Answer:
1) The sine function relates a real number t to the y-coordinate of the point where the corresponding angle intercepts the unit circle.
2) The secant function is the reciprocal of the cosine function (secx=1cosx) x = 1 cos .The co-secant function is the reciprocal of the sine function (cscx=1sinx) x = 1 sin . It can be found for an angle t by using the y -coordinate of the associated point on the unit circle: csct=1y t = 1 y .
Step-by-step explanation:
Final answer:
Sine and cosine functions are related to the unit circle with their values representing the y and x coordinates of a point on the circle, respectively. They oscillate between +1 and -1, repeating every 2π radians and are used to model simple harmonic motion, differing by a phase shift of π/2 radians.
Explanation:
The sine and cosine functions are directly related to the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate system. When an angle θ is drawn from the positive x-axis, the coordinates of the point where the terminal side of the angle intersects the unit circle are (cos θ, sin θ).
For the sine function, think of it as projecting the point on the unit circle onto the y-axis. This projection gives the y-coordinate, which is the sine of the angle θ. Therefore, the sine function oscillates between +1 and -1 as the angle θ increases, repeating every 2π radians because this is the circumference of the unit circle.
Similarly, the cosine function is obtained by projecting the point onto the x-axis, providing the x-coordinate or the cosine of the angle θ. It also oscillates between +1 and -1 and repeats every 2π radians. Both sine and cosine functions describe simple harmonic motion when modeling periodic phenomena, and they differ by a phase shift of π/2 radians.
The initial conditions of a sine function with zero phase shift are that the function starts at 0, indicating that, for simple harmonic motion, the initial position is at equilibrium. With a cosine function, the initial value is 1 when the phase shift is zero, indicating that the motion starts at its maximum displacement. This concept can also be used to model wave functions and determine scalar components using triangles.
How can one variable equations have more than one solution in some cases and no solutions in others?
Answer:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).
Step-by-step explanation:
Answer:
There can be more than one solution to a system of equations. A system of linear equations will have one point of intersection, or one solution. To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.
Step-by-step explanation:
On the first day it was posted online, a music video got 1750 views. The
number of views that the video got each day increased by 20% per day. How
many total views did the video get over the course of the first 5 days, to the
nearest whole number?
To find the total views a music video got over the first 5 days with a 20% daily increase, calculate the views for each day using a geometric sequence formula and sum them, resulting in approximately 13023 views.
Explanation:To calculate the total views a music video got over the course of the first 5 days with a 20% daily increase starting at 1750 views, we use the geometric sequence formula V = V0 × (1 + r)n, where V0 is the initial number of views (1750), r is the daily increase rate (0.20), and n is the day number. The total views (TV) over 5 days is calculated by summing the individual daily views.
Day 1: 1750 views
Day 2: 1750 × (1 + 0.20) = 2100 views
Day 3: 1750 × (1 + 0.20)2 = 2520 views
Day 4: 1750 × (1 + 0.20)3 = 3024 views
Day 5: 1750 × (1 + 0.20)4 = 3628.8 views, rounded to 3629 views
The total views over the five days is the sum of daily views: 1750 + 2100 + 2520 + 3024 + 3629 = 13023 views.
The circumference of a circle is 60 kilometers. What is its radius?
Answer: 9.5493
Step-by-step explanation: circumference = 2pi*r
Answer:
9.55 simplified
Eighty percent of all dentists surveyed agree: Zilch toothpaste tastes best.
Percent of Dentists Surveyed
Disagree
Do you think this information is misleading? Why or why not?
a. Yes, because it does not state how many dentists were surveyed.
b. Yes, because it does not state on the graph what percentage agrees with the statement.
C. No, because the graph shows eighty percent of the dentists agreeing with the statement.
No herause it states which toothnaste was used in the survey
Answer: the answer is gonna be A if you want to be exact
Step-by-step explanation: does not state how many dentist were interviewed.
The height of a cylinder is 12 inches and the radius is 3.5 inches. What is the approximate volume of the cylinder?
Answer:
V≈461.81in³ That is the answer!
V = pi*r^2*h
V = pi*(3.5)^2*12
V = pi*12.25*12
V = pi*147
V = 147pi .... exact volume in terms of pi
V = 461.8141200777 is the approximate volume (use a calculator here)
The units for the volume are in cubic inches
Side note: If you use pi = 3.14, then you'll get an approximate volume of 147*pi = 147*3.14 = 461.58 which is a bit off from the other value we got earlier due to the fact pi = 3.14 is not as accurate as using the calculator's internal value of pi.
a box in the shape of a rectangular prism has the dimensions shown. what length of the interior diagonal of the box? round to the nearest tenth.
100 cm
80 cm
60 cm
Answer:
I keep getting 141.421... so rounded it would be 141.4
Step-by-step explanation:
The length of the interior diagonal of the box is approximately 141.4 cm.
How to find the volume and base's area of a right rectangular prism?Suppose the base of the prism has length = l units, and width = w units.
Suppose that the height of the prism is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that prism.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
We are given that;
Height= 100cm
Width=80cm
Length=60cm
Now,
Using the Pythagorean theorem, we can find the length of the interior diagonal as:
diagonal = sqrt(l^2 + w^2 + h^2)
diagonal = sqrt(100^2 + 80^2 + 60^2)
diagonal = sqrt(10000 + 6400 + 3600)
diagonal = sqrt(20000)
diagonal ≈ 141.4
Therefore, the length of the diagonal of prism will be 141.4
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What’s the square root of -16?
Answer:
It can`t be -4 because -4² = +16 and it can`t be 4² because 4² = +16
In other words, there is nothing you can square to get -16.
Step-by-step explanation:
It izz wat it izzzz!!!
15+7r+r(r-3)-r^2 simplified
Answer:
15+4r
Step-by-step explanation:
15+7r+r(r-3)-r^2
Distribute
15+7r+r^2-3r-r^2
Combine like terms
15+7r-3r+r^2-r^2
15 +4r
Answer:
15 + 4r
Step-by-step explanation:
15+7r+r(r-3)-r²
15 + 7r + r² - 3r - r²
15 + 4r
Which is the asymptote of the graph? y=0, y=1, y=2, y=3
Answer:
the asymptote would be zero because the graph is approaching zero, but never actually touches it.
A company manufactures handband a wirleless
Answer:
1. 21 represents the cost of manufacturing one handband.
3. The initial start up cost is $15000.
5. The company spends $57000 to manufacture 2000 handbands.
Step-by-step explanation:
We are given the cost function for manufacturing 'h' amount of handbands and it is provided that there was initial start up costs involved.
Now, as the cost function is given by, C(h) = 21h + 15000.
We can see that the initial start up cost is $15000.
As, 'h' is the number of handbands being made. So, 21h in C(h) is the cost of manufacturing 'h' handbands.
Therefore, 21 is the cost of manufacturing one handband.
Since, C(h) = 21h + 15000.
Substituting h = 2000, we get,
C(2000) = 21×2000 + 15000.
i.e. C(2000) = 42000 + 15000.
i.e. C(2000) = 57000.
The company spends $57000 to manufacture 2000 handbands.
Since, we are provided with only cost function, we can not talk about the profit.
Hence, option 1, 3 and 5 are correct.
PLEASE MARK ME BRAINLIST!
Answer:
1. 21 represents the cost of manufacturing one handband.
3. The initial start up cost is $15000.
5. The company spends $57000 to manufacture 2000 handbands.
Step-by-step explanation:
Which equation results from adding the equations in this system?
Negative 8 x + 8 y = 8. 3 x minus 8 y = negative 18.
5 x = negative 10
5 x = 26
Negative 5 x = 26
Negative 5 x = negative 10
Answer:
D)-5x = -10
Step-by-step explanation:
The equation results from adding the equations in this system is -5x = -10.
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
-8x + 8y = 8 _____(1)
3x - 8y = -18 _____(2)
Now,
Adding (1) and (2) we get,
-8x + 8y + 3x - 8y = 8 - 18
-5x = -10
Thus,
-5x = -10 is the equation.
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a cube has an edge of D cm. What is the volume of the cube
Answer:
The volume of the cube is D * D * D or D³ cm³
Step-by-step explanation:
The heights of a group of boys and girls at a local middle school are shown on the dot plots below.
Boys' Heights
40 41 44 46 48 50 52 54 56 58 60
Inches
Girls' Heights
40 41 44 46 48 50 52 54 56 58 60
Answer:
The girls and boys heights are equal and none are shorter or taller.
You get this answer from identifying the numbers, seeing if there is any number that is larger or shorter than 40-60.
Hope this helped!
Model the following equation:
2x - 5 = -7
Answer:
[tex]x = -1[/tex]
Step-by-step explanation:
[tex]2x - 5 = -7[/tex]
Rearrange terms
[tex]2x=-2[/tex]
Solve for x
[tex]x=-1[/tex]
Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to
the nearest integer).
es )
A)
12 units
25 units?
30 units?
Answer:
25
use the formula for hypotenouse of a triangle to find the diangles as if they were the hypotenouse so 5 squared plus 10 squared is 25 plus 100 which is 125 which has the square root 11.2. so now you have the length (longer side) so for the width it's 1 squared plus 2 squared which is 1 plus 4 is 5 so the square root of 5 is about 2.2 so that's the width (shorter side) so now for the area it's 11.2 (length) times 2.2 (width) which is about 25. hope this hopes let me know if you have a question
Answer:30
Step-by-step explanation:
write an equation in point-slope form of the line that passes through the point (-2,4) and has a slope of 5
Answer:
y=mx+b m= slope b=Y-Intercept
4=5(-2)+b
Answer:
4=5(-2)+b
Step-by-step explanation:
hope this helps
Which statements are true about surface area and volume? Check all that apply.
Answer:
where are the choices?
Step-by-step explanation:
#5 If the diameter of a circle is 3 inches, what is the circumference to the nearest tenth? *
Answer:
9.4 inches
Step-by-step explanation:
The formula for circumference is πd
Since the diameter is 3 inches, multiply that by pi to get your answer
3π ≈ 9.4 inches
What is the probability of someone preferring phone
calls, given the person is a female?
O 43%
O 46%
O 54%
O 57%
Answer: 54
Step-by-step explanation:
Multiply and simplify
Answer: The answer you clicked on in the picture is correct, (B)
Step-by-step explanation: I put the equation through a thing I know of (faMATHWAce) and got that as the answer.
On a coordinate plane, a circle has a center at point (negative 6, 4). What is the equation of the circle shown in the graph? ( )² + ()² =
Answer:
1) x+6 2)y-4 3)36
Step-by-step explanation:
(x+6)² + (y-4)² = 36
Answer:
First Drop down: X+6
Second: Y-4
Third: 36
Step-by-step explanation:
Please help me :( solve for x and y. y = 4x and 3x + 2y = 55
Final answer:
To solve the system of equations y = 4x and 3x + 2y = 55, you can substitute 4x for y in the second equation, simplify to find x = 5, and then calculate y = 20.
Explanation:
To solve for x and y using the equations y = 4x and 3x + 2y = 55, you can use substitution or elimination. Let's use substitution since we already have y expressed in terms of x.
Substitute 4x for y in the second equation: 3x + 2(4x) = 55.
Simplify and solve for x: 3x + 8x = 55 becomes 11x = 55, so x = 5.
Substitute x back into the first equation to find y: y = 4(5), so y = 20.
Therefore, the solution to the system of equations is x = 5 and y = 20.
Find the point slope equation for the line that passes through the points ( -2, -20 ) and (9, 79). Use the first point in your equation y+ =
The point-slope equation for the line passing through (-2, -20) and (9, 79), is y = 9x - 2.
To find the point-slope equation for the line that passes through the points (-2, -20) and (9, 79), we first need to calculate the slope (m). The formula for the slope is given by:
m = (Y2 - Y1) / (X2 - X1)
Using the given points, we get:
m = (79 - (-20)) / (9 - (-2)) = 99 / 11 = 9
Now, using the point-slope form of the equation y - y1 = m(x - x1), and the first point (-2, -20), we have:
y - (-20) = 9(x - (-2))
Simplifying this, we get:
y + 20 = 9(x + 2)
Or
y = 9x + 18 - 20
y = 9x - 2
This is the point-slope equation for the line that passes through the points.
1Which extegory do both shapes belong to?
If the dimensions of a solid proportionally increase by a scale factor of 5, by what factor does the surface area
increase?
5/2
5/4
25/2
25/4
Answer:
25/4
Step-by-step explanation:
What is the equation of the line through the origin and (2,5)
Answer:
y = 5/2 x
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (5-0)/(2-0)
= 5/2
We know the y intercept is 0 since it goes through the origin
y = mx+b
y = 5/2 x +0
y = 5/2 x
Can you simplify 7 (2x -3)
Answer:
simplification of the equation is:
14x-21
The circumference of a circle is 9 m what is the area of the circle
Answer:
so maybe the answer will be 20.25m^
Solve for b.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
–67b+ 6 < 96 + 43
Answer:b>-1 and 66/67
Step-by-step explanation:
First you add like terms. So 96+43. Your problem should now look like this -67+6=139. Now subtract 139 from 6 and you will be left with this -67b<133. Now divide 133 by -67 and you get -1.985074627. Or -1 66/67 as a fraction. You have to flip the sign because you divided by a negative number. You answer should look like this b>-1 and 66/67.
Can someone please help me ASAP
Answer:
(-4,0) (0,3)
(3-0)/(0+4)= 3/4
y - 0 = 3/4(x + 4)
y = 3/4x + 3
answer is a
Step-by-step explanation:
Answer:
It¨s A
Step-by-step explanation:
you first have to find the slope by doing rise over run,I checked the table and labeled the values for the x-axis and y-axis,the found the y-intercept which is when x is always zero and y is any random number so one of the points on the table show the x is 0 and y is 3 so that means the y-intercept is 3 also written as (0,3).