Distance between the points [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex] is [tex]a[/tex]. (Option D)
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by [tex]d= \sqrt{(x^{2}-x) ^{2}+(y^{2}-y) ^{2} }[/tex]. This formula is used to find the distance between any two points on a coordinate plane or x-y plane. This formula is called distance formula.
Let A= [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and B= [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex].
Putting values in above formula:
AB=[tex]\sqrt{a^{2}[cos(0+\frac{\pi }{3})-cos(0+\frac{2\pi }{3})]^{2}+a^{2}[sin(0+\frac{\pi }{3})-sin(0+\frac{2\pi }{3})]^{2} }[/tex]
AB= [tex]a\sqrt{cos^{2}(0+\frac{\pi }{3})+sin^{2}(0+\frac{\pi }{3})+cos^{2}(0+\frac{2\pi }{3})+sin^{2}(0+\frac{2\pi }{3})}[/tex]
AB= [tex]a\sqrt{cos(0+\frac{\pi }{3})cos(0+\frac{2\pi }{3})sin(0+\frac{\pi }{3})sin(0+\frac{2\pi }{3})}[/tex]
AB=[tex]a\sqrt{1+1-2cos(0+\frac{2\pi }{3}-0-\frac{\pi }{3}) }[/tex]
AB= [tex]a\sqrt{2-2cos\frac{\pi }{3} }[/tex]
AB= [tex]a\sqrt{2-2\frac{1}{2} }[/tex]
AB= [tex]a\sqrt{2-1} =a[/tex]
Hence, the distance between the two given points is [tex]a[/tex].
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I dont understand this at all so here is 100 points
Answer:
Step-by-step explanation: First row, first column 500 * 7 = 3500
1st row , second column 7 * 60 = 420
1st row, third column 7 * 3 = 21
Do similary for the others
2nd row, 40,000 4800 240
3rd row , 100000 12000 6000
Answer:
[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]
Step-by-step explanation:
For each box, multiply the number of the row by the number of the column:
[tex]\large\text{ \quad \quad \quad \quad \quad 500 \quad \quad \quad\;\;60 \quad \quad \quad \;\;\;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{7 \times 500} &\boxed{7 \times 60} & \boxed{ 7 \times 3}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{80 \times 500} & \boxed{80 \times 60} & \boxed{80 \times 3}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{200 \times 500} & \boxed{200 \times 60} & \boxed{200 \times 3}\\\cline{2-4} \end{array}[/tex]
When multiplying numbers ending in zeros (multiples of 10, 100, etc.), first multiply the numbers as if they didn't have zeros, then add all the zeros to the final answer.
For example:
200 × 500 has a total of 4 zeros.
Multiply 2 × 5 = 10
Then add 4 zeros: 10 0000
Therefore, 200 × 500 = 100000
Final Solution
[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]
Sally receives the following scores on her math tests: 78, 92, 83, 99. What score does she need on the next test in order to have an average of 90 on her math tests?
Answer:
they would need a 98 on the next math test.
Look at the Example. The area of Rhode Island is about 43.07 billion square feet. About how many times as many times as great is the area of Colorado than the area of Rhode Island? Show your work.
According to the given statement
The area of Colorado is 67.43 times greater than the area of Rhode Island
Define Area?Area is typically thought of as a specific instance of volume for two-dimensional regions. By applying axioms, one can define area as the relationship between a set of real numbers and a collection of particular plane figures.
Area is a mathematical concept that describes the size of a region on a planar or curved surface. The area of an open surface or the border of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
According to the given values;
The area of Rhode Island = 43.07 billion square feet.
The area of Colorado = 2.9045 trillion square feet.
43.07 billion =43,070,000,000
2.945 trillion =2,9045,000,000,00
Now we have to find how many times as great is the area of Colorado than the area of Rhode Island.
For this ,we divide area of Colorado by area of Rhode Island.
=2,9045,000,000,00/43,070,000,000
=67.43
So, the area of Colorado is 67.43 times greater than the area of Rhode Island.
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-10+5x=7x-4 what is the answer
Answer:
x = -3
Step-by-step explanation:
-10 + 5x = 7x - 4
-7x -7x
-10 - 2x = -4
+10 +10
- 2x = 6
÷-2 ÷-2
x = -3
Use the substitution method (show your work and good luck!)
x+y=2
x-y=-10
Find the geometric mean between pair of numbers.
a. 5 and 45
For numbers 5 and 45 the value of the geometric mean of these numbers is
Gm (5, 45) = 15
What is the geometric mean?The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:
Gm (a,b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 5b = 45We substitute and solve for the square root
Gm (5, 45) = √5×45
Gm (5, 45) = √225 ; In this case the square root is direct-
Gm (5, 45) = 15
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1. 2ײ + 5× - 11 + 3ײ - 11 × + 2
please solve this thankyou!!!
I believe it's 3ײ - 6x - 7.56
Sorry if this isn't helpful!
The other option would be -6x + 3ײ-7.56 (but this is the problem in a simplified form and not when it is evaluated).
-9 - (x + 1) = -2-(3x - 5)
Answer: The answer is x = 6.5
A dragonflies wings beat 41 times per second. How many times do they beat in a minute
Find the surface area of water tower that is 40 feet tall and has a diameter of 30 feet. DO NOT ROUND YOUR ANSWER!
================================================
Work Shown:
[tex]SA = 2\pi r^2 + 2\pi r h\\\\SA \approx 2*3.14*15^2 + 2*3.14*15*40\\\\SA \approx 5181\\\\[/tex]
The cylinder has a surface area of about 5181 square feet.
Side notes:
The diameter of d = 30 leads to a radius of r = d/2 = 30/2 = 15.The picture is misleading. The conical top is ignored and we only are finding the surface area of the cylinder.Answer:
Step-by-step explanation:
3768 feet. Is this right?
There are 24 baseball teams in a league each team plays two matches against each of the other teams
work out the total number of matches played
PLSSSSSSSSSSSSSSSSSSSS URGENT
The total number of matches played will be 46. matches.
How to calculate the value?From the information, there are 24 baseball teams in a league each team plays two matches against each of the other teams.
The total number of matches that will be played will be:
= (24 - 1) × 2
= 23 × 2
= 46 matches.
Therefore, the total number of matches played will be 46. matches.
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FH bisects ZEFG. Find the indicated angle measures.
m/EFG = 119 °. Find m/EFH and m/GFH.
m/EFH =
m/GFH =
The measures of the indicated angles are
m ∠EFH = 59.5°
m ∠GFH = 59.5°
Calculating anglesFrom the question, we are to determine measures of the indicated angles
The angles are ∠EFH and ∠GFH
From the given information,
FH bisects ∠EFG
Since FH bisects ∠EFG,
Then,
m ∠EFH = m ∠GFH
and
m ∠EFH + m ∠GFH = m ∠EFG
Then,
We can write that
m ∠EFH + m ∠EFH = m ∠EFG
2 × m ∠EFH = m ∠EFG
2 × m ∠EFH = 119°
m ∠EFH = 119°/2
m ∠EFH = 59.5°
Thus,
m ∠GFH = 59.5°
Hence, the measures of the indicated angles are
m ∠EFH = 59.5°
m ∠GFH = 59.5°
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PLEASEEE HELP!!!!! I’m desperate!
If f(x) and its inverse function, f superscript negative 1 baseline (x), are both plotted on the same coordinate plane, where is their point of intersection? (0, 6) (1, 4) (2, 2) (3, 0)
The point of intersection for the function is (2, 2)
Considering to the line passing through the points (0,6) and (3,0) to be f(x).Therefore the slope intercept of the function is
m = 0-6/3-0 = -2
So, the functions F(x) in the slope-intercept form f(x)= -2x+6 ......1
interchanging the variable x to y and y to x
=> x =-2y + 6
=> 2y = -x + 6
=> y= -0.5x + 3
let f⁻¹(x)= y
f⁻¹(x) =-0.5x+3 ......2
Solving the equation 1 and 2, we get
=> -0.5x + 3 = -2x + 6
=> 2x - 0.5x = 6 - 3
=> 1.5x = 3
=> x = 2
Substituting the values of x in the function we get,
f( x) = -2(2) + 6 = 2
Thus, the outcome is (2,2)
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It is important to check your credit card bill each month. In the next section, you will carefully examine a credit card statement and learn how to look for errors. Most people would notice a major, expensive purchase that they did not make. A smaller, incorrect charge of $6, for example, might go unnoticed unless the entire statement was checked with a calculator. If one million credit card holders were each overcharged $6 each month for five years, what would be the total amount that debtors were overcharged, not including the extra
finance charges? million
The total amount that debtors are overcharged is 360 million dollars.
The unitary method is a technique to find the necessary value by multiplying the single unit value by finding the value of single unit value. We will use the same technique to solve this problem
According to question, $6 is charged per month for 5 years period from 1 million credit card holders
so, the total amount will be
1000000 × $6 × 12 × 5 = $360000000
Final answer: amount will be 360 million dollars
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What is the acceleration in this graph
2 m/s^2 is the acceleration in the given graph .
WHAT IS ACCELERATION?Acceleration is the general term for any process where the velocity changes. There are only two ways to gain speed: by changing your speed or direction, or by doing both. This is thus because speed and direction both affect velocity.
CALCULATIONSince we formula for acceleration is =
(v - u) / t
where u represents initial velocity , v represents final velocity
so acceleration from graph will be = (7 - 0)/3.5
= 7/3.5
= 2 m/s^2
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Use the given information to write an equation of a circle.
center at (0,0) , radius 6
The equation of the circle with radius 6 and center at (0 , 0) is x^2 + y^2 = 36.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = 6
(x - 0)^2 + (y - 0)^2 = 6^2
x^2 + y^2 = 36
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What two numbers add to (-6) and multiply to (-9)?
Answer: not possible
Step-by-step explanation:
I think you're doing quadratics and if that's the case probably go and rework the problem because that doesn't work.
Write an explicit formula for each arithmetic sequence. 62,59,56,53, . . .
The explicit formula of arthmetic sequence is [tex]a_{n}[/tex] = a + (n-1)d
Here is an explicit formula of the sequences 62, 59, 56, and 53...
[tex]a_{n}[/tex] = 62 + (n-1)(-3)
In the formula, n is any term number and [tex]a_{n}[/tex] is the nth term.
This formula allows us to simply plug on the number of the term we are interested in, and we will get the value of that term.
In order to find the fifth term, for example, we need to plug n = 6
[tex]a_{6}[/tex] = 62 + (6-1)(-3) = 62 + 5× -3
= 62- 15
= 47
In this way, we can find any term by using the explicit formula of an arithmetic sequence.
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HELP ASAP What should you substitute for y in the second equation (bottom equation) in order to solve the system by the substitution method?
4x+2y=10
3x+5y = 11
y=____
Answer:
y = 1
if you need answer of x
x = 2
Step-by-step explanation:
Let's solve your system by substitution.
4x+2y=10;3x+5y=11
Step: Solve4x+2y=10for x:
4x+2y=10
4x+2y+−2y=10+−2y(Add -2y to both sides)
4x=−2y+10
4x/4 = −2y+10/4
(Divide both sides by 4)
x= −1/2y+5/2
Step: Substitute −1/2y+5\2 for x in3x+5y=11:
3x+5y=11
3(−1/2y+5/2)+5y=11
7/2y+15/2=11(Simplify both sides of the equation)
7/2y+15/2+−15/2=11+/−152
(Add (-15)/2 to both sides)
7/2y=7/2
7/2y/7/2 = 7/2/7/2
(Divide both sides by 7/2)
y=1
Step: Substitute1for y in x= −1/2y+5/2:
x=−1/2y+5/2
x=−1/2(1)+5/2
x=2(Simplify both sides of the equation)
Kudi and Ladi share 20 oranges in the ratio 2 is to 3 how many oranges has Ladi
Answer:
12 oranges
Step-by-step explanation:
The ratio is K/L where K = Kudi's oranges and L = Ludi's oranges
K/L = 2/3
To find the number of oranges that Kudi has, divide the numerator by the sum of numerator and denominator.Then multiply by total number of oranges
For Ladi, divide the denominator by the sum of numerator and denominator. Then multiply by total number of oranges
[tex]K = 20\cdot \dfrac{2}{2+3} = 20 \cdot \dfrac{2}{5} = 8 \; \mathrm {oranges}\\\\L = 20\cdot \dfrac{3}{2+3} = 20 \cdot \dfrac{3}{5} = 12 \; \mathrm {oranges}[/tex]
So answer is Ladi has 12 oranges
Please resolve it and list the steps the simplest way possible, thanks
Using the graph of g we get (a) value of function g at x=0 is 5
(b) [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist
(c) value of function g at x=1 is 4
(d) [tex]\lim_{x \to \11} g(x)[/tex] or limit of g(x) at x=1 is 4
What is limit of a function how can limit be interpreted using graph of that function?
Limit : Limit is the value that a function output approaches as the input approaches to a certain value.
For any function g(x) ,[tex]\lim_{x \to \22} g(x)[/tex] means that the value g(x) approaches as the x approaches to 2 .
From any graph we can easily see that to what value g(x)=y on the curve is approaching when the x is approaching to some value on x axis and if the graph is breaking on the value where x is approaching then the limit does not exist for that value of x.
For given graph
We can see value of value of function g at x=0 is 5 and value of function g at x=1 is 4
As the graph is breaking on x=0 into two functions then [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist
As the graph is not breaking at x=1 or we can say that graph of g(x)is approaching to 4 as x approaches to 1 then [tex]\lim_{x \to \11} g(x)[/tex] or limit of g(x) at x=1 is equal to g(1) that is 4
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Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠4 and ∠5
The relationship between the ∠4 and ∠5 is that both are consecutive interior angles
Given,
The angles =∠4 and ∠5
Here, ∠4 and ∠5 are interior angles.
Both are lies on the opposite sides of the transversal.
So, ∠4 and ∠5 are consecutive interior angles
Hence, The relationship between the ∠4 and ∠5 is that both are consecutive interior angles
The complete question is :
Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠4 and ∠5
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Let g be a reflection in the x-axis and a vertical stretch by a factor of 3, followed by a translation 4 units down and 1 unit right of the graph of f(x)=|x|
What do we mean by decimal writing or writing in base 10?
Answer:
decimal is the number system of 10base .
The operator *= is called a(n) _____ operator.
a) increment
b) multiple assignment
c) double compound
The operator *= is called multiple assignment operator.
How to determine the name of the operator?The operator is given as
*=
Take for instance, we have the following statement in Python
a *= b
The meaning of the above statement is
a = a * b
Assume the following values for the variables
a = 6 and b = 3
The value of the operation a *= b would be
a *= b --- given expression
a = a * b --- expanded expression
a = 6 * 3 ---- when the values are substituted
a = 18 --- the result
This implies that the operator represents an assignment and a multiply operator
Hence, the operator *= is called multiple assignment operator.
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Draw and label two triangles that could be proved congruent by ASA.
Two diagrams have been drawn that could be proved congruent by the ASA condition.
What exactly seems to be "triangle congruency?"Two triangles are said to be congruent when their three corresponding sides and angles are the same size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will align if they are moved.Congruence exists when two triangles meet the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Two diagrams have been drawn that could be proved congruent by the ASA condition.(Refer to the diagram below)Therefore, two diagrams have been drawn that could be proved congruent by the ASA condition.
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In order to scuba dive safely, divers must be aware that the water
pressure in the ocean is a function of depth. The water pressure increases by
0.445 pounds per square inch (psi) for each foot of depth. The pressure at the
surface is 14.7 psi. Write a function to represent water pressure. What is the
value of the function for an input of 50, and what does it represent?
The value of the function at an input of 50 will be 36.95.
How to calculate the value?Since the pressure at the surface is 14.7 psi, a function to represent water pressure will be:
= 14.7 + (0.445 × p)
where p is the increase in pressure for each foot
= 14.7 + 0.445p
Therefore when the input is 50, the amount will be:
= 14.7 + 0.445p
= 14.7 + 0.445(50)
= 14.7 + 22.25
= 36.95
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three boys have a total of 24 apples. the littlest boy has 2 times more than the second boy. the second boy has 2 less than the first boy. how much has all the boys
help asp show ur work you’ll get BRAINILEST
Answer:
x = -14
Step-by-step explanation:
Solve:
7x - 28 = 2(4x - 7)
7x - 28 = 8x - 14
Substrate 8x from both sides.
7x - 28 - 8x = 8x - 14 - 8x
-x - 28 = -14
Add 28 to both sides.
-x - 28 + 28 = -14 + 28
-x = 14
Divide both sides by -1.
-x/-1 = 14/-1
x = -14
Therefore x = -14
