A pendulum swings through an angle of 14° each second. If the pendulum is 14 cm in length and the complete swing from right to left last two seconds what area is covered by each complete swing?
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Answer;
[tex]\text{Area = 47.90 cm}^2[/tex]Explanation;
Firstly, we need a diagrammatic representation to get what is described in the question.
We have this as follows;
Now, from what we have here, the total angle swept by the pendulum moving from left to right is 28 degrees
To get the area, we simply need to find the area of the sector formed by the by pendulum
Mathematically, we have the area of a sector calculated as follows;
[tex]A\text{ = }\frac{\theta}{360}\times\pi\times R^2[/tex]theta is the angle made by the pendulum in one complete swing which is 28 degrees
pi is 22/7
R is the length of the pendulum which is 14 cm
Substituting these values in the formula above, we have it that;
[tex]\begin{gathered} A=\frac{28}{360}\times\frac{22}{7}\times14^2 \\ \\ A=47.90cm^2 \end{gathered}[/tex]
Related Questions
Put the equation y = x2 - 10x + 16 into the form y = =(x - h)² + ki Answer: y = > Next Question
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To complete the perfect square ((x-h)²) we add and subtract constants:
[tex]\begin{gathered} y=x^{2}-10x+16 \\ y=x^{2}-10x+25-25+16 \\ y=x^{2}-10x+5^{2}-9 \\ y=(x-5)^{2}-9 \end{gathered}[/tex]Is this continous or discrete?Fees for Overdue Books
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The following graph is given, representing the fees due for Overdue books:
I got the first part I’m not sure of the 2nd is it 38.5
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We will have the following:
The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:
[tex]A_s=4\pi(\frac{3.5}{2})^2\Rightarrow A_s\approx38.5[/tex]2+2=im in kendergardenin. pls help.
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The addition is the operation that puts together two quantities of numbers. It is represented by the signal "+". To add the two numbers we can use a visualization method as shown below:
We have two sticks on the left and two sticks on the right, we need to add them both, this is the same as joining them together, the result is 4 sticks. The answer is 4.
Answer:
the answer is 11
duuuh
Step-by-step explanation:
which are thrwe ordered pairs that make the equation y=7-x true? A (0,7) (1.8), (3,10) B (0,7) (2,5),(-1,8) C (1,8) (2,5),(3,10)D (2,9),(4,11),(5,12)
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In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.
If we substitute the points from option A, we get
[tex]\begin{gathered} 7=7-0 \\ 7=7 \end{gathered}[/tex]for (1,8), we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option A is false.
Now, if we substitute the points in option B, for point (2,5), we have
[tex]\begin{gathered} 5=7-2 \\ 5=5 \end{gathered}[/tex]which is correct. Now, for point (-1.8) we obtain
[tex]\begin{gathered} 8=7-(-1) \\ 8=8 \end{gathered}[/tex]Since all the points fulfil the equation, then option B is an answer.
Lets continue with option C and D.
If we substitute point (1,8) from option C, we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option C is false.
If we substite point (4,11) from option D, we get
[tex]\begin{gathered} 11=7-4 \\ 11=2\text{ !!!} \end{gathered}[/tex]then, option D is false.
Therefore, the answer is option B.
19. The table below shows the population of Florida from 2010 to 2019.YearPopulation (millions)201018.7201119.1201219.3201319.6201419.9201520.2201620.6201721.0201821.2201921.5(a) Use a graphing calculator to build a logistic regression model that best fits this data, letting t=0 in 2010. Round each coefficient to two decimal places.Pt = (b) What does this model predict that the population of Florida will be in 2030? Round your answer to one decimal place. million people(c) When does this model predict that Florida's population will reach 23 million? Give your answer as a calendar year (ex: 2010).During the year (d) According to this model, what is the carrying capacity for Florida's population? million people
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The formula for the logistic regression model that best fits the data is,
[tex]y_1=\frac{a}{1+b\cdot e^{t\cdot x_{1}}}[/tex]The graph, tables and details of the population data will be shown below
a) The equation that best fits the regression model is,
[tex]\begin{gathered} P_t=y_1 \\ t=x_1 \\ a=93.2861\approx93.29(2\text{ decimal places)} \\ b=3.98291\approx3.98(2\text{ decimal places)} \\ t=-0.0198742\approx-0.02(2\text{ decimal places)} \end{gathered}[/tex]Substitutes the data above into the equation
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]Hence,
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]b) In the year 2030, t = 20
[tex]\begin{gathered} P_{20}=\frac{93.29}{1+3.98\cdot e^{-0.02\times20}}=\frac{93.29}{1+3.98\cdot e^{-0.4}}=\frac{93.29}{1+3.98\times0.67032} \\ P_{20}=\frac{93.29}{1+2.6678736}=\frac{93.29}{3.6678736}=25.43435521\approx25.4(1\text{ decimal place)} \\ P_{20}=25.4million\text{ people} \end{gathered}[/tex]Hence, the answer is
[tex]P_{20}=25.4\text{million people}[/tex]c) Given that
[tex]\begin{gathered} _{}P_t=23\text{million people} \\ 23=\frac{93.29}{1+3.98\cdot e^{-0.02t}} \end{gathered}[/tex]Multiply both sides by 1+3.98e^{-0.02t}
[tex]\begin{gathered} 23(1+3.98e^{-0.02t})=1+3.98e^{-0.02t}\times\frac{93.29}{1+3.98\cdot e^{-0.02t}} \\ \frac{23(1+3.98e^{-0.02t})}{23}=\frac{93.29}{23} \\ 1+3.98e^{-0.02t}=4.056087 \end{gathered}[/tex]Subtract 1 from both sides
[tex]\begin{gathered} 1+3.98e^{-0.02t}-1=4.056087-1 \\ 3.98e^{-0.02t}=3.056087 \end{gathered}[/tex]Divide both sides by 3.98
[tex]\begin{gathered} \frac{3.98e^{-0.02t}}{3.98}=\frac{3.056087}{3.98} \\ e^{-0.02t}=0.767861055 \end{gathered}[/tex]Apply exponent rule
[tex]\begin{gathered} -0.02t=\ln 0.767861055 \\ -0.02t=-0.264146479 \end{gathered}[/tex]Divide both sides by -0.02
[tex]\begin{gathered} \frac{-0.02t}{-0.02}=\frac{-0.264146479}{-0.02} \\ t=13.20732\approx13(nearest\text{ whole number)} \\ t=13 \end{gathered}[/tex]Hence, the population will reach 23million in the year 2023.
d) The carrying capacity for Florida's population is equal to the value of a.
[tex]\begin{gathered} \text{where,} \\ a=93.29\text{ million people} \end{gathered}[/tex]Hence, the carrying capacity fof Florida's population is
[tex]93.29\text{million people}[/tex]
the fraction 1-2 equals?
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The given fraction is 1/2.
IF we divide, we have
[tex]\frac{1}{2}=0.5[/tex]Therefore, the answer is 0.5.what would be the value if m in a angle on 50 degrees and 10m
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50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.
10m = 90 - 50
10m = 40
m = 40/10
m = 4
Find the perimeter and area of the polygon with given vertices
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Let's begin by listing out the information given to us:
[tex]\begin{gathered} A(-3,3),B(-3,-1),C(4,-1),D(4,3) \\ AB=3-(-1)=3+1=4_{} \\ BC=|-3-4|=|-7|=7 \\ CD=|-1-3|=|-4|=4 \\ AD=|-3-4|=|-7|=7 \\ \\ Perimeter=2(l+w)=2(7+4)_{}=2(11)=22 \\ Perimeter=22unit \\ \\ Area=lw=7\cdot4=28unit^2 \\ Area=28unit^2 \end{gathered}[/tex]g(x) = 2x - 5f(x) = 4x + 2Find g(f(x))
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Explanation
Step 1
Let
[tex]\begin{gathered} g(x)=2x-5 \\ \text{and} \\ f(x)=4x+2 \end{gathered}[/tex]then
[tex]\begin{gathered} g(f(x))= \\ g(x)=2x-5 \\ g(f(x))=2(4x+2)-5 \\ \text{apply distributive property} \\ g(f(x))=8x+4-5 \\ g(f(x))=8x-1 \end{gathered}[/tex]I hope this helps you
Hello! I'm hitting a bit of a snag on this. I think I'm reading it too many times
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The solution:
Given:
[tex]\begin{gathered} \text{ A sphere of radius 4m.} \\ \\ A\text{ cube of side 6.45m} \end{gathered}[/tex]Required:
To compare the volume and area of bot shapes.
The Sphere:
[tex]\begin{gathered} Area=4\pi r^2=4(4)^2\pi=64\pi=201.062m^2 \\ \\ Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\times\pi\times4^3=268.083m^3 \end{gathered}[/tex]The Cube:
[tex]\begin{gathered} Area=6s^2=6\times6.45^2=249.615m^2 \\ \\ Volume=s^3=6.45^3=268.336m^3 \end{gathered}[/tex]Clearly, we can see that:
Both shapes have approximately the same volume.
But the cube has a greater volume than that of the sphere.
Therefore, the correct answer is [option 4]
How many possible values for y are there where y = Cos-lo? O A. O Ο. O B. Infinite O C. 1 O D. 2
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Answer:
B. Infinite
Explanation:
Given that:
[tex]y=\cos ^{-1}(0)[/tex]This implies that:
[tex]\cos (y)=0[/tex]From the graph of f(x)=cos(x), we observe that:
[tex]\cos (x)=0\text{ for }x=\frac{\pi}{2}+k\pi\text{ for any }k\in\Z,\text{ }\Z\text{ being the set of integers}[/tex]Therefore, there are infinitely possible values of y.
Find the real solutions of the equation by graphing. 4x^3-8x^2+4x=0
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x = 0,1 are the real solutions of the equation .
What are real solutions in math?
Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.4x³ - 8x² + 4x = 0
x( 4x² - 8x + 4 ) = 0
x( 4x² - 4x - 4x + 4 ) = 0
x ( 4x ( x - 1) -4 ( x - 1 )) = 0
x ( ( 4x - 4 ) ( x - 1 ) ) = 0
x = 0
4x - 4 = 0 ⇒ x = 1
x - 1 = 0 ⇒ x = 1
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Solve this system of equations by elimination. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer. If your answer is no solution, type "no solution". If your answer is infinitely many solutions, type "infinitely many solutions".
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5x + 2y = -12 (a)
3y + 5x =-8 (b)
First, write (b) in the ax+by=c form:
5x + 3y = -8 (b)
Now, subtract (b) to (a) to eliminate x
5x + 2y = -12
-
5x + 3y = -8
__________
-y = -4
solve for y:
Multiply both sides by -1
y=4
Replace y=4 on (a) and solve for x:
5x + 2 (4) = -12
5x + 8 = -12
5x = -12-8
5x = -20
x = -20/5
x = -4
Solution: (-4,4)
Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3
Answers
Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex](x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]Answer:
• Slope: -5/2
,• y-intercept: 3
The correct answer is option B
Find the solution to following system of equations A+ 10C = 54 A +9C = 50 A. A=10 C= 4 B. A= 14 C= 4 C. A=4 C= 14 D. A= 10 C= 6
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Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
Кр2.345 67 8Identify each angle as acute, obtuse, or right123345678.
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we have the following:
Therefore:
Carlos is saving money to buy a new Nintendo Switch game. He has $25. After he receives his allowance (n), he will have $45. Which of the following equations models this situation?
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ANSWER
25 + n = 45
EXPLANATION
We have that Carlos already has $25.
His allowance is n. After receiving it, he now has $45.
This means that if we add the amount he had and his allowance, we will have $45.
Therefore:
25 + n = 45
This equation models the situation accurately.
Given slope of m=2/3 and y-intercept b=1 graph the line
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ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)
graph that
because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)
we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)
create a line connecting all the points
What does the slower car travel at Then what does the faster car travel at
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Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
what is 3/8 * 1/5 and 6/10 * 3/4
Answers
Answer
(3/8) × (1/5) = (3/40)
(6/10) × (3/4) = (9/20)
Explanation
We are asked to solve the given expressions
(3/8) × (1/5)
And
(6/10) × (3/4)
For (3/8) × (1/5)
[tex]\frac{3}{8}\times\frac{1}{5}=\frac{3\times1}{8\times5}=\frac{3}{40}[/tex]For (6/10) × (3/4)
[tex]\begin{gathered} \frac{6}{10}\times\frac{3}{4}=\frac{6\times3}{10\times4}=\frac{18}{40} \\ We\text{ can now reduce this to the simplest form} \\ \text{Divide numerator and denominator by 2} \\ \frac{18}{40}=\frac{9}{20} \end{gathered}[/tex]Hope this Helps!!!
find the first term when the 31st 32nd and 33rd are 1.40, 1.55, and 1.70
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jadeymae06, this is the solution:
This is an arithmetic sequence, where d (common difference) = 0.15
(1.70 - 1.55) or (1.55 - 1.40)
•
,• a + 30d = 1.40
,• a + 30(0.15) = 1.4
,• a + 4.5 = 1.4
,• a = 1.4 - 4.5
,• a = -3.1
Jade, the first term is -3.1
Find the first five terms in sequences with the following 3n+2
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To determine the first five terms of the sequence we substitute n by 1, 2, 3, 4, and 5.
For n=1, we get:
[tex]3(1)+2=3+2=5.[/tex]For n=2, we get:
[tex]3(2)+2=6+2=8.[/tex]For n=3, we get:
[tex]3(3)+2=9+2=11.[/tex]For n=4, we get:
[tex]3(4)+2=12+2=14.[/tex]For n=5, we get:
[tex]3(5)+2=15+2=17.[/tex]Answer: The first five terms of the sequence are:
[tex]5,\text{ 8, 11, 14, 17.}[/tex]the remainder when f(x)is divided by x-3 is 15. Does f(-3) =15? explain why or why not
Answers
We will see that the function f(x) is:
f(x) = 15*(x - 3)
Evaluating it in x = -3 we can see that:
f(-3) = -90
Is the statement true?We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)
so we can write the equation:
f(x)/(x - 3) = 15
And we can solve this for f(x) as if it were a variable, then we get:
f(x) = 15*(x - 3)
Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:
f(-3) = 15*(-3 - 3) = 15*(-6) = -90
So the statement:
f(-3) = 15
Is false
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I would like to make sure my answer is correct ASAP please
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step1: Write out the formula for exponential growth
[tex]y=a(1+r)^n[/tex][tex]\begin{gathered} a=\text{initial population} \\ r=\text{rate} \\ n=\text{years} \end{gathered}[/tex]Hence we have
[tex]a=800,r=3\text{ \%, n=x}[/tex]Step2: substitute into the formula in step 1
[tex]\begin{gathered} y=800(1+\frac{3}{100})^x \\ y=800(1+0.03)^x \\ y=800(1.03)^x \end{gathered}[/tex]Hence the right option is A
Referring to the figure, find the value of x in circle C.
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The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
Graphically,
[tex]PA\cdot PB=(PD)^2[/tex]In this case, we have:
[tex]3x\cdot5=10^2[/tex]Now, we can solve the equation for x:
[tex]\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ \frac{15x}{15}=\frac{100}{15} \\ \text{Simplify} \\ x=\frac{20\cdot5}{3\cdot5} \\ x=\frac{20}{3} \\ \text{ or} \\ x\approx6.67 \end{gathered}[/tex]Therefore, the value of x is 20/3 or approximately 6.67.
A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?
Answers
Given:
The sequence of number of stars is 2,4,8,16
a) To find the common ratio of the pattern.
[tex]\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]Hence the common ratio is 2.
b) To find the explicit formula for the pattern.
The general for a geometric progression sequence is,
[tex]a_n=a_1(r)^{n-1}_{}_{}[/tex]Hence, the formula for the above pattern will be,
[tex]a_n=2(2)^{n-1}[/tex]c) To find the number of stars in 11th set.
Substitute n=11 in the explicit formula of the pattern.
[tex]\begin{gathered} a_{11}=2(2)^{11-1} \\ a_{11}=2(2)^{10} \\ a_{11}=2(1024) \\ a_{11}=2048 \end{gathered}[/tex]Hence, the number of stars in 11th set will be 2048.
How many soultions?x + 3 = 2x - 18A single solutionInfinite solutionsNo solution
Answers
The given equation is expressed as
x + 3 = 2x - 18
Subtracting x from both sides of the equation, it becomes
x - x + 3 = 2x - x - 18
3 = x - 18
Adding 18 to both sides of the equation, it becomes
3 + 18 = x - 18 + 18
21 = x
x = 21
Since there is only one value for x, the correct option is
a. A single solution
Convert €3.2 per kilogram to unit price dollars per pound
Answers
We get 1.45 dollars per pound when we convert 3.2 Euros per kilogram to dollar per pound.
According to the question,
We have the following information:
3.2 Euros per kilogram
We need to convert its units into dollars per pounds.
We know that 1 Euro is approximately equal to 1 US dollar and 1 kilogram of weight is equal to 2.205 pounds.
(Note that there are various conversions from Euro to dollars which have 1 Euro equal to 1.00755 and many other values. In this case, we have rounded it off to 1 to avoid any confusion.)
(We know that per means the unit given is in divide.)
So, we have:
(3.2*1)/(1*2.205)
3.2/2.205
1.45 dollar per pounds
Hence, the conversion to dollars per pounds is 1.45 dollar per ponds from Euros per kilogram.
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I need help with finding the rational approximation of 37 using perfect squares
Answers
SOLUTION
For rational approximation of 37, it means we are to obtain the close estimate for the square root of 37.
using perfect squares,
The perfect square number immediately lower than 37 is
[tex]36[/tex]The perfect square number immediately higher than 37 is
[tex]49[/tex]Then we set up the problem as in the image below
The distance between 36 to 37 is lower than the distance between 49 to 37, hence the rational aproximation of 37 will be closer to the square root of 36 than the square root of 49.
This accouunt for the sqaure root of 37 in the image above
[tex]\sqrt[]{37}=6.08\approx6.1[/tex]Therefore
The rational aprosimation of 37 using perfect square is 6.1