radius = 20 inches
angle = θ= 45°
We would apply length of an arc:
[tex]length\text{ of an arc = }\frac{\theta}{360\text{ }}\text{ }\times2\pi r[/tex][tex]\begin{gathered} \text{length of the arc = }\frac{45}{360}\times2\times\pi\times20 \\ =\text{ }\frac{1}{8}\times\text{ 40}\pi \end{gathered}[/tex]Since the options is in terms of π, the answer will be in that form
[tex]\text{length of }arc\text{ = 5}\pi\text{ inches (option B)}[/tex]Write a cosine function for the graph.
The correct option A: y = -4 cos Ф/4, is the cosine function for the graph.
Define the term cosine function?The ratio between the angle's adjacent leg and the hypotenuse when it is regarded as a leg of a right triangle is a trigonometric function for an acute angle.
One of the three fundamental trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.Y=cos(x) has its greatest value when x = 2nπ, wherein n is an integer. Y=cos(x) has a lowest value for x= π+2nπ , wherein n is an integer.For the given graph,
cosine function: y = -4 cos Ф/4.
In which, -4 is the amplitude (maximum displacement from the x axis).
Negative sign shows, the displacement is taken along negative y-axis.
And, Ф/4 is the phase angle.
Thus, the cosine function for the graph is y = -4 cos Ф/4.
To know more about the cosine function, here
https://brainly.com/question/27587720
#SPJ1
Answer:
b. [tex]\displaystyle y = -4cos\:4\theta[/tex]
Step-by-step explanation:
[tex]\displaystyle y = 4cos\:(4\theta \pm \pi) \\ \\ \\ y = Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = -Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from [tex]\displaystyle [0, -4][/tex] instead of downward from [tex]\displaystyle [0, 4],[/tex] telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -4],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{2}, -4],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:4\theta.[/tex] Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the rightward graph is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.[/tex]So, one equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(4\theta \pm \pi).[/tex] Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is [tex]\displaystyle y = -4cos\:4\theta.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Find the measure of indicated angle. Round to the 10th.
29.6 °
Explanation
we have a right triangle( a triangle with an angle of 90°), so we can use a trigonometric function
so
Step 1
a) Let
[tex]\begin{gathered} \text{angle}=\text{ ?} \\ \text{ hypotenuse( the longest side)= 23} \\ adjacent\text{ side= }20 \end{gathered}[/tex]so, we need to use a function that relates those values, it is
[tex]\begin{gathered} \cos \emptyset=\frac{adjacen\text{t side}}{\text{hypotenuse }} \\ \text{where }\emptyset\text{ is the angle} \end{gathered}[/tex]b) replace the values in the function and solve for the angle
[tex]\begin{gathered} \cos \emptyset=\frac{adjacen\text{t side}}{\text{hypotenuse }} \\ \cos \text{ ? =}\frac{20}{23} \\ \text{ inverse cosine in both sides } \\ \cos ^{-1}(^{}\cos \text{ ?) =}\cos ^{-1}(\frac{20}{23}) \\ \text{ ? = }29.59\text{ \degree} \\ \text{rounded to 10th} \\ \text{ ? = }29.6\text{ \degree} \end{gathered}[/tex]therefore, the answer is
29.6
I hope this helps you
triangle PQR with vertices P(6,-6) Q(9,-7) and R(7,-4) what is the area in square units of triangle PQR
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
P(6,-6)
Q(9,-7)
R(7,-4)
A = ?
Step 02:
To solve the exercise we must know the length of the sides.To solve the exercise we must know the length of the sides.
A = (b * h) / 2
side PR = b
side PQ = h
[tex]d\text{ = }\sqrt[]{(x2-x1)^{2}+(y2-y1)^{2}}[/tex][tex]b\text{ = }\sqrt[]{(7-6)^2+(-4-(-6))^2}[/tex][tex]b=\text{ }\sqrt[]{1+4}=\sqrt[]{5}=2.236[/tex][tex]\begin{gathered} h\text{ = }\sqrt[]{(9-6)^{2}+(-7-(-6))^{2}} \\ h\text{ = }\sqrt[]{9+1}=\sqrt[]{10}=3.162 \end{gathered}[/tex]Step 03:
A = (2.236*3.162) / 2 = 3.5355
The answer is:
3.54 ft²
What is the total sum of the interior degree of this polygon?What is the value of x?What is the measure of angle T
we are given a polygon with 6 sides, therefore, is a hexagon. The interior angles of a hexagon always add up to 720 degrees.
Using the expression and the given angles, we can construct the following relationship:
[tex](x+80)+135+(x+50)+130+(x+75)+115=720[/tex]Solving the operations we get:
[tex]3x+585=720[/tex]Now we solve for "x" first by subtracting 595 to both sides:
[tex]\begin{gathered} 3x=720-585 \\ 3x=135 \end{gathered}[/tex]Now we divide by 3:
[tex]x=\frac{135}{3}=45[/tex]Therefore, x = 45.
Now we use the expression for angle T:
[tex]\angle T=x+50[/tex]Replacing the value of x, we get:
[tex]\angle T=45+50=95[/tex]Therefore, angle T is 95 degrees.
An isosceles triangle has two equal angles. Find the measure of the third angle of triangle please help me understand
Given:
The angles of an isosceles triangle are,
∠M=40°
∠N=70°
The objective is to find the measure of ∠O.
An isosceles triangle is a triangle with two equal sides or two equal angles.
From the above figure, the two equal angles x are always larger than the third angle y.
Thus, the third angle will also be equal to the larger angle from the given agle.
Hence, the third angle is, ∠O = 70°.
A sample has mean 97 and standard deviation 12.Part: 0/2Part 1 of 2(a) What value is 2.5 standard deviations above the mean?The value that is 2.5 standard deviations above the mean is
The value that is 2.5 standard deviations above the mean is 127
f(x)=3x+12 find f(15)
f(15) = 57
Explanation:Given that
f(x) = 3x + 12
To find f(15), perform the following:
Step 1: Replace x by 15 in the given function
f(15) = 3(15) + 12
Step 2: Evaluate the expression
f(15) = 45 + 12
= 57
what digit is in the
The thousands digits are the fourth digit, in this case, 8. but you need to round to the nearest thousand, and like the number after 8 on 8958 is 9, the nearest thousand is 9.
So the answer is 9000
8. Jenise throws a ball 75 times and hits the larget 41 times. What is the experimental probability that she will hit the target? State your answer as a percent. The experimental probability that she will hit the target is (Round to the nearest hundredth as needed.)
OK
Number of throws = 75
Number of targets = 41
Probability = number of targets / number of throws
Probability = 41/75 x 100
Probability = 0.54666 x 100
Probability = 54.67 %
[tex]f(x) = 2( {x})^{2} + 5 \sqrt{(x + 2} [/tex]the domain for f(x) is all real numbers greater then or equal to _____.
the domain for f(x) is all real numbers greater than or equal to -2.
Remember in the real number domain we can't have negative values inside the square root because they are not defined.
What is the efficiency of a lever if you push 100 N over 5m to move 350 N over 1 m?
The efficiency of a lever is 70%.
From the question, we have
Efficiency = F_out/F_in
=350*1/100*5 = 350/500 = 0.7*100% = 70%
Efficiency:
Efficiency is the proportion of work done by a machine or throughout a process to the overall amount of energy or heat used.
Efficiency is the degree to which a given input may produce a specific outcome with the least amount of waste possible. Efficiency is the capacity to minimize wastage of resources, labor, time, and energy when completing an action or achieving a goal.
The ratio of usable output to total input can be used to objectively measure efficiency. The efficiency of the device is defined as the ratio of energy converted to a useable form to the original amount of energy supplied.
To learn more about efficiency visit: https://brainly.com/question/14619564
#SPJ9
Plot the value of 8 x 1/2 on the number line shown.
Step 1: Firstly, simplify the expression
[tex]\begin{gathered} 8\text{ }\times\text{ }\frac{1}{2} \\ =\text{ }\frac{8\text{ x 1}}{2} \\ =\text{ }\frac{8}{2} \\ =\text{ 4} \end{gathered}[/tex]Step 2: The value may be less than or greater than 4.
Positive numbers are plotted to the right of the origin while negative numbers are plotted to the left of the origin.
Step 3: Plot the number line
Raina has scored 32, 20, 26, and 24 points in her four basketball games so far. How many points does she need to score in her next game so that her average(mean) is 24 points per game
Given the number of points Raina scored in her four basketball games:
[tex]32,20,26,24[/tex]Let be "x" the number of points Raina needs to score in her next game so that her average is 24 points per game.
By definition, the Mean (average) can be calculated by dividing the sum of the values by the total number of values. Therefore, you can set up the following equation:
[tex]\frac{32+20+26+24+x}{5}=24[/tex]Then, when you solve for "x", you get:
[tex]\begin{gathered} \frac{102+x}{5}=24 \\ \\ 102+x=(24)(5) \\ \\ x=120-102 \\ \\ x=18 \end{gathered}[/tex]Hence, the answer is:
[tex]18\text{ points}[/tex]Hello! I’m not sure what are the correct answers could you please help?
a) 400 ft in 15 seconds
d) 1200 ft in 45 seconds
Explanation:Given:
Danny claimed the speed of his airplane was 27 feet per second
To find:
The statements in the options that support the above claim
rate of Danny's airplane = 27 ft/sec
a) rate = 400 feet in 15 seconds
We need tio get the rate in ft/sec
in 1 second = 400/15 = 26.67
Approximately, the rate = 27 ft/sec
b) rate = 3ft in 81 seconds
in 1 second = 3/81 = 0.037 ft/sec
c) rate = 1320 ft in 60 seconds
In 1 second = 1320/60 = 22
rate = 22 ft/sec
d) 1200 ft in 45 seconds
In 1 second = 1200/45 = 26.67
Approximately, rate = 27 ft/sec
The examples below that support his claim are the 1st and last option
I need to find the value of x. can you help me?
The angle on a line is 180°
The sum of the three given angles is 180°:
[tex](6x-10)+(x-5)+(x-5)=180[/tex]Use this equation to find the value of x:
[tex]\begin{gathered} 6x-10+x-5+x-5=180 \\ 8x-20=180 \\ 8x=180+20 \\ 8x=200 \\ x=\frac{200}{8} \\ \\ x=25 \end{gathered}[/tex]Then, the value of x is 25Which tells about surface area of solid or space figures
Given
we are given solid or space figures
Required
we need to find what gives surface area of a solid figure.
Explanation
The surface area of any solid shape is the sum of areas of all faces in that solid figure.
Example: when finding surface area of cube we add the area of each square constituting the cube.
Find the slope of the lines between two points (4,8);(-1,8)
We want to find the slope, the slope formula is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Inserting the values, (4,8), (-1,8), we have;
[tex]m=\frac{8-8}{-1-4}=\frac{0}{-5}=0[/tex]Thus, the slope is zero
ms sandlers wants to display his american flag in a triangular case.The height is 8.5 in.the base is 14 2/5 in.what is the area of a triangular case
Here, we want to get the area of the triangular case
Mathematically, this is half the product of the base and the height of the case
We have this as;
[tex]undefined[/tex]A triangle with area of 28 square inches has a height that is two less than four times the base. Find the base and the height of the triangle. Base is _ inches Height is __ inches
We write the following equations from the data of the statement of the problem:
• the area of the triangle is A = 28,
,• the height h and the base b are related by the following equation:
[tex]h=4b-2[/tex]The formula for the area of the triangle:
[tex]A=\frac{1}{2}\cdot b\cdot h\text{.}[/tex]Replacing the data of the problem in the equation above:
[tex]28=\frac{1}{2}\cdot b\cdot(4b-2).[/tex]We rewrite the equation in the following way:
[tex]\begin{gathered} 2\cdot28=b\cdot(4b-2), \\ 56=4b^2-2b, \\ 4b^2-2b-56=0. \end{gathered}[/tex]We have a quadratic equation for the length of base b, the solutions to this equation are:
[tex]b=4\text{ and }b=-\frac{7}{2}\text{.}[/tex]Because b is the length of one side of the triangle, and lengths are positive quantities, we must select the positive value of b, so we have:
[tex]b=4.[/tex]Replacing this result in the equation for the height, we get:
[tex]h=4b-2=4\cdot4-2=16-2=14.[/tex]Answer
• Base is ,4, inches,
,• Height is, 14, inches.
DeShawn has $53. He needs at least $76 to buy the jacket he wants. How much more money does he need for the jacket?[tex]x + 76 \geqslant 53[/tex][tex]X - 53 \geqslant 76[/tex][tex]X + 53 \leqslant 76[/tex][tex]X + 53 \geqslant 76[/tex][tex]X \geqslant 23[/tex][tex]X \geqslant 129[/tex][tex]X \geqslant - 26[/tex][tex]X \leqslant 23[/tex]can you please walk me though to the right answer thank you
Based on the given situation, we can define the following expression
[tex]x+53\ge76[/tex]"at least" indicates that we have to use "greater than or equal to".
Let's solve for x
[tex]\begin{gathered} x\ge76-53 \\ x\ge23 \end{gathered}[/tex]Hence, he needs $23 more to buy the jacket.The answers are[tex]\begin{gathered} x+53\ge76 \\ x\ge23 \end{gathered}[/tex]The expression under the square root sign is 3y+x and not 3v+x
The question asked to for the value of the expression below
[tex]\begin{gathered} \frac{w^2-\sqrt[]{3y+x}}{w+(y-1)} \\ \text{where,} \\ y=6,w=-9,x=7 \end{gathered}[/tex]Concept: Substitute the values in the formula given
[tex]\begin{gathered} \frac{w^2-\sqrt[]{3y+x}}{w+(y-1)} \\ \frac{(-9)^2-\sqrt[]{3(6)+7}}{-9+6-1} \\ =\frac{81-\sqrt[]{18+7}}{-4} \\ =\frac{81-\sqrt[]{25}}{-4} \\ =\frac{81-5}{-4} \\ =\frac{76}{-4} \\ =-19 \end{gathered}[/tex]Hence,
The final answer = -19
Find the arc AB. Round your answer to the nearest hundredth
STEP 1
The formular for the length of an arc is denoted below:
[tex]\text{Length of arc =}\frac{\theta}{360}\times\text{ 2}\Pi R[/tex][tex]\theta=115^0,\text{ }\Pi=\text{ 3.142, Radius(R)=13}[/tex]STEP 2
Substitute the above value into the formular.
[tex]L\text{ =}\frac{115^{}\text{ x2 x 3.142x 13}}{360}[/tex][tex]\begin{gathered} L=\text{ }\frac{9394.58}{360} \\ L\text{ = 26.096 inches} \end{gathered}[/tex]In conclusion, the Length of
What is the solution set to this equation?1054(= + 3) + 108.7
ANSWER
[tex]C.\text{ }x=1\text{ and }x=-4[/tex]EXPLANATION
We want to find the solution set to the equation given:
[tex]\log_4(x+3)+\log_4x=1[/tex]According to the laws of logarithm, we have that:
[tex]\begin{gathered} \log_ax+\log_ay=\log_a(x*y) \\ \\ and \\ \\ \log_aa=1 \end{gathered}[/tex]Therefore, we can rewrite the equation as follows:
[tex]\log_4[(x+3)*x]=\log_44[/tex]Since the logarithms on both sides have the same base, it implies that:
[tex](x+3)*x=4[/tex]Simplify and solve for x:
[tex]\begin{gathered} x^2+3x=4 \\ \\ x^2+3x-4=0 \\ \\ x^2+4x-x-4=0 \\ \\ x(x+4)-1(x+4)=0 \\ \\ (x-1)(x+4)=0 \\ \\ x=1\text{ and }x=-4 \end{gathered}[/tex]Hence, the correct answer is option C.
3 What is the product of and? 6 6 49 6 49 6 o
You have to multiply the fractions
[tex](-\frac{2}{7})\cdot(-\frac{3}{7})[/tex]First note that both values are negative. As a rule, when two negative values are mutiplied, the result will be positive, always.
Next, you have to multiply the numerators together and the denominators together as follows:
[tex]\frac{2}{7}\cdot\frac{3}{7}=\frac{2\cdot3}{7\cdot7}=\frac{6}{49}[/tex]1.) Write a sequence with at least 5 terms that forms a pattern . Identify the rule.2.) The first term in a sequence is an odd number. The rule is to multiply by 2 . Explain why the rest of the terms in sequence will be even numbers.
1. Increases by 5 units
2. Any odd number multiplied by an even one yields an even number.
1) We can write out a sequence, an arithmetic one, to follow a pattern.
[tex]5,10,15,20,25,\ldots[/tex]Note that the pattern here is the common difference between each term the first one is 5 and all the other ones increase by 5 units.
2) In this second case, we can pick "5" as well, but in this one, we'll make a Geometric Sequence for the following numbers will be written as the product of the prior term times 2:
[tex]5,10,20,40,\ldots[/tex]Note that all the terms will be even numbers because any odd number multiplied by an even one yields another even number.
If y varies directly as x, and y = 6 when x= 3, find y when x = 9.
y =when x= 9.
We know that:
- y varies directly as x
- y = 6 when x= 3
And we must find y when x = 9
To find it:
1. we must use that y varies directly as x
[tex]y=kx[/tex]2. We must find k using that y = 6 when x = 3
[tex]\begin{gathered} 6=k\cdot3 \\ k=\frac{6}{3} \\ \Rightarrow k=2 \end{gathered}[/tex]3. Finally, to find y when x = 9 we must replace x = 9 and k = 2 to solve it for y
[tex]\begin{gathered} y=2\cdot9 \\ y=18 \end{gathered}[/tex]ANSWER:
y = 18 when x = 9
10.Write the equation in slope-intercept form for the line that passes through the given pointand is perpendicular to the given equation.6x + 3y = -9 and passes through (-2, 2)
Let first put the equation of the first line in the form of slope intercept
[tex]\begin{gathered} 6x+3y=-9\rightarrow \\ y=\frac{-9-6x}{3}=-3-2x \end{gathered}[/tex]So it's slope is -2, so the new slope is
[tex]m=-\frac{1}{-2}=\frac{1}{2}[/tex]Having the slope, we have that
[tex]\begin{gathered} y-2=\frac{1}{2}(x+2)=\frac{1}{2}x+1 \\ y=\frac{1}{2}x+1+2=\frac{1}{2}x+3 \end{gathered}[/tex]so the equation is
[tex]y=\frac{1}{2}x+3[/tex]a transformation where a figure is flipped over a line1. dilation2.translation3.refelction4rotation
The answer is reflection
If I have found my slope intercept form and I need to graph the line but my slope and y intercept are fractions do I need to make the denominators the same to graph the line?
The formula for the slope-intercept form of a line is:
[tex]\begin{gathered} y=mx+b \\ m=slope \\ b=intercept \end{gathered}[/tex]If you have found the slope-intercept form and need to graph the line, but your slope and y-intercept are fractions, you do not really need to make the denominators the same. All you need to do is make a table of values on a range of values from which your graph can be plotted.
9 The Social Security number contains nine digits, if the form of 000-00-0000. How many differentSexial Security numbers can be formed using any numerals from 0 to 9?
Each digit has 10 possible values (the numbers from 0 to 9), so in order how many different numbers can be formed, we need to multiply the number of possible values of each digit.
If we have 9 digits, and each digit has 10 possible values, we need to multiply the number 10 by itself 9 times, that is:
[tex]N=10^9[/tex]So the number of different social security numbers is 10^9 (1,000,000,000, one billion)