Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
\(\begin{gathered} Arc\text{ length =}\frac{\theta}{360^0}\text{ x 2}\pi\text{ r} \\ where\text{ arc length = 4 units} \\ and\text{ the radius, r = 3 units} \end{gathered}\)\(\begin{gathered} puttin\text{g the values, we have that:} \\ \text{4 =}\frac{\theta}{360^0}\text{ x 2 x }\pi\text{ x 3} \\ Then,\text{ we have that:} \end{gathered}\)\(\begin{gathered} cross\text{ - multiply, we have that:} \\ 4\text{ x 360}^0\text{ = }\theta\text{ x 6}\pi \\ 1440^0\text{ = }\theta\text{ x 6}\pi \end{gathered}\)\(\begin{gathered} Divide\text{ both sides by 6}\pi\text{, we have that:} \\ \theta\text{ =}\frac{1440^0}{6\pi}=\frac{240}{\pi} \end{gathered}\)\(\begin{gathered} Note\text{ that:} \\ 2\pi\text{ }rad\text{ = 360}^0 \end{gathered}\)\(\begin{gathered} 2\pi rad\text{ = 360}^0 \\ ?\text{ = }\frac{240}{\pi}=\text{ 76}\frac{4}{11}\text{ }^0\text{ = }\frac{840^0}{11^} \end{gathered}\)\(?\text{ =}\frac{2\pi\text{ rad x }\frac{840}{11}}{360}\)\(?\text{ = }\frac{\pi\text{ rad}}{180}\text{ x }\frac{840}{11}\)\(?\text{ =}\frac{14}{33}\text{ }\pi\text{ rad }\approx\text{ 0.42 }\pi\text{ rad \lparen correct to 2 decimal places\rparen}\)CONCLUSION:
The measure of the central angle ( in radians) =
\(0.42\pi\text{ \lparen correct to 2 decimal places\rparen}\)
Related Questions
The LCM of 6 and 9 is
Numerical Answers Expected!
Answer for Blank 1:
Answers
Answer:
18
Step-by-step explain:
6, 12, 18, 24, 30
9, 18, 24
Kelly and gemma each pick a pumpkin from the pumpkin patch. kellys pumpkin weighs 5 pounds more than twice the weight of gemma pumpkin. kellys pumpkin also weighs 25 pounds less than 4 times the weight of gemmas pumpkin.
Answers
The equation that can be used to determine that weight of the pumpkin would be = 5 +2x + x or 25 -4x + x.
What is weight?Weight is defined as the unit that is used to measure the degree of heaviness of a body.
The weight of Gemma's pumpkin = x
The weight of Kellys pumpkin = 5 + 2x
The weight of Kellys pumpkin = 25 - 4x
The equation that can be used to find the weight of the pumpkin include the following:
5 +2x + x or
5 +2x + x or25 -4x + x.
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The complete question:
Kelly and Gemma each pick a pumpkin from the pumpkin patch. Kelly's pumpkin weighs 5 pounds more than twice the weight of Gemma's pumpkin. Kelly's pumpkin also weighs 25 pounds less than 4 times the weight of Gemma's pumpkin. Write an equation to find the weights of the pumpkins.
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
Answers
Given
ABCΔ is a triangle.
D is a point on [BC]
|BD|=4
|AD|=|CD|
m(CBAˆ)=α=30∘
m(ACBˆ)=β=20∘
To Find
What is |AC|=x?
Solution
Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b
and applying law of cosines to all three triangles yields;
x=2acos20∘16=a2+b2+2abcos70∘(a+4)2=b2+x2+2bxcos50∘respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4
The complete question is -
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
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Please do the second question.
Answers
Using a formula for the percentage, we can see that 100 is9.09% smaller than 110
How to find the percent the first number is less than the second?
To find this percentage, we need to use the equation:
percentage = 100%*(second number - first number)/second number
Where:
second number = 110
first number = 100
Then we have:
percentage = 100%*(110 - 100)/110 = 9.09%
So the first number is 9.09% smaller than the second one.
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The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
Answers
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
Hello help me out thank you !
Answers
Answer:
1130.4
Step-by-step explanation:
The volume of a cylinder is πr^2h, where r is the radius and h is the height.
We are given the height, 10m.
The diameter is 2m more than the height, so 2+10=12m.
The radius is half the diameter, so 12m/2=6m.
Use r=6 and h=10 in the formula to get the volume
π6^2*10≈1130.4
A room is 12 m long,10m broad and 6 m high. It has a door of size 1m×2m and a windows of size 2m × 1.5m. Calculate the cost of plastering the walls at the rate of Rs 15/m².
Answers
The cost of plastering the rectangle walls at rate of Rs.15/\(m^2\) is Rs.5565.
What is rectangle?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.
Given,
Length of room =12m
Breadth of room =10m
Height of room =6m
So, Area of four walls =2(l+b)×h
=>area of four wall=2(12+10)×6=264\(m^2\)
Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)
=> area of 2 doors and 3 windows = 13\(m^2\)
Area of ceiling =l×b=12×10=120 \(m^2\)
Thus, total area for plastering =(264−13+120)= 371\(m^2\)
Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.
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The width of a rectangle is 11 inches less than its length. Find the dimensions of the rectangle if the area is 80 squares inches. Then find the perimeter of the garden.
Answers
Answer:
8r1000000
Step-by-step explanation:
Answer:
Dimensions = 16 inches & 5 inches
Perimeter = 42 inches
Step-by-step explanation:
X x (X + 11) = 80
X = 16
Dimensions = 16 & 5
Perimeter = 16 x 2 + 5 x 2 =
32 + 10 =
42 inches
Hope that helps!
Hope that helps!
Can you help me figure out the typical price and how the prices vary using this box plot?
Answers
Given the box plot shown in the exercise, you can observe that:
\(Median=350\)The Median is represented by the line located inside the box.
You can identify that the Lower Quartile is:
\(Q_1=300\)And the Upper Quartile is:
\(Q_3=450\)Because the end of the left whisker is located on the value 300 and the end of the right whisker is located on the value 450.
Notice that the highest point on the right is located at 500 and the lower point on the left is located at 225 (approximately). The Difference between these values is:
\(500-225=275\)The Median tells you the typical price of a bicycle (in dollars).
Hence, the answer is: Third option.
Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
A = (0.97)t
y=3.7(0.2)t
y= 9/11(4)t
P=7/9(5/4)t
V=0.8(9)t
P=0.9(8.3)t
g(x) = 2.1(x)
Answers
Solving the provided question, we can say that Not exponential growth or decay (no exponent) G(x)=1.3(x)
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially.
The base of the exponentiation is the strongest indicator of whether an equation exhibits an exponential growth or decline.
It will be an exponential growth if the base is greater than 1.
It will be an exponential decay if the base is less than 1.
There won't be any exponential growth or decay if the function's exponent is zero.
Therefore: Decay exponential (base less than 1:
W = 9/8(3/5)t
f(t) = (3/4)t
L = 4.2(0.6)t
Exponential Growth (base larger than 1:
L = 0.25(12)t
W = 0.5(2.1)t
f(t) = 2/3(6)t
Not exponential growth or decay (no exponent):
G(x)=1.3(x)
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There are 10 numbers listed below. 13.5 12.5 10.8 9 11 10 12.5 13 10.5 12 What is the mode of these numbers?
Answers
Answer:
12.5
Step-by-step explanation:
13.5 12.5 10.8 9 11 10 12.5 13 10.5 12
The mode is the number that appears the most number of times.
We place the numbers in ascending order just for convenience.
9 10 10.5 10.8 11 12 12.5 12.5 13 13.5
Every number appears once except 12.5 that appears twice.
Answer: 12.5
help 50 brainly for first answer
Answers
Answer: B
Step-by-step explanation:
Let
f(x)={x2+2xx+1if x≤−1if x>−1.
Evaluate the following:
1. f(−7) =
2. f(−1) =
3. f(0) =
Answers
The required solutions of the functions are given as follows,
1. f(−7) = 35
2. f(−1) = -1
3. f(0) = 1
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
1 .
for x = -7
f(x) = x² + 2x
f(-7) = (-7)² + 2(-7) = 35
2.
for x = -1
f(x) = x² + 2x
f(−1) = (-1)² + 2(-1) = -1
3.
For x = 0
f(x) = x + 1
f(0) = 0 + 1 = 1
Thus, the required solutions are given as follows,
1. f(−7) = 35
2. f(−1) = -1
3. f(0) = 1
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use the sketch below to decide if congruence can be proved, and if so, which method would prove the congruence.
Answers
Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.
The convergence method which proves this congruence is SSS(side-side-side) congruence.
We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF
Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,
so, AB ≅ FG
Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,
so, AC ≅ FH
To find the lengths of BC and GH , we can use distance formula.
Length of BC :
BC = √[(x₂ - x₁)² + (y₂ - y₁)²]
(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).
BC = √[(-4 + 7)² + (5 - 0)²]
= √[32 + 52]
= √[9 + 25]
= √34
Length of GH :
GH = √[(x₂ - x₁)² + (y₂ - y₁)²]
(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).
GH = √[(6 - 1)² + (5 - 2)²]
= √[52 + 32]
= √[25 + 9]
= √34
Conclusion :because BC = √34 and GH = √34,
=>BC ≅ GH
All the three sides of one triangle is congruent to the corresponding sides of other triangle.
By SSS congruence postulate,
ΔABC ≅ ΔFGH
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Find the midpoint of the segment with the given endpoints.
(-7,10) and (6.-10)
Answers
Answer:
c
Step-by-step explanation:
cc
You leave home at 10 AM on a trip and arrive at 12 noon. The trip is a total of 100 miles. How fast are you going at 11AM
Answers
Answer:
50mph
Step-by-step explanation:
What should be subtracted from minus 3 / 4 so has to get 5 / 6 ?
Answers
Answer:
Step-by-step explanation:
Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and
6,which is 12.
3*3/4*3=9/12
5*2/6*2=10/12
Step 2:Subtract 9/12 from 10/12,which is 1/12.
¿De qué número 64 es el 80%?
Answers
18. Find the value of 3x² x 2(x-3y) divide by 6 when x is 6 and y is 1
Answers
Answer:
11664
Step by Step:
Evaluate for x=6,y=1
3(6^2)(6^2)(6−(3)(1))
3(6^2)(6^2)(6−(3)(1))
=11664
Factor f(x) = x2 + 3x − 4.
Answers
Answer:
(x - 1)(x + 4)Step-by-step explanation:
Find zero's of function:
x² + 3x - 4 = 0x = (-3 ± √(3² + 4*4))/2x = (-3 ± √25)/2x₁ = (-3 + 5)/2 = 1x₂ = (-3 - 5)/2 = -4The factors are:
x² + 3x - 4 = (x - 1)(x + 4)a sales manager analyzed the sales, in dollars, y, of snow shovels compared to the outside temperature, in degrees fahrenheit, x. the manager calculated the correlation coefficient of r
Answers
The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.
The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.
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2x+y+4z=16
5x-2y+2z=-1
X+2y-3z=-9
Answers
Answer:
24
Step-by-step explanation:
I need help on this question
Answers
Answer:
Go download CameraMath on playstore
What’s the value of x? :/
Answers
Answer:
\( x = 27 \)
Step-by-step explanation:
According to congruent chords and arcs theorem, if \( \overline{XY} \cong \overline{ZY} \) then \( \arc{XY} \cong \arc{ZY} \).
This means that \( \arc{XY} = \arc{ZY} = (6x - 20) degrees \)
Thus:
\( \arc{XY} + \arc{ZY} + \arc{ZX} = 360 \) (full circle = 360°)
\( \arc{XY} = (6x - 20) \)
\( \arc{ZY} = (6x - 20) \)
\( \arc{ZX} = 76 \)
Plug in the values into the equation
\( (6x - 20) + (6x - 20) + 76 = 360 \)
\( 6x - 20 + 6x - 20 + 76 = 360 \)
Add like terms
\( 12x + 36 = 360 \)
Subtract 36 on both sides
\( 12x = 360 - 36 \)
\( 12x = 324 \)
Divide both sides by 12
\( x = 27 \)
What is the meaning of "an axiom of predicate calculus"?
Answers
An axiom of predicate calculus is the foundation of predicate calculus that is based on a fundamental and obvious principle or statement
What is the axiom of calculus?The foundation of predicate calculus is based on a fundamental and obvious principle or statement known as an axiom.
The aforementioned axioms act as a foundation for deducing rational conclusions and evidence within the domain of predicate calculus.
Universally accurate and accepted without the need for additional reasoning is how they are commonly perceived.
The fundamental regulations and connections that oversee quantifiers, predicates, and logical operations, including conjunction, disjunction, and implication, are determined by the axioms of predicate calculus. They offer a sturdy groundwork for rationalizing statements that involve variables, quantification, and logical connectors in formal systems of logic.
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2/3 es equivalente a 4/5?
Answers
we can conclude that 2/3 is not equal to 4/5.
To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.
To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.
For 2/3 and 4/5, we have:
2 * 5 = 10
3 * 4 = 12
Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.
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The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
Answers
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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Find the equation of the linear function represented by
the table below in slope-intercept form.
Answers
An intercept is a point on the y-axis through which the slope of a line passes in mathematics.
What is meant by slope-intercept form?An equation for a line stated using a single point on the line and the line's slope is a straightforward definition of point-slope form. The slope is defined as the rise over run, or the proportion of the change in the y values over the change in the x values, and the point form is denoted by the letters (x, y).
These statistics are here. When a linear equation is expressed in this way, it has the benefit that the values for m and b are the slope and y-intercept, respectively. Consequently, it is easy to graph the line that the equation depicts. M stands for slope, and B for intercept.
An intercept is a point on the y-axis through which the slope of a line passes in mathematics. A place where a straight line or a curve intersects the y-axis is designated by its y-coordinate. The equation for a line, y = mx+c, which has m for the slope and c for the y-intercept, represents this.
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A down payment of $195 is made on a television that costs $1300. What percent of the
cost is the down payment?
Answers
Answer:
15%
Step-by-step explanation:
Add 195 to 1300, which gives you, 1495.
Use the formula for percent change: Difference = % * original price.
So what is the difference between 1495 and 1300? It’s 195.
Now we have 195 as the difference.
Do we know the original price of the TV? Yes we do. What is it? Its 1300 because the question states the TV costs $1300.
Now we have the equation 195 = % * 1300
We don’t know the percentage, right? So now we have to solve for %. To do that, you have to do 195 divided by 1300, which gives you 0.15. Lastly, you have to turn 0.15 into a percentage, to do that, multiply 0.15 by 100, and it should give you 15%.
Therefore, 15% is the down payment. Hope this helps!
He jogging track has a length of 792 yards how long is this in miles
Answers
By performing the division, the jogging track is 0.45 miles long.
What is division?Division is a mathematical operation that involves the splitting of a quantity into equal parts or groups.
According to given information:The problem asks us to convert a length of 792 yards to miles. To do this, we need to use a conversion factor to relate yards to miles. We know that there are 1760 yards in a mile, so we can use this relationship to convert the length in yards to miles.
To convert yards to miles, we divide the length in yards by the number of yards in a mile. This is because we want to cancel out the units of yards and be left with the corresponding number of miles.
So, 792 yards / 1760 yards/mile gives us the length of the jogging track in miles. We can simplify this expression by performing the division to get the result of 0.45 miles. Therefore, the jogging track is 0.45 miles long.
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