Find the arc length of the partial circle.
Either enter an exact answer in terms of pi or use 3.14, point, 14 for pi and enter your answer as a decimal.
Answers
The length of the arc of the partial circle is 18.84 units.
As per the question statement, we are supposed to find out the length of the arc of the partial circle as given in the figure provided.
Before solving this question, we need to know the formula for calculating the arc length of the circle i.e.,
Arc Length = [tex]2\pi r(\frac{\alpha }{360} )[/tex]
where [tex]\alpha[/tex] is the angle provided between the arc end in degrees
[tex]r[/tex] is the radius of the given circle in given units and
[tex]\pi =3.14[/tex]
In the given circle, the angle subtended by the arc is complete angle minus 90 degrees i.e.,
[tex]\alpha =360 - 90 = 270 degrees[/tex]
radius [tex]r[/tex] = 4 units (given)
Therefore Arc Length = [tex]2\pi r(\frac{\alpha }{360} )[/tex]
[tex]= 2*3.14*4*(\frac{270}{360})\\ =25.12(0.75)\\=18.84 units[/tex]
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Related Questions
Find the distance between each pair of points.
(0,-5) and (18,-10)
Answers
Answer:
18.7 units (3 s.f.)
Step-by-step explanation:
The distance between two points is given by the formula below, where [tex](x_1, y_1)[/tex] is the first coordinate and [tex](x_2, y_2)[/tex] is the second coordinate.
[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
Substitute the given points into the formula:
Distance between (0, -5) and (18, -10)
= [tex]\sqrt{[-10 -(-5)]^{2} + (18-0)^{2} }[/tex]
= [tex]\sqrt{(-10+5)^2+18^2}[/tex]
= [tex]\sqrt{(-5)^2+18^2}[/tex]
= [tex]\sqrt{349}[/tex]
= 18.7 units (3 s.f.)
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Through how many radians will the hour hand on a clock rotate in (a) 23 hr? In (b) 6 hr? (a) In 23 hr, the hour hand on the clock will rotate radians
Answers
The radians will the hour hand on a clock rotation for 23hr and 6hr is 23/6π and π.
We have to find the radians will the hour hand on a clock rotation for 23hr and 6hr.
One revolution is done by fully around the circle with the radius. After one full rotation, the radius subtends an angle of 2π radians at the circle's center. To illustrate the conversion of 1 radian to degrees, we will use the knowledge that 2π radians = 360 degrees.
2π radians = 360°
Divide the above equation by 2,
⇒ π radians = 180°
Divide the above equation by π,
⇒ 1 radian = 180°/π
⇒ 1 radian = 57.296°
Only 12 hours are represented by one full rotation of the hour hand. A whole rotation equals 360°, or two radians.
11 hours rotation equals to 330°, or 11π/6 radians.
23 hours=12+11
=360°+330° (or) 2π+11π/6
=690° (or) 23π/6
Now, 6 hours=12/2
=360°/2 (or) 2π/2
=180° (or) π.
Therefore, the radians will the hour hand on a clock rotation for 23hr and 6hr is 23/6π and π.
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How much more can paula shovel in 1 minute than melinda? 3 square feet per minute 6 square feet per minute 9 square feet per minute 15 square feet per minute
Answers
Paula shovels 3 square feet more than Melinda in 1 minute.
We are given two equations relating the distance covered by each while they shovel. Assuming the x to be representative of Melinda's speed and y to be representative of Paula's speed. Making at least one coefficient same for both the equation.
Equation 1 : 30x + 30y = 450
Equation 2 : 20x + 25y = 345
Dividing equation 1 and equation 2 by 5.
Equation 3 : 6x + 6y = 90
Equation 4 : 4x + 5y = 69
Multiplying equation 3 with 4 and equation 4 with 6.
Equation 5 : 24x + 24y = 360
Equation 6 : 24x + 30y = 414
Subtracting Equation 5 from Equation 6.
24x + 30y = 414
- 24x + 24y = 360
6y = 54
y = 9
Keep the value of y in equation 3
6x + 6×9 = 90
6x + 54 = 90
6x = 90 - 54
6x = 36
x = 6
So, Melinda's speed is 6 square feet per minute and Paula's speed is 9 square feet per minute.
Difference between speed = 9 - 6
Difference = 3 square feet per minute
Hence, Paula's speed is 3 square feet per minute more than Melinda.
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The complete question is -
Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway.
30x + 30y = 45020x + 25y = 345
How much more can Paula shovel in 1 minute than Melinda?
3 square feet per minute
6 square feet per minute
9 square feet per minute
15 square feet per minute
Answer:
A: 3 square feet per minute
Step-by-step explanation:
Can theses lengths form a right triangle (5,6,V30)
Answers
No these lengths does not form a right triangle
There is a property of triangles which says that some of two sides of the triangle should be more than the third side of the triangle
So first case 6,30,5
30+6 =36 which is more than 5
second case 5,30,6
5+30 =35 which is more than 6
third case 5,6,30
5+6 =11 which is not more than 30
as in third case the property is breached because sum of two sides of triangle is not more than third side so the figure cannot be a triangle .
And hence we cannot check whether it is a right angle triangle or not.
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✓ A G.P has 6 terms. If the 3rd 4th term and are 28 and -56 respectively. Find (a) the common ratio (b) the first term (c) the sum of the G.P.
Answers
[tex]r = \frac{u_{4}}{u_{3}} = \frac{ - 56}{28} = - 2[/tex]
(b)[tex]u_{n} = u_{1} \times r {}^{n - 1} \\ ie \colon \: u_{4} = u_{1} \times r {}^{4 - 1} \\ \: \: \: - 56 = u_{1} \times ( - 2) {}^{3} \\ u_{1} = \frac{ - 56}{ - 8} = 7[/tex]
(c)[tex]S_{n} = ( \frac{1 - r {}^{n} }{1 - r} ) \: (u_{1}) \\ S_{6}=( \frac{1 - ( - 2) {}^{6} }{1 - ( - 2)} ) \: (7) \\ S_{6}= - 147[/tex]
a. The common ratio is -2.
b. The first term is 7
c. The sum of the GP is -147
What is the common ratio?
(a) To find the common ratio (r), we can use the formula for the nth term of a geometric progression (G.P):
[tex]A_n = A_1 * r^(^n^-^1^)[/tex],
where Aₙ is the nth term, A₁ is the first term, r is the common ratio, and n is the term number.
Given that the 3rd term (A₃) is 28 and the 4th term (A₄) is -56, we can set up two equations using the formula above:
[tex]28 = A_1 * r^(^3^-^1^)[/tex], (Equation 1)
[tex]-56 = A_1 * r^(^4^-^1^)[/tex]. (Equation 2)
Dividing Equation 2 by Equation 1, we get:
[tex]-56/28 = (A_1 * r^(^4^-^1^)^) / (A_1 * r^(^3^-^1^))\\-2 = r.[/tex]
Therefore, the common ratio (r) is -2.
(b) To find the first term (A1), we can substitute the known values into one of the equations. Let's use Equation 1:
[tex]28 = A_1 * (-2)^(^3^-^1^)\\28 = A_1 * (-2)^2\\28 = A_1 * 4\\A_1 = 7[/tex]
Therefore, the first term (A₁) is 7.
(c) To find the sum of the geometric progression, we can use the formula for the sum of the first n terms of a geometric progression:
[tex]S_n = (A_1 * (1 - r^n)) / (1 - r)[/tex],
where Sₙ is the sum of the first n terms.
Given that there are 6 terms (n = 6), A₁ = 7, and r = -2, we can calculate the sum (S₆):
[tex]S_6 = (7 * (1 - (-2)^6)) / (1 - (-2)).[/tex]
Simplifying:
S₆= (7 * (1 - 64)) / (1 + 2),
S₆ = (7 * (-63)) / 3,
S₆ = -147.
Therefore, the sum of the geometric progression is -147.
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I really need some help
Answers
Answer:
a. zy = yz
Step-by-step explanation:
Commutative property of multiplication rule:
(a)(b) = (b)(a)
Solve the equation.
- 2(2x - 4) = 4x
(Simplify your answer.)
Answers
Answer:
x=1
Step-by-step explanation:
-2(2x-4)=4x
Distributive property.
-4x+8=4x
+4x +4x
8x=8
/8 /8
x=1
Hope this helps!
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write as a single equation, 2x + 3 / 3 + x - 4 / 4
Answers
we get that the expression ( 2 x + 3 ) / 3 + ( x - 4 ) / 4 can be written as an equation as 11 x / 12.
We are given an expression:
( 2 x + 3 ) / 3 + ( x - 4 )/ 4
We need to simplify it and write it as an equation.
Taking the LCM, we get that:
4( 2 x + 3) + 3 (x - 4) / 12
simplifying brackets, we get that,
8 x + 12 + 3 x - 12 / 12
Combining the like terms, we get that:
8 x + 3 x / 12
11 x / 12
Therefore, we get that the expression ( 2 x + 3 ) / 3 + ( x - 4 ) / 4 can be written as an equation as 11 x / 12.
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What is the average accerlation during the time interval 0 seconds to 10 seconds?
Answers
The average acceleration during the time interval 0 seconds to 10 seconds is [tex]\frac{V_{1}-V_{2} }{10}[/tex] unit per second per second.
As per the question statement, we are supposed to find out the average acceleration during the time interval 0 seconds to 10 seconds. But before solving this question we should be aware about what actually average acceleration is.
Average acceleration : [tex]\frac{change in velocity}{total time interval}[/tex]
Here in the question, we are not given information about velocity of the object hence we assume the initial and final velocities of the object to be [tex]V_{1}[/tex] and [tex]V_{2}[/tex] respectively, hence
Change in velocity = [tex]V_{1}-V_{2}[/tex]
Total time interval = [tex](10 - 0)sec=10sec[/tex]
Therefore by definition of average acceleration we get
[tex]A_{avg}[/tex][tex]= \frac{V_{1}-V_{2} }{10}[/tex] unit per sec per second
Average acceleration: The rate at which the velocity changes is referred to as average acceleration. To determine the average acceleration of something, we divide the change in velocity by the amount of time that has passed.To learn more about acceleration and kinetics, click on the link given below:
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Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.Given: If Elan stays up late, he will be tired the next day. Elan is tired.
Conclusion: Elan stayed up late.
Answers
Based on the explanation below, the conclusion that Elan is tired because Elan stayed up late is invalid.
How do we use reasoning to determine a conclusion?In the question, it is stated that if Elan stays up late, he will be tired the next day.
However, staying up late is not the only thing that could make Elan get tired.
This implies that there are so many other things than can make Elan get tired such as working for long hours.
It is possible that Elan was tired because Elans worked long hours.
By implication, the conclusion is invalid.
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If K is the midpoint of JL, JK = 8x +11 and KL = 14x - 1, find JL
Answers
Since K is the midpoint both equations are equal to eachother so the first equation is
8x+11=14x-1
-6x+11=-1
-6x=-12
x=2
Now since we have x we can solve so youre going to put x into one of the equations. It doesnt matter which once cause they are both equal. So we can do 8x+11
8(2)+11
16+11
27
So now we have 27 we can add both together since 27=27
So you have JL=54 un
Use un if you dont have a distance
Hope this helps!!
One number is 5 less than twice another
number. If the sum of the numbers is 7, find
both numbers
Answers
Answer:
4 and 3
Step-by-step explanation:
You can create an equation with this. If your first number is y and your second is x, then we know that y is 5 less than 2x. This leads to your equation - y = 2x - 5.
With your equation, you can then figure out your numbers; we know there's a limited number of possibilities - anything 7 or less added to a number can equal 7 so:
7+0=7
6+1=7
5+2=7
4+3=7
3+4=7
2+5=7
1+6=7
0+7=7
From there, plug in one number for x and see if y matches the expected number. For example:
2(7)-5=9, so we know the 7,0 combination cannot be correct. As we go through the list, we find that 4,3 works:
2(4)-5=3
which of the expressions are equivalent to the one blown? check all that apply (4•1)-6
Answers
The expressions that are equivalent to the given expression are 4 - 6 and -6 + 4
How to determine the expressions that are equivalent to the given expression?The expression is given as:
(4 * 1) - 6
Evaluate the product of 4 and 1
So, we have:
(4 * 1) - 6 = 4 - 6
By the subtractive property of and equation, we have:
(4 * 1) - 6 = -6 + 4
Hence, the expressions that are equivalent to the given expression are 4 - 6 and -6 + 4
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On Friday nights, you enjoy staying at home and doing complex math problems. In 45 minutes, you can solve 9 math problems. How many problems can you solve in 210 minutes?
Answers
Answer:
42
Step-by-step explanation:
45 divided by 5 is 9.
210 divided by 5 is 42.
Hope It Helps
Sorry If I'm Wrong
Factor 6x + 36y using the greatest common factor
Answers
Answer:
6
Step-by-step explanation:
Answer:
6(x+6y)
Step-by-step explanation:
The greatest common factor is 6.
6x+36y=
=6(x+6y)
The expression with the GCF factored out is 6(x+6y)
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how to solve this problem
Answers
Step-by-step explanation:
...........................
What is 6.33 time as 6
Answers
Answer: 37.98 (I assume you mean times)
Step-by-step explanation:
Calculator :)
Rubin has 6 rolls of pennies containing 50 coins each, 5 rolls of nickels
containing 40 coins each, 4 rolls of dimes containing 50 coins each, and 3
rolls of quarters containing 40 coins each. How much money does he have?
A. $17.50
B. $8.20
• C. $63.00
D. $68.40
Answers
Write inequalities to describe the region between the yz-plane and the vertical plane x = 9.
Answers
the region of space between the parallel planes x = 0
and x = 5
0 < x < 5
What is vertical plane?A direction or plane traveling past a specific place is considered to be vertical in astronomy, geography, and other relevant fields and settings if it contains the local gravity direction at that location. On the other hand, if a direction or plane is perpendicular to the vertical direction, it is said to be horizontal. The y-axis in the Cartesian coordinate system is an example of something that can generally be drawn from up to down (or down to up). The word vertical is derived from the late Latin verticalis, which is from the same root as vertex and means "highest point" or more literally the "turning point" such as in a whirlpool.
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Nadir and Jennifer Salazar are moving into a new apartment with a
monthly rent of $1,058. They must pay a security deposit of $523 and a
pet deposit of $291. According to their lease, they must also pay the first
and last month's rent up front. What will be the total move-in cost for
the Salazar's new apartment?
Answers
Answer:
the answer is becareful
El colegio compró 234 libros a €14 cada uno cuánto costaron en total
Answers
The total cost of the books will be €3276.
How to calculate the cost?It should be noted the school bought 234 books at €14 each.
Therefore, the total cost of the books will be:
= Price × Total books
= €14 × 234
= €3276
Therefore, the total cost of the books will be €3276.
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What is the inverse of the function f(x)=1/9x+2
Answers
The correct answer is 9x-18.
The ability to reverse other functions makes a function an inverse function. It is somewhat similar to undoing another function, which returns you to your starting point. Driving from home to the shop is a function, and driving from the shop back to home is a function.
The inverse of a trigonometric function, the inverse of a rational function, the inverse of a hyperbolic function, and the inverse of a log function are just a few examples of the various types of inverse functions.
Substituting f(x) with y
f(x)=1/9x+2
y=1/9x+2
x=1/9y+2
x-2=1/9y
y=9x-18
Thus inverse is f^-1(x)=9x-18
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11/12 - 3/4 = ?
1/2 + 4/9 =?
Please answer in simplest form
Answers
11/12 - 3/4 = 1/6
1/2 + 4/9 = 17/18
How calculate the expression in it's simplest form ?11/12 - 3/4
= 11-9/12
= 2/12
= 1/6
1/2 + 4/9
= 9+8/18
= 17/18
Hence the solution to the expression in it's simplest form is 1/6 and 17/18
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Answer:
1/6and 17/18
Step-by-step explanation:
11/12-3/4
find the l.c.m
11/12-3/4=11-9/12=2/12=1/6
1/2+4/9=9+8/18=17/18
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Find the general solution of the given second-order differential equation. 3y'' 2y' y = 0
Answers
The general solution of the given differential equation are: [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]
What are differential equations?A differential equation is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the two.Now,
Given: 3y'' + 2y' + y = 0
To find: General solution of the given differential equation.
Finding:
=> [tex]3\frac{d^{2}y}{dx^{2}} + 2 \frac{dy}{dx} + y = 0[/tex]
The characteristic equation of this equation is:
=> 3m² + 2m + 1 = 0
=> m = [tex]\frac{(-2)± \sqrt{4 - 4(3)(1)}}{2(3)}[/tex]
=> m = [tex]\frac{(-2)±\sqrt{4-12}}{6}[/tex]
=> m = [tex]\frac{(-2)±2\sqrt{2}i}{6}[/tex]
=> m = [tex]\frac{(-1)±\sqrt{2}i}{3}[/tex] = [tex]\frac{-1}{3}[/tex] ± [tex]\frac{\sqrt{2}}{3}[/tex]
Thus, For a = -1/3 and b = (√2)/3,
General solution of the differential equation => [tex]e^{\frac{-x}{3}}[/tex] [A cos(x√ 2/3) + B sin(x√ 2/3) i ]
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question 29(multiple choice worth 1 points) (01.07 mc) multiply (2.4 ⋅ 1014) ⋅ (4 ⋅ 107). express the answer in scientific notation. 9.6 ⋅ 1021 9.6 ⋅ 1022 96 ⋅ 1021 96 ⋅ 1022
Answers
The multiplication of [tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex]in scientific notation is [tex]9.6 \times {10}^{21} [/tex]
How to find the answer in scientific notation?Multiply the decimal numbers to multiply the integers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.
given that [tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex]
Now, find the answer in scientific notation
[tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex]
combine the all the like terms
[tex](2.4 \times 4)( {10}^{14} \times {10}^{7} )[/tex]
According to the exponent same base rule, an exponent will be added if the bases of two exponents are the same.
[tex](9.6) \times ( {10}^{14 + 7)} ) \\ 9.6 \times {10}^{21} [/tex]
Hence,the multiplication of[tex](2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )[/tex] in scientific notation is [tex]9.6 \times {10}^{21} [/tex]
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find the value of x if pq is equal to rs, pq= 9x-7, and rs=29
Answers
Based on the information given, the value of x is 4
What is a line segment?A line segment can be defined as the part of a straight line bounded by two distinct end points, and also contains every point on the line that is between its endpoints.
From the information given, we have PQ and RS are on the the same line with points Q and R as the line segments
We have that;
PQ = 9x - 7RS = 299x - 7 = 29
collect like terms
9x = 29 + 7
9x = 36
Make 'x' the subject
x = 36/ 9
x = 4
Thus, the value of x is 4
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Use with problems 11 and 12. Round to the nearest hundredth place.
C-3,1)
D(0, -6)
Answers
Answer:
Step-by-step explanation:
Not sure..
What type of question is this?
Lilly needs to ship 16 yo-yos, 24 teddy bears, and 8 tops. She can pack only one type of toy in each box, and he must pack the same number of toys in each box. What is the greatest number of toys Lilly can pack in each box?
Group of answer choices
-GCF
-LCM
Answers
The type of question is GCF .
What is the greatest number of toys she can pack?The factor of a number is a number that can divide another number perfectly without leaving any remainder. Highest common factor is the highest factor that is common to two or more numbers
Factors of 8, 16 and 24 = 1, 2, 4, 8,
Highest common factor = 8
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What number is halfway between 73.7 and 73.71?
Answers
Answer:
73.39
Step-by-step explanation:
Answer:
73.705
Step-by-step explanation:
73.700
73.705
73.710
Divide 0.01 by 2 and u would get 0.005
Convert the fraction or mixed number to a percent.
6 3/5
Answers
Answer:
660%
Step-by-step explanation:
6 x 100= 600%
3/5 = 0.6 × 100 = 60%
600% + 60% = 660%