles to
Then the remained miles to cover = number of days remained × miles covered in each day
Thus, his trip length = already completed miles + remaining miles
= 437 + 36x
As per the question,
Total miles ≥ 500 miles
⇒ 437 + 36x ≥ 500
Thus, the required inequality is 437 + 36x ≥ 500.
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Solve the system of linear equations by graphing.y=2x+5 y=1/2x−1 can someone help with this and show the graph that would be helpful thanks.
The graph of the system of equations can be seen on the last image, there we can see that the solution is (-4, -3).
How to solve the system of equations graphically?To do so, we just need to graph both equations no the same coordinate axis, and then find the point where the graphs intercept (if they do).
That point will be the solution of the system of equations.
Here the system is:
y = 2x + 5
y = (1/2)*x - 1
And the graph of the equations can be seen below. There we can see that the lines intercept at (-4, -3), so that is the solution.
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Graph the function. y=3/2x+1
Which is the correct equation for finding the value of x?
A. 2x + 6 + 5x + 8x - 11 = 180
B. 5x + 2x + 6 = 180
C. 2x + 6 + 8x - 11 = 5x
D. 5x + 2x + 6 = 8x - 11
Answer:
C.
Step-by-step explanation:
1. 2x + 6 = 8x
2. 8x + 8x = 16x
3. 16x - 11 = 5x
From the top of a 72 m high vertical cliff,
a boat has an angle of depression of 32
degrees. How far is the boat from the
base of the cliff? Round your answer to
the nearest whole number.
If from the top of a 72 m high vertical cliff, a boat has an angle of depression of 32° then the distance of boat from the base of the cliff is, 115 m.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
We can use trigonometry to solve for the distance of the boat from the base of the cliff.
Let's call the distance from the base of the cliff to the boat "d".
Then we have:
tan(32°) = 72 / d
Solving for d, we get:
d = 72 / tan(32°)
d = 115.22
Rounding to the nearest whole number, d = 115.
So the boat is 115 meters away from the base of the cliff.
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What is the difference between the area of Figure A and the
area of Figure B? Each grid square represents 1 square foot.
The difference between the area of Figure A and the area of Figure B is 2ft, So correct option is A.
What do you mean by grid?A square grid is a two-dimensional pattern formed by a series of equally spaced horizontal and vertical lines that intersect at right angles, creating a regular array of squares. It can be thought of as a flat, two-dimensional lattice with a consistent spacing between the lines. A square grid can be used to represent many things, such as a map, a game board, a city plan, or a spreadsheet. In mathematics and geometry, a square grid is often used to represent coordinate systems, where each intersection of horizontal and vertical lines corresponds to a specific point with a unique set of coordinates. Square grids are also used in graphic design and art as a foundation for creating patterns, textures, and compositions.
The area of A= 3×4= 12 ft
The area of B= 4×3×1/2×4×2×1/2= 10 ft
12ft - 10 ft= 2ft
Cut down the triangle on the right of figure A, move it to left to form a rectangle, and then calculate the area of A.
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The complete question is:
In a group of 24 students attending a party, the average age is 25.3 years. A 27-year-old student joins the party.
The new average of the students is 25.368.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, in a group of 24 students attending a party, the average age is 25.3 years.
A 27-year-old student joins the party.
So, the new average is (24×25.3+27)/25
= 634.2/25
= 25.368
Therefore, the new average of the students is 25.368.
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Please help ASAP
Find the area of the rectangle
What is the area of the rectangle?
The area of the rectangle is given by the equation A = ( 9x² - 64 ) yards²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the width of the rectangle be W = ( 3x - 8 ) yards
Let the length of the rectangle be L = ( 3x + 8 ) yards
Now , Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Area of Rectangle = ( 3x - 8 ) ( 3x + 8 )
On simplifying the equation , we get
Area of Rectangle = ( 3x )² - ( 8 )²
Area of rectangle A = ( 9x² - 64 ) yards²
Hence , the area of the rectangle is ( 9x² - 64 ) yards²
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3. Manufacturing firm which manufactures office furniture find's that it has the
following variable costs per unit in dollar/unit.
Desks Chairs Tables Cabinets
Material
2
Labor
3
Overhead 5 5
10 13 5
15
12
10
18
5
20
Assume that an order of 10Desks, 60Chairs, 40 Tables and 2 Cabinets has just been
received.
Using matrix multiplication and addition, the total production cost for the items ordered by a customer is $2,692.
How is the total production cost determined?The total production cost consists of the costs of direct materials, direct labor, and overheads.
Overhead costs include indirect costs of materials, labor, and other production costs not traceable to each produced unit.
The total production cost is determined using matrix multiplication where the number of columns of the first matrix equal the number of rows of the second matrix.
Desks Chairs Tables Cabinets
Materials $5 $5 $10 $13
Labor 15 12 10 18
Overhead 5 5 3 20
Ordered Items:Number
Desks 10
Chairs 60
Tables 40
Cabinets 2
Production Costs for the Ordered Items:
Desks Chairs Tables Cabinets Total
Materials $150 $300 $400 $26 ($13 x 2) $876
Labor 150 720 400 36 ($18 x 2) 1,306
Overhead 50 300 120 40 (20 x 2) 510
Total costs $350 $1,320 $920 $102 $2,692
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Question Completion:What is the total production cost of the ordered units?
3 1/2 is = ?/2 ????????????????????????????
Answer:
7/2
Step-by-step explanation:
number 8 only please help
Answer:
14/70
Step-by-step explanation:
2. Explain the relationship between the constant of proportionality and the unit rate. Be specific.
Answer: The constant of proportionality and the unit rate represent the same value. A constant of proportionality can be any value, including fractions and decimals. The main difference between the constant of proportionality and a unit rate is how they are written.
Which of the following is the graph
Option A : The circle represented in the third quadrant has the centre lying at (-3, -1)
What is equation of a circle ?The location of a circle in the Cartesian plane is represented by a circle equation. We can construct the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.
The group of points whose separation from a given point has a constant value are represented by a circle. The radius of the circle, abbreviated r, is a constant that describes this fixed point, which is known as the circle's center. The equation (x- x₁)²+(y-y₁)²=r²describes a circle with a center at (x₁,y₁) and a radius of r.
There are different forms to represent the equation of a circle :
General formStandard formParametric formPolar formThe equation of the circle is
(x + 3)² + (y + 1)² = 9
The centre of the circle will be at (-3, -1) from the equation .
Option A :The circle represented in the third quadrant has the centre lying at (-3, -1)
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Use the graph or table to find the equation that represents the relationship.
The equations that represent each line are, respectively:
y = - 3 · x + 5 y = x - 4 y = 2 · x - 1 y = (4 / 5) · x - 4How to determine the equations of the line
According to Euclidean geometry, we can generate any line from two distinct points on a plane. Herein we find two tables and two Cartesian representations of the lines, of which we must construct the corresponding line equations, whose definition is shown below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.The slope can be found by secant line formula:
m = Δy / Δx
Now we proceed to determine each equation of the line:
Case 1
Slope
m = [- 34 - (- 10)] / (13 - 5)
m = - 24 / 8
m = - 3
Intercept
b = y - m · x
b = - 10 - (- 3) · 5
b = - 10 + 15
b = 5
Equation of the line
y = - 3 · x + 5
Case 2
Slope
m = [- 3 - (- 11)] / [1 - (- 7)]
m = 8 / 8
m = 1
Intercept
b = y - m · x
b = 3 - 1 · 7
b = 3 - 7
b = - 4
Equation of the line
y = x - 4
Case 3
Slope
m = [0 - (- 1)] / (0.5 - 0)
m = 2
Intercept
b = y - m · x
b = - 1 - 2 · 0
b = - 1
Equation of the line
y = 2 · x - 1
Case 4
Slope
m = [0 - (- 4)] / (5 - 0)
m = 4 / 5
Intercept
b = y - m · x
b = - 4 - (4 / 5) · 0
b = - 4
Equation of the line
y = (4 / 5) · x - 4
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How many digits do you need to number all 178 buildings on a street?
The number of digits which one would need to number all 178 buildings on a street is 426 numbers.
What is a Digit?This is referred to as a single symbol used alone or in combinations, to represent numbers in a positional numeral system.
1-9 = 1 × 9 = 9
10-99 = 90 × 2 = 180
100-178 = 79 × 3 = 237
The total = 9 + 180 + 237 = 426 numbers.
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3.6= − a/0.8 − 1.6 − 0.8 a −1.6
The value of a for the given expression will be -3.31.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a −1.6. The value of a will be calculated as below,
3.6 = − a/0.8 − 1.6 − 0.8 a −1.6
3.6 + 1.6 + 1.6 = -a / 0.8 - 0.8a
6.8 = ( -a - 0.64a ) / 0.8
5.44 = -1.64a
a = -3.31
Therefore, the value of a will be -3.31.
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Match the polynomial on the left with the appropriately factored expression on the right.
x² + 6x +9. x²-9
(x - 3)(x-3)
(x-3)(x + 3)
(x+3)(x + 3)
3(x+3)(x + 3)
The polynomial x² + 6x + 9 can be factored as (x + 3)(x + 3).
What is polynomial?
The term "polynomial" in mathematics refers to a mathematical expression that consists of two or more algebraic terms that are added, subtracted, or multiplied (no division!). Constants and positive exponents are frequently used, along with at least one variable, in polynomial expressions. Polynomial definition: x2 = 4x + 7
A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.
The polynomial x² + 6x + 9 can be factored as (x + 3)(x + 3).
Therefore, the correct match is:
x² + 6x + 9 ------> (x + 3)(x + 3)
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jim sells cars for a living in 3 months he sells 24 cars which option below shows a proportional relationship
A:Selling 2 cars in 1 month
B:Selling 5 cars in 1 month
C:Selling 16 cars in 2 months
D:Selling 94 cars in 1 year
The option that shows a proportional relationship is selling 94 cars in 1 year (option D)
What is proportional?Two numbers or elements are said to be proportional if they have the same ratio. In this case, the ratio is 24 cars every 3 months, which can be simplified as 8 cars per month.
What option shows a proportional ratio?Based on this ratio, the option that is proportional is selling 96 cars in a year because this will means 96 cars in 12 months and 96/12= 8, which shows the ratio is the same.
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I need help with this
Frederick deposit 1050 into account that pays 5.1% annual interest compounded daily enter an equation to represent Fredericks account balance after t years
Answer:
The equation to represent Frederick's account balance after t years is:
A = 1050 * (1 + (0.051/365))^(365t)
Where A is the account balance and t is the number of years.