Thus, the object travels a distance of 10π units along the given trajectory.
To find out how far an object travels along a given trajectory, we need to calculate the arc length of the curve. The formula for arc length is given by:
L = ∫_a^b √[dx/dt]^2 + [dy/dt]^2 dt
where L is the arc length, a and b are the start and end points of the curve, and dx/dt and dy/dt are the derivatives of x and y with respect to time t.
In this case, we have the trajectory r(t) = (10 cos 2t, 10 sin 2t) for 0 ≤ t ≤ π/2. Therefore, we can calculate the derivatives of x and y as follows:
dx/dt = -20 sin 2t
dy/dt = 20 cos 2t
Substituting these values into the formula for arc length, we get:
L = ∫_0^(π/2) √[(-20 sin 2t)^2 + (20 cos 2t)^2] dt
= ∫_0^(π/2) √400 dt
= ∫_0^(π/2) 20 dt
= 20t |_0^(π/2)
= 10π
Therefore, the object travels a distance of 10π units along the given trajectory.
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PLEASE HELP!! 40 POINTS!!
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
Answer:
the second option
Step-by-step explanation:
y=mx+c
therefore y=10x+20
20 is the y intercept, 10 is the gradient
Amelia is making a hair bow that requires
one yard of ribbon. The ribbon that she
needs is sold by the meter. Will one meter
of ribbon be enough to make the bow?
Explain.
Yes, one meter of ribbon will be enough to make the bow because one meter is equal to 1.094 yards.
How to determine if one meter of ribbon be enough to make the bow?One meter is equal to 1.094 yards. So, one meter is longer than one yard.
Since Amelia needs one yard of ribbon to make the bow, and she can only find ribbon sold by the meter, which is longer than a yard, one meter of ribbon will be enough to make the bow.
Thus, She can purchase one meter of ribbon to make the bow.
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I Need help asap, This is due in less than an hour!!
Can you please copy and paste it here?
-
I cannot read it clearly.
ANSWER PLS!! NEED ASAP!!
Angela baked an apple pie that had a radius of 6 inches. She wants to cut the pie into eight equal slices. How wide will each piece of pie be at the outer edge?
A- 5.2 in.
B- 4.7 in.
C- 4.4 in.
D- 4.2 in.
Answer:
Angela baked A-5.2 inches of baked apple pie.
Step-by-step explanation:
do -3 and 4 and -1 and 12 have a positive sum
Answer:
Yes, they do because -3+4=1 and -1+12=11
Step-by-step explanation:
Hope it helps!
Answer: If you mean + then, 12
Step-by-step explanation:
-3 + 4 = 1 -1 + 1 = 0 0 + 12 = 12
which of the following is not the solution of 3x+6y=12?A) (-4,4) B) (0,2)C) (8,-2)D) (3,1)
(3,1) is not the solution of the equation 3x + 6y = 12. So the option D is correct.
In the given question, we have to check which of the following is not the solution of 3x+6y=12.
To check which is not the solution of the given equation, we put the value of x and y from the given point. If for any point the condition is true then that point is the solution of the given equation. If that point doesn't satisfy the condition then that point is not the solution of the given equation.
The given equation is 3x+6y=12.
Firstly we check for the point (-4,4), where x = -4, y = 4
3(-4) + 6(4) = 12
-12 + 24 = 12
12 = 12(True)
Now we check for the point (0,2), where x = 0, y = 2
3(0) + 6(2) = 12
0 + 12 = 12
12 = 12(True)
Now we check for the point (8,-2), where x = 8, y = -2
3(8) + 6(-2) = 12
24 - 12 = 12
12 = 12(True)
Now we check for the point (3,1), where x = 3, y = 1
3(3) + 6(1) = 12
9 + 6 = 12
15 = 12(False)
Hence, (3,1) is not the solution of the equation 3x + 6y = 12. So the option D is correct.
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P(x<15) round 2 decimal places
When rounded to two decimal places, numbers like 0.7035 and 2.836220364, for instance, become 0.70 and 2.84, respectively.
What is Round to Two Decimal Places?To simplify their interpretation and use in calculations, decimal numbers are frequently rounded off.
The hundredths place, which is the second place to the right of the decimal point, is where a decimal number is rounded to when it is rounded to two decimal places.
When rounded to two decimal places, numbers like 0.7035 and 2.836220364, for instance, become 0.70 and 2.84, respectively.
If you look closely, you will see that instead of 2.83, we have increased the digit in the first number's hundredths position by 1.
We did not, however, add 1 to the digit in the hundredths place for the second number (i.e 0).
The Complete Question is two decimal places.
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Complete question:
Round the function P(x<15) to 2 decimal places.
Can someone help me with this ? Please
Value of gof(-1) is 2. The solution has been obtained by applying the multiplication operation on the given functions.
What are operations on functions?
Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.
Suppose there are two functions f(x) and g(x). The notations are as follows:
For Addition: (f+g)(x) = f(x) + g(x)For Subtraction: (f-g)(x) = f(x) - g(x)For Multiplication: (f×g)(x) = f(x) × g(x)For Division: (f/g)(x) = (f(x))/(g(x))Now, gof= g(f) = 3-f
We are given f = 2+x
So, f(-1) = 2+(-1) = 1
Now, substituting the value of f(-1) in g(f) , we get
gof(-1)= 3-1=2
Hence, the value of gof(-1) is 2.
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8+5x=-2
show work
check
What are the 4 properties of subtraction?
There are various properties of subtraction , out of which four of them are ,
Commutative propertyAssociative property Identity propertyDistributive propertySubtraction means to reduce one number or quantity from another. It is one of the most common mathematical operations which are present as well as it is represented by the symbol , " - " .
The associative property does not apply to subtraction which are performed between whole-number. The order of subtraction is significant.
The distributive property helps to simplify the difficult algebraic expression. As a result, the distributive property favors multiplication over subtraction. The property states that subtracting any number from the same number results in the number 0.
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Write the rule for the linear function I will give brainliest
Answer:
2
Step-by-step explanation:
The rule is multiplying by 2 every time
-2 times 2 is -4
0 times 2 is 0
2 times 2 is 4
Classify this pair of events: A flavor of ice cream is selected at random; A
topping for the ice cream is selected at random.
A. independent
B. dependent
A A flavor of ice cream is selected at random; A topping for the ice cream is selected at random. This is B. dependent events.
What are dependent event?Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.
If one event is accidentally altered, another is probably going to be different.
If two events are interdependent, then the result of the first event will influence the result of the second even more.
The ice cream in this case represented dependent event.
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Fatoumata is going to invest in an account paying an interest rate of 1.7% compounded continuously. How much would Fatoumata need to invest, to the nearest hundred dollars, for the value of the account to reach $6,300 in 5 years?
Fatoumata requires an investment of $4390.24
What is basic interest or amount?
The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest.
Rate r= 1.7%
Total A is $6300.
t = 5 years
Primary P =????
A=P(1+r)^t
6300= P(1+0.017)^5
6300= P(1.017)^5
6300= P(1.435)
P= 6300/1.435
P = 4390.24
Should be the answer. if I'm right can I get Brainiest if I'm wrong then it's fine
Answer:
$5786.63
Step-by-step explanation:
the equation for interest compounded continuously is A=Pe^rt
6300=Pe^.017(5)
then in your calculator put e raised to the .085 (which is .017 times 5)
then divide that by 6300
and P=5786.62739
In 2006, the U.S. Population (or persons) per square mile of land area was 85. In 2014, the persons per square mile was 89.48.
a. Write an equation describing the relationship between year and persons per square mile. Use ordered pairs of the form (years past 2006, persons per square mile)
b. Use equation on question 7 to predict the persons per square mile in 2023. Round to the nearest whole person.
In 2006 we have 93.3 people per sq mile .
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
In order to determine the equation for this relationship, we need to first find the slope between these two values. There are two ways to do this:
1. Create a graph
*Create a graph with the x-axis representing the years past 2000 (so 2000 would be 0 and 2003 would be 3 and so on)
*Use the fact that slope=rise/run to get slope=2.7/3 (because we rise 87-84.3=2.7 and run 3 (from 2000 to 2003), and 2.7/3=27/30=9/10
*Plug this and the point (0, 84.3) into the formula y=mx+b to find the y-intercept of your equation
--> 84.3=(9/10)(0)+b --> b=84.3
So, your equation can be written now as y=(9/10)x+84.3
[Note: To check, if you plug in 3 you should get 87, and you do, so it works!]
2. Use the slope formula
Alternatively, you could have did slope=(y2-y1)/(x2-x1)=(87-84.3)/(3-0)=2.7/3=9/10
The process here would be the same as above
b) Here, just plug 10 into the equation above (since 10 is the number of years 2010 is after 2000, or 2010-2000=10). Doing this we get:
y=(9/10)(10)+84.3=9+84.3=93.3
So, in 2006 we have 93.3 people per sq mile
Therefore, In 2006 we have 93.3 people per sq mile .
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help please i need answers
The expressions that have a sum or difference equal to 3/4 are:
11/12 - 1/6 3/5 + 3/202/3 + 1/12The correct options are B, C, and E
What are sums and differences?
Sum mean the addition of numbers or expression
Difference means the subtraction of numbers or expressions.
The sum or difference of the number are as given below:
a. 1/2 + 2/4 = 4/4
b. 11/12 - 1/6 = (11 - 2) / 12
11/12 - 1/6 = 9/12
9/12 = 3/4
c. 3/5 + 3/20 = (12 + 3)/20
3/5 + 3/20 = 15/20
15/20 = 3/4
d. 7/8 - 1/2 = (7 - 4)/8
(7 - 4)/8 = 3/8
e. 2/3 + 1/12 = (8 + 1)/12
(8 + 1)/12 = 9/12
9/12 = 3/4
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enter in the missing numbers to create equivalent ratios i need helpppppp i don’t understand
Answer:
[tex]8....on \: the \: first \: box \: and \\ 64......on \: the \: second \: box[/tex]
Step-by-step explanation:
Greetings!!!
so first let's see how it comes by changing it into ratios
[tex] \frac{1}{4} ....the \: first \\ \frac{2}{8} cancel(simplify) = \frac{1}{4}...the \: second [/tex]
Thus, following the same order
[tex] \frac{8}{32} simplify = \frac{1}{4} \\ \frac{16}{64} simplify = \frac{1}{4} [/tex]
so we get the same ratios.
If any questions tag it on the comments.
Hope it helps!!!
How do you identify the base and exponent in an exponential notation?
We can identify the base and its exponent as the exponent indicates the number of times the base is used as a factor in an exponential notation.
What is Exponent ?An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively. Remember that every number multiplied by one is equal to itself.
Exponents are a technique of expressing extremely large numbers in terms of powers. The number of times a number has been multiplied by itself is the exponent, so to speak. For instance, the result of multiplying the number 6 by itself four times is 6 6 6 6. This can be expressed as 6⁴. Here, the exponent and base are 4 and 6, respectively.
An exponential number takes the shape of a, where an is multiplied by itself n times. The simple example is 8=23=222. In exponential notation, A is referred to as the base, whereas n is referred to as the power, exponent, or index. In scientific notation, 10, which is a specific illustration of exponential numbers, is typically always used as the base number.
Exponential notation make it easy to express powers succinctly. The exponent displays the base's multiplicative power. It can be written as 2 2 2 2=25 for the integer 32 because 2 is the "base" and 5 is the "exponent." The correct translation of this phrase is "two to the fifth power."
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Is it possible to have a triangle with sides 2cm 2cm and 5cm justify your answer?
Answer:
No, it is not possible to have a triangle with sides of 2cm, 2cm, and 5cm. This is because a triangle's sides must adhere to the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 2cm + 2cm (4cm) is not greater than 5cm, so it is not possible to form a triangle with these side lengths.
Step-by-step explanation:
Answer:
Yes u can
Step-by-step explanation:
U can create a triangle with that because 2+2 is 4 which is less than 5 meaning it would work as a triangle
20.25- (-5) - 11.75 + 15.
Answer:
28.5
20.25 - (-5) = 25.25
25.25 - 11.75 = 13.5
13.5 + 15 = 28.5
Step-by-step explanation:
Sorry it took so long. Hope it helps! =D
A candy store sells Nerds in two different sizes. Which is the best buy?
14 oz. for $4.20 OR 18 oz. for $5.04
Answer: 18oz
Step-by-step explanation:
What circles are drawn on the score sheet at the end of a set?
In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.
Following are the circles that are drawn at the end of a set on the NCAA women's volleyball scorecard:
who has the first opportunity to serve:
Based on our existing knowledge of how NCAA Women's Volleyball functions, we can see that each period is divided into sets and that there is a scorecard where each team's points are given. In light of this, the scorer circles the S on the scorecard at the end of a set to designate the team that would serve first after a coin flip.
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How do you find a prime number multiples?
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number can only be divided evenly by 1 and itself.
To find the multiples of a prime number, you can use the following steps:
Start with the prime number itself. This is the first multiple of the prime number.Multiply the prime number by 2. This will give you the second multiple of the prime number.Multiply the prime number by 3. This will give you the third multiple of the prime number.Repeat step 3 for larger and larger integers (4,5,6,7,8....) until you reach the desired number of multiples.For example, if the prime number is 5, the multiples of 5 are 5, 10, 15, 20, 25, and so on.
It's important to note that a prime number only has two divisors: 1 and itself. This means that a multiple of a prime number will never be a prime number.
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What is true about exponential functions with a base between 0 and 1?
Answer:1 always rise to the left and approach 0 to the right.
Step-by-step explanation:
A ferris wheel can accommodate 40 people in 20 minutes. How many people could ride the ferris wheel in 5 hours? What was that rate per hour?
Answer:
600 people
Step-by-step explanation:
40 people in 20 minutes => 120 people per hour. 5 hours, so 5 x 120 = 600 people.
if you can solve this that would be great
Answer:
I wish you luck
Step-by-step explanation:
Probability of being a senior or white
The probability of being a senior citizen and white is: (0.63)(0.3) = 0.189.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.
Given that the probability of identifying white is 0.63.
Then the probability of not white is:
1 - 0.63 = 0.37
Given that the probability of being a senior citizen is 0.3.
Then the probability of not a senior citizen is:
1-0.3 = 0.7
Hence, the probability of being a senior citizen and white is:
(0.63)(0.3) = 0.189
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Two angle measures of this triangle are 60°. Which type of triangle is it?
A.
obtuse
B.
scalene
C.
equilateral
D.
right
Answer: C. Equilateral
Step-by-step explanation:
Answer: option C is correct. two angle measures of an equilateral triangle is 60°
Step-by-step explanation: All the sides of an equilateral triangle are of equal lengths—each interior angle of this triangle measures 60°.
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = x2 +1. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer: The graph of f(x) = x^2 will have only one x-intercept (0,0) since it is a parabola that opens upward and its vertex is at the origin. On the other hand, the graph of g(x) = x^2 +1 is a transformation of the parent function, the graph of f(x) = x^2, where the function was shifted up by 1 unit. Therefore this function g(x) = x^2 +1 will not have any x-intercept because when x=0 the y value becomes 1 so the x-intercept will not be on the x-y plane.
In summary, the graph of f(x) = x^2 has one x-intercept, while the graph of g(x) = x^2 +1 has no x-intercepts due to the transformation of the parent function.
Step-by-step explanation:
In ΔTUV, t = 70 inches, mm∠T=99° and mm∠U=53°. Find the length of u, to the nearest inch.
The length of u is 56.60 inches. The nearest inches it is 57 inch
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.
Given that ΔTUV is a triangle with m∠T=99° and m∠U=53°.
The length of t is 70 inches.
The opposite side of ∠T is t, the opposite side of ∠U is u, and the opposite side of ∠V is v.
Sine rule of ΔABC:
a/sin A = b/sin B = c/sin C
Apply sine law in ΔTUV:
t/sin T = u/sin U = v/sin V
Putting ∠T=99°, ∠U=53°, and t = 70.
70/ sin 99° = u/sin 53°
u = (70sin 53°)/ sin 99°
u = 56.60 inches
The digit after the decimal point is greater than 5, thus add 1 with the 56 to get the nearest inch.
u = 57 inches
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A number between 55 and 101 multiple of 2, 6, and 8
Answer:72
Step-by-step explanation:
8x9=72
2x36= 72
12x6=72