ANSWER
EXPLANATION
The circumference of a circle is calculated using the formula:
[tex]C=2\pi \: r[/tex]
From the question, the radius of the circle is 10 inches.
We substitute the radius into the formula to get:
[tex]C=2\pi \times 10[/tex]
Let us multiply out to get:
[tex]C=20 \pi \: in[/tex]
The question required that we leave the answer in terms of π.
The correct choice is C.
Answer:
the correct answer is 14 nStep-by-step explanation:
A Ferris wheel has a radius of 35 m. Its center is 36 m above the ground. It rotates once every 60 s. Suppose you get on the bottom at t = 0 .
Write an equation that expresses your height as a function of elapsed time.
h = 36 cos 2π (t - 30) / 60 + 35
h = 60 cos 2π (t - 35) / 36 +60
h = 35 cos π (t - 30) / 60 + 36
h = 35 cos 2π (t - 30) / 60 +36
The equation expressing the height as a function of elapsed time for the provided Ferris wheel scenario is: h = 35 cos 2π (t - 30) / 60 + 36. This assumes the highest point is reached halfway through the rotation and uses a cosine function to map the cycle.
Explanation:The subject of this question is mathematics, specifically it's about trigonometric functions and their applications to real world scenarios. The question is seeking for an equation that can express the height of a point on a Ferris wheel as a function of elapsed time.
Here's the solution: The highest height will be the radius of the Ferris wheel (35m) plus the height of the wheel's center above the ground (36m), which is a total of 71m. This height will be reached halfway through the rotation period of the wheel (30s). So, as the function of time, height can be represented by a cosine function shifted to the right by 30s with a period of 60s. Therefore, the equation to represent this scenario correctly is:
h = 35 cos 2π (t - 30) / 60 + 36
In this equation, 'h' stands for height, 't' represents time, 'cos' is the cosine function, 'π' is pi, and '35', '60', '30', and '36' are specific constants representing the radius of the Ferris wheel, the period of rotation, the time shift, and the wheel's center height respectively.
Learn more about Trigonometric Functions here:https://brainly.com/question/31540769
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What is the maximum number of turns in the graph of this function?
[tex]f(x) = x^4-x^3+3x+1[/tex]
Answer:
The maximum number of turns is 3
Step-by-step explanation:
The given function is
[tex]f(x)=x^4-x^3+3x+1[/tex]
The degree of this polynomial is 4.
If the degree of a given polynomial is n, then the polynomial has at least n-1 turns.
Therefore the number of turns of this 4th degree polynomial is at least 3.
use the equation to answer the following question y=(x-3(x+2)/(x+4)(x-4)(x+2)
a. Find all points of discontinuity
b. Determine whether each point is removable(hole) or non-removable (vertical asymptote)
c.find the equation of the horizontal and vertical asymptotes for the rational function if any
Answer:
See below
Step-by-step explanation:
The given rational function is;
[tex]y=\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}[/tex]
The given function is not continuous where the denominator is equal to zero.
[tex](x+4)(x-4)(x+2)=0[/tex]
The function is discontinuous at [tex]x=-4,x=4,x=-2[/tex]
b) The point at x=-2 is a removable discontinuity(hole) because (x+2) is common to both the numerator and the denominator.
The point at x=-4 and x=4 are non-removable discontinuities(vertical asymptotes)
c) The equation of the vertical asymptotes are x=-4 and x=4
To find the equation of the horizontal asymptote, we take limit to infinity.
[tex]\lim_{x\to \infty}\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}=0[/tex]
The horizontal asymptote is y=0
A theater can hold 160 giants or 240 elves. If 109 giants are inside how many elves can also be admitted.
Answer:
it depends
Step-by-step explanation:
If the tradeoff between giants and elves is linear, then about 76 elves can be admitted. If it is non-linear, we need more information about the tradeoff.
For example, elves may fit in the spaces between giants in such a way that they take up proportionately less room. Or, elves may repel giants in such a way that they take up proportionately more room.
See the attached graph for some possibilities.
_____
The linear equation can be written as ...
g/160 + e/240 = 1
Then for g=109, we can solve for "e" as ...
109/160 + e/240 = 1
240(1 -109/160) = e = (3/2)(51) = 76.5
If the tradeoff is linear, 76 elves can be admitted.
Please help with #5 only
Answer:
1680Step-by-step explanation:
[tex]\sum\limits_{n=1}^{42}2n-3\\\\a_n=2n-3\\\\a_{n+1}=2(n+1)-3=2n+2-3=2n-1\\\\a_{n+1}-a_n=(2n-1)-(2n-3)=2n-1-2n+3=2=constant\\\\\text{Therefore it's an arithmetic sequence with first term}\\\\a_1=2(1)-3=2-3=-1\\\\\text{and common difference}\\\\d=2[/tex]
[tex]\text{The formula of a sum of terms of an aithmetic sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{Substitute:}\\\\n=42,\ a_1=-1,\ d=2:\\\\S_{42}=\dfrac{2(-1)+(42-1)(2)}{2}\cdot42=[-2+(41)(2)](21)=(-2+82)(21)\\\\=(80)(21)=1680[/tex]
Fins the zeros, multiplicity, and effect on the graph of the function in
f(x) = -x (3x-2)^2(x+9)^5
and
f(x) = x^3+10x^2+25x
Answer:
See explanation
Step-by-step explanation:
Zeroe of the function is such velue of x at which f(x)=0.
1. Consider the function [tex]f(x)=-x(3x-2)^2 (x+9)^5.[/tex]
Zeros are:
[tex]-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.[/tex]
Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=\dfrac{2}{3}[/tex] has multiplicity of 2, zero [tex]x=-9[/tex] has multiplicity of 5.
At [tex]x=0[/tex] or [tex]x=-9[/tex] the graph of the function crosses the x-axis, at [tex]x=\dfrac{2}{3}[/tex] the graph of the function touches the x-axis.
2. Consider the function [tex]f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.[/tex]
Zeros are:
[tex]x(x+5)^2=0\\ \\x=0\text{ or }x=-5.[/tex]
Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=-5[/tex] has multiplicity of 2.
At [tex]x=0[/tex] the graph of the function crosses the x-axis, at [tex]x=-5[/tex] the graph of the function touches the x-axis.
What is the recursive rule for the sequence?
Answer:
C
Step-by-step explanation:
Since we are dealing with recursive equations, we can use a simple format.
[tex]a_{1}=x \\ \\ a_{n}=a_{n-1}+y[/tex]
x is the starting value and y is the change.
We can see that the change is -5.6 since 5.6 is being subtracted from each term each time.
So the equation would be
[tex]a_n=a_{n-1}-5.6[/tex]
We can check this by plugging in the numbers.
Let's see if -8.3 works, which is the 2nd term in the equation.
[tex]a_2=a_{2-1}-5.6 \\ \\ -8.3=a_{1}-5.6 \\ \\ -8.3=-2.7-5.6 \\ \\ -8.3=-8.3[/tex]
Therefore, the recursive rule is the third one.
Max's T-shirt business uses the demand function P = -Q + 28 and the supply function P = Q - 12. According to these functions, what will the equilibrium point be for Max's T-shirt business?
A. (20,8)
B. (12,28)
C. (8,20)
D. (28,12)
A and c —————- Bc 20 +8 is 28
Answer:
The answer is (8,20) on APEX. just did the test. good luck!
Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=12⋅P(x)?
Answer:
The picture where the red image is the skinniest
Step-by-step explanation:
The graph P(x) is the parent graph for all absolute functions. It has a vertex of (0,0) and has the following points:
x f(x)
-2 2
-1 1
0 0
1 1
2 2
The image of l(x) = 12P(x) changes the points of the function to
x f(x)
-2 24
-1 12
0 0
1 12
2 24
This makes the graph much skinnier. The graph with the skinniest red graph is the graph.
Answer:
The second graph is the right answer.Step-by-step explanation:
The parent function is
[tex]P(x)=|x|[/tex]
(Remember, a parent function refers to the simplest function of its type)
The image function is
[tex]I(x)=12P(x)[/tex]
Which is [tex]I(x)=12|x|[/tex].
Observe in the image attached, the image function is vertically stretched by a factor of 12.
Therefore, the right answer is the second graph.
Need help
Choices
4
3
2
1
Answer:
1
Step-by-step explanation:
The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.
Answer:
1
Step-by-step explanation:
How do I algebraically solve this? (solve for x)
Check the picture below.
Use the drop-down menus to identify the key values of the box plot. The median is . The minimum is . The maximum is . The lower quartile (Q1) is . The upper quartile (Q3) is .
ANSWERS:
C
A
E
B
D
Answer: The lower quartile is Q1) is your minimum & your maximum is quartile Q3) bc is the larger one
Step-by-step explanation:
c
a
e
b
d
is none of your answer.
Answer:
person above is correct
Step-by-step explanation:
show them some love
A rectangular prism is 4 inches long, 6 inches wide, and has a height of 5 inches. What is its volume?
60 in 3
120 in 3
148 in 3
240 in 3
Answer:
Step-by-step explanation:
The volume of a rect. prism is V = (length)(width)(height).
Here the volume is V = (4 in)(6 in)(5 in) = 120 in³ or 120 in^3
Note: Please use " ^ " to indicate exponentiation: 120 in^3
Answer:
120 in 3
Step-by-step explanation:
Though it is true I enjoy your writing style, I don't agree with your main point of view about this one. I do delight in your website nevertheless. Gedefkkfdefd
Answer:
34.
Step-by-step explanation:
Determine the area of a sector with a central angle of 90° and a radius of 10 meters.
A. 25 meters2
B. 90π meters2
C. 100π meters2
D. 25π meters2
Area of circle
= 90/360 x π x (10)^2
= 1/4 π x 100
= 25 π meter^2
Final answer:
The area of a sector with a central angle of 90° and a radius of 10 meters is calculated using the formula A = θ/360 × πr². Substituting the given values, the area is found to be 25π m². The correct answer is D. 25π meters².
Explanation:
Finding the Area of a Sector
To find the area of a sector with a central angle of 90° in a circle with a radius of 10 meters, we use the formula for the area of a sector, which is A = θ/360 × πr², where θ is the central angle in degrees, π is the mathematical constant approximately equal to 3.14159, and r is the radius. Since the central angle θ is 90°, and the radius r is 10 meters, we have:
A = 90°/360° × π × (10 m)²
= 0.25 × π × 100 m²
= 25π m².
Therefore, the correct answer is D. 25π meters².
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule?
Enter your answer, as a decimal, in the box.
Answer:
0.22
Step-by-step explanation:
The point estimate is the average of the upper and lower bounds of the interval.
Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
A:Point B is the result of a 180° rotation.
B:Point A and B have the same x-coordinate.
C:Point B is the result of a 90° counterclockwise rotation.
D:Point A and point B are the same distance from the origin.
Answer:
D:Point A and point B are the same distance from the origin.
Step-by-step explanation:
hope this helps :)
Answer:
D
Step-by-step explanation:
Hit the THANKS button pls >.<
V
V
V
Decide which trigonometric ratio to use. Solve for x in the triangle below. Round your answer to the hundredths place.
Options
4.59
0.07
6.55
5.60
Answer: 4.59
sin(35)=x/8
8*sin(35)=x
x=4.59
The value of x in the given triangle round to the nearest hundredths is:
4.59
Step-by-step explanation:From the given triangle we observe that the side x is the opposite side corresponding to angle 35°.
i.e. we will use sine trignometric ratio in the triangle to get the value of x.
We know that:
[tex]\sin 35=\dfrac{x}{8}ddd[/tex]
Since the sine of an angle is the ratio of opposite side to the hypotenuse of the right angled triangle.
i.e.
[tex]x=8\times \sin 35\\\\i.e.\\\\x=8\times 0.5736\\\\i.e.\\\\x=4.588[/tex]
which is approximately equal to 4.59 units.
The center is a(?,?)
The radius is _____ units.
Answer:
The center is at [tex](2,4)[/tex]
3 units
Step-by-step explanation:
You can observe in the graph a circle.
The x-coordinate and the y-coordinate of the center of the circle shown in the figure are:
[tex]x=2[/tex] and [tex]y=4[/tex]
Therefore, the point of the center of the circle is:
[tex](2,4)[/tex]
You can observe that the diameter goes from -1 to 5, then the diameter is:
[tex]diameter=1units+5units\\\\diameter=6units[/tex]
The radius is half the diameter. Therefore, you can say that the radius of this circle is:
[tex]radius=\frac{diameter}{2}\\\\radius=\frac{6units}{2}\\\\radius=3units[/tex]
ANSWER
The center is (2,4)
The radius is 2√2 units
EXPLANATION
Each of the ticks is 1 unit
Counting two ticks from the origin to the right and 4 units up will land us at the center of the circle.
Hence the center is (2,4)
The circle passes through (0,2).
The radius is
[tex]r = \sqrt{ {(2 - 0)}^{2} + {(4 - 2)}^{2} } [/tex]
[tex]r = \sqrt{8} = 2 \sqrt{2} [/tex]
It took Otis 6 hours to travel to the Grand Canyon. Along the way he took 18 minutes to get gasoline and 53 minutes to eat. How much time did Otis spend driving? With work
The answer is 4 hours and 49 minutes HERE IS MY WORK
4 hours and 49 minutes
Please help me with this
Answer:
8.4
Step-by-step explanation:
hope it helped
The period of this function is
2π
π/8
π/4
π/2
I’m not quite sure what the function is but if it’s sine the period is pi/8
ANSWER
The period is
[tex] \frac{\pi}{8} [/tex]
EXPLANATION
The given function completes four cycles on the interval
[tex]
[ - \frac{\pi}{4} , \frac{\pi}{4} ][/tex]
Therefore the period is
[tex] = \frac{ \frac{\pi}{4} - \frac{\pi}{4} }{4} [/tex]
Simplify the numerator:
[tex] = \frac{ \frac{\pi}{2}}{4} [/tex]
Simplify further to get:
[tex]= \frac{\pi}{8} [/tex]
Prove or disprove the identity. if you find the identity is true, state the first line of the proof. if you find the identity is false, write the correct equation by replacing the right side. sec2 x(1 – sin2 x) = csc2 x cos x
Answer:
False
Step-by-step explanation:
Using the trigonometric identities
• sin²x + cos²x = 1
• secx = [tex]\frac{1}{cosx}[/tex]
Consider the left side
sec²x(1 - sin²x)
= [tex]\frac{1}{cos^2x}[/tex] × cos²x = 1
The correct identity is
sec²x(1 - sin²x) = 1
6 / 2 (1 + 2) = 9
PLEASE EXPLAIN HOW IT IS 9!!! I followed PEMDAS, and I keep getting 1
Answer:
9
Step-by-step explanation:
6 / 2 (1 + 2) = 9
PEMDAS
Parentheses first
1+2 =3
Substitute this in
6 / 2 (3) = 9
Multiplication and Division from left to right
Division first
6/2 =3
Substitute this in for 6/2
3 (3) =9
3*3 =9
Kevin caught some fish. Of them 4/9 were herring, and 2/9 salmon. What was the total amount of fish, amount of herring and amount of salmon if there were 12 flounders?
There were 3 different fish caught, Salmon, Herring and Flounder.
4/9 were Herring, 2/9 were Salmon, 4/9 +2/9 = 6/9
This means 3/9 were Flounders ( 3/9 + 6/9 = 9/9 = 1)
3/9 can be reduced to 1/3.
1/3 of the fish were Flounders.
Divide the amount of flounders by the portion caught:
12 / 1/3 = 12 * 3/1 = 36 total fish.
Now you have total number of fish, multiply the total by each portion for each type of fish.
Total fish = 36
Herring = 4/9 x 36 = 16
Salmon = 2/9 x 36 = 8
Solve: 110°20'
PLS TRY to translate degrees and minutes to degrees! BRAINLIEST for 1st answer :)
Answer:
110 1/3 or 100.33 degrees (to the nearest hundredth).
Step-by-step explanation:
There are 60 ' (minutes) in a degree.
So 20' = 20/60 = 1/3 of a degree.
Answer:
110 1/3°
Step-by-step explanation:
Recall that 1° = 60'. Then 20' is 1/3 of 1°, or (1/3)°.
Then 110° 20' = 110° + (1/3)° = 110 1/3°.
1. x/5 = 10 *
2. x + 2 = 15 *
3. 5x = 40 *
4. 2y = 44 *
5. r - 15 = 30 *
Answer:
Step-by-step explanation:
1) x/5 = 10
multiply by 5 : x = 50
2) x + 2 = 15
add -2 : x = 13
3) 5x = 40
divid by 5 : x =8
4) 2y = 44
divid by 2 : y = 22
5. r - 15 = 30
add 15 ; 5r =45
divid by 5 : r = 9
HELP PLEASE!!! I WILL FIVE STAR!!
Answer:
Step-by-step explanation:
You can't answer c. There is not enough information. Other than there are 14 boys that went, you know nothing about how many went.
Girls going = (3/5) * 20 = 12
Girls not going = 20 - 12 = 8
Which of the following ordered pairs represents an output of 5 and an input of -8?
(-8,-8)
(-8,5)
(5, 5)
(5, -8)
Answer:
(-8,5)
Step-by-step explanation:
The output corresponds to the y-value of an ordered pair while the input corresponds to the x-value of an order pair.
An ordered pair is written like this (x,y)
Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.
Answer:
(1 , 1)
Step-by-step explanation:
Given in the question two equations
Equation 1
y = x² – x + 1
Equation 2
y = x
Equate both equations
x² – x + 1 = x
0 = x² – x + 1 - x
x² – 2x + 1 = 0
x² - x - x + 1 = 0
x(x - 1) -1(x - 1) = 0
(x - 1)(x - 1) = 0
(x-1)² = 0
x - 1 = 0
x = 1
Plug x = 1 in first equation
y = 1² – 1 + 1
y = 1
Answer:
The answer is option A, or (1,1)
Step-by-step explanation:
I just took the test