Cam rode her bike 5 times as far as Dante did. Dante rode 187 meters farther than Michael did. Cam rode 15.25 Kilometers. How many meters did Michael ride? Explain how you know you got your answer

Answers

Answer 1

Let Dante's distant be x, Cam's will be 5x
Given that Cam rode 15.25 km
then
5x=15.25
x=3.05 km

thus Dante rod 3.05 km
but
1 km=1000m
thus
3.05 km=3050 m
But Dante rod 187 m more than Michael, the distance Michael will ride then will be:
3050-187
=2863 m

Answer 2

It was found that Michael rode 2863 meters.

To find out how many meters Michael rode, we first need to establish the relationship between the distances Cam, Dante, and Michael rode. According to the problem, Cam rode 5 times as far as Dante did. If Cam rode 15.25 kilometers, we first convert this to meters by multiplying by 1000 (since there are 1000 meters in a kilometer):

15.25 km × 1000 = 15250 meters.

Now that we know Cam rode 15250 meters and that this is 5 times the distance Dante rode, we can find Dante’s distance:

15250 meters / 5 = 3050 meters.

Dante rode 3050 meters, which is 187 meters farther than Michael did. To find the distance Michael rode, we subtract 187 meters from Dante’s distance:

3050 meters - 187 meters = 2863 meters.

Therefore, Michael rode 2863 meters.

Related Questions

help! I will give thanks!

Answers

Mode = 60

Reason: 60 appeared 4 times.

6\000= 60 7/00=70 8/00 =80 9/0=90

the probability of winning the game is 7/10. What is the probability that they will lose?

Answers

3/10 is the probability of them losing.

The probability of losing the game is 3/10 or 0.3 when the probability of winning is 7/10, because the total probability must always equal 1.

If the probability of winning the game is 7/10, then the probability of losing the game is the complement of the probability of winning. This means we subtract the probability of winning from 1. Therefore, the probability of losing the game is 1 - 7/10 = 3/10 or 0.3. This is because the sum of the probabilities of all possible outcomes in a probability distribution must equal 1.

Which equation in point-slope form contains the point (4, –1) and has slope 3? y – 1 = 3(x + 4) y – 4 = 3(x + 1) y + 1 = 3(x – 4)

Answers

Hello!

The equation for point-slope form is

y - b = m(x - a)

m is the slope
(a, b) is a point the line goes through

Put in the values into the equation

y - -1 = 3(x - 4)

Simplify

y + 1 = 3(x - 4)

The answer is C) y + 1 = 3(x - 4)

Hope this helps!

Answer:

the answer is option d y+1 =3 (x-4)

how do you do 27?????

Answers

Hey there!

To start, the equation needed to represent this problem would be an equation:
y= ab^x

a represents the initial amount. In this case, the initial amount would be 4 billion. It would be represented as 4 since each 1= one billion.

b represents the rate. Because the problem discusses a growth, convert the rate, 1.9% to a decimal and add 1 to it (add one if it is a growth, subtract one if it is a decay). b would be 1.019.

x represents the time in which the population grows or t.

When you piece this together, your equation should look like:
y=4(1.019)^t

or

Choice A.

Hope this helps and have a nice day! Feel free to ask any questions about my work. :)

The correct answer is: [A]: " P(t) = 4 * (1 .019)^t " .
_______________________________________________________
Explanation:
______________________________________________________
Use the formula for "exponential growth" :
______________________________________________________
→ " y = A * (1 + r)^t " ;
______________________________________________________
in which:
______________________________________________________
A = the "beginning population" ;

→ (in number representing "billions of people") ;

→ given the "beginning population" is "4 billion" ;

→ " A = 4 " ;
______________________________________________________
r = rate (of change) = 1.9% ; expressed as a decimal:

→ "r = rate = 1.9% = { 1.9 ÷ 100 } ;

→ {Take the "1.9" ; & move the decimal point 2 (two) spaces backward }:

→ 1.9% = 1.9 ÷ 100 = 0.019 ;

→ " r = 0.019 " ;

→ " t = time" ; (usually in "years" ; however, all the answer choices provided leave the "t" as it is; so we shall do so, too.
________________________________________________________

→ Replace "y" with: " P(t) " ;

→ And rewrite the equation of the function with our known values:

→ " y = A * (1 + r)^t " ;
____________________________________________________
→ becomes:

→ " P(t) = 4* (1 + 0.019)^t " ;

→ " P(t) = 4 * (1 .019)^t " ;
____________________________________________________
→ which is: Answer choice: [A]: " P(t) = 4 * (1 .019)^t " .
____________________________________________________

If p(x) = 2x^3 - 3x + 5, what is the remainder of p(x) divided by (x - 5)

Answers

Dividing the function given, P(x) by (x-5) will give us the following
P(x)/(x-5)
=(2x^3-3x+5)/(x-5)
=(2x^2+10x+47)+240/(x-5)
thus the remainder is:
240

Final answer:

Using the Remainder Theorem, after substituting 5 into the polynomial p(x), we find that the remainder when p(x) is divided by (x - 5) is 240.

Explanation:

To find the remainder of p(x) divided by (x - 5), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial p(x) divided by (x - a) is p(a). Thus, we need to evaluate p(5).

Let's substitute x with 5 in the polynomial p(x):

p(5) = 2(5)^3 - 3(5) + 5
= 2(125) - 15 + 5
= 250 - 15 + 5
= 240.

Therefore, the remainder when p(x) is divided by (x - 5) is 240.

can someone help me on trigonometry ?

Answers

Using the image I gave you, you don't need to solve for x.
So tan is opposite/adjacent
sin: opposite/hypotenuse
cos: adjacent/hypotenuse
Take theta and do: adjacent/hypotenuse which is cosine
cos theta = adjacent/hypotenuse
cos theta = 1.5/9
inverse cos = 1.5/9 and the answer is: 80.4 degrees

sketch one cycle of the cosine function y=-cos 3 theta

Answers

The graph of the equation given by y=-cos³θ will be as follows:

Answer with explanation:

The given cosine function is

y= - cos 3 (theta)= -3 cos A, where , theta =A.

→→Domain of Cos A

= All Real number

= Period is from (-π , π)

Range of Cos A=[-1, 1]

→Domain of Cos 3 A,will be also, all real number.

Period is from,

[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]

But range of Cos 3A,will be same as ,Cos A which is equal to ,[-1,1].

→Plotted the graph of ,y=-cos 3 A, having cycle ,

[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]

what is 3√27x^9

3x^6
3x^3
9x^3
9x^6

Answers

The first step for solving this expression is to know that the root of a product is equal to the product of the roots of each factor. Knowing this,, the expression becomes the following:
[tex] \sqrt[3]{27} \sqrt[3]{ x^{9} } [/tex]
Write the number in the first square root in exponential form with a base of 3.
[tex] \sqrt[3]{ 3^{3} } \sqrt[3]{ x^{9} } [/tex]
Now reduce the index of the radical and exponent in the second square root with 3.
[tex] \sqrt[3]{ 3^{3} } [/tex] x³
Lastly,, reduce the index of the radical and exponent with 3 to get your final answer.
3x³
This means that the correct answer to your question will be option B.
Let me know if you have any further questions.
:)

The value of the expression ∛27x⁹ is 9x³.

The given expression is ∛27x⁹.

Cube root of twenty seven times of x power nine.

We can split the terms inside the cube root.

27=3×3×3

∛x⁹ = x³

Now let us plug in the above expression.

= 3√3³ × x⁹

= 3√3³ × √ x⁹

= 3 × 3 × x³

= 9x³.

Hence, the value of the expression ∛27x⁹ is 9x³.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ6

Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?

Answers

500 x(1.04)^3=562.432
562.432-500= 62.432
62.432 / 3= 20.8106

Which graph would help solve the equation 5log(x+3)=5

Answers

5log(x+3)=55log(x+3)=5Simplify 5log(x+3)5log(x+3) by moving 55 inside the logarithm.log((x+3)5)log((x+3)5)Simplify the right side of the equation.55Graph each side of the equation. The solution is the x-value of the point of intersection.x=7

The value of x is 7 for the given equation.

What is logarithm?

Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.

For the given situation,

The equation is 5log(x+3)=5.

On solving this equation, we can get value of x.

⇒ [tex]5log(x+3)=5[/tex]

⇒ [tex]log(x+3)=1[/tex]

We know that, log 10 = 1

Then,

⇒ [tex]log(x+3)=log10[/tex]

⇒ [tex]x+3=10[/tex]

⇒ [tex]x=7[/tex]

Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.

Learn more about the logarithm here

https://brainly.com/question/20785664

#SPJ2

If a scare as side lengths of 5 inches what is the lengths of the diagonal to the nearest 10th of in inch

Answers

A 5 by 5 square would have a diagonal equal to

square root (25 + 25) =
square root (50) =
7.07106781 =
7.1 (rounded to nearest 10th of an inch.

what is 3 ^9? how to solve?

Answers

3⁹ is the same as doing:

3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3

What I would do it is narrow it down piece by piece.

3 * 3 * 3 = 27. Do that 3 times, now you are left with:

27 * 27 * 27

27 * 27 or 27² = 729.

That leaves you with:

729 * 27

You can multiply by hand or use a calculator to get your answer of 19683.

To check your answer, plug 3⁹ into a calculator. Your answer should match this.

An equiangular triangle can be scalene. A. True B. False

Answers

False is correct answer.

Because equiangular triangle is not to be scalene.

Hope it helped you.

-Charlie

:)

False, Scalene triangles have three unequal sides and equilateral have three equal sides

Karen is considering taking out a 20-year loan with monthly payments of $260 at an APR of 5.5%, compounded monthly, and this equates to a loan of $37,796.89. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?

Answers

The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89

How to calculate EMI?

The EMI formula is :

[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]

Where r = 5.5/12/100 = 0.00425

p = 37,796.89

and n = 20 x 12 = 240

Putting the values in formula we get'

= (37,796.89x 0.00425 x 2.767)/1.767

= $350

Hence,

The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89

Learn more about the compounded here;

brainly.com/question/11814596

#SPJ5

Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.

Step-by-step explanation:

What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.

To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.

Answers

we know that
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²

so
the volume of a sphere=(r/3)*surface area of sphere
therefore

if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere

if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere

if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere

example
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area

2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area

3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area

Please someone help Me with this problem. I really need help.

Answers

The distance between (4, 7) and (2, 2) might be A, 10. Hope this helps, sorry if I'm wrong.

The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.

A.26.5cm3
B.44.2cm3
C.79.5cm3
D.132.5cm3

Answers

Para resolver este problema, debe aplicar el procedimiento que se muestra a continuación:

1of the first figure in the image attached, is:

a ^ 2 = b ^ 2 + c ^ 2
c =
c=√(6 cm)^2-(4.8 cm)^2
c=3.6 cm

2. The area of the base of the first figure is:

A=BxH/2
A=3.6x4.8/2
A=8.64 cm^2

3. Therefore, the volume of the cone is:

V=(8.64 cm^2)(9.2 cm)
V=79.5 cm^3

Therefore, the answer is: C. 79.5 cm^3

Find the Mean Median Mode and range of each data set that is obtained after adding the given constant. 12,10,15,17,15,9,10,15,12,14,+9. Please show work.

Answers

The given number arranged in order are:
9, 9, 10, 10, 12, 12, 14, 15, 15, 15, 17
1. To find the mean, add all the number together and divide the summation by 11[ which is the total number of the figures given]
Mean = [9 + 9 + 10 + 10 + 12 + 12 + 14+ 15 + 15 + 15 + 17] / 11 = 138 / 11
Mean = 12.5
Therefore, the mean is approximately equal to 13.

2. The median of a number refers to the number in the middle of a sorted set of number.
To find the median of a set of numbers, the numbers have to be arranged first in the correct increasing order and the number that falls in the middle will be the median. If two numbers fall in the middle, add the two together and find the average. For the set of number given above, the number that falls in the middle is 12.
Therefore, the median = 12.

3. The mode of a set of number refers to the number in the set, which has the highest frequency of occurrence, that is, it is the number that occur most. Looking at the set of number given above, 15 occurred three different times. Therefore, the mode of the set of number given above is 15.
Mode = 15.

4. The range of a set of number refers to the difference between the highest and the lowest numbers in the set of a given number. It represents the spread of the data. In the set of numbers given above the range is determined thus:
Range = 17 - 9 = 8.
Therefore, Range = 8.

Mean: 12.545454545455

Median: 12

Range: 8

Mode: 15, appeared 3 times

Largest: 17

Smallest: 9

Sum: 138

Count: 11

A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)

Answers

the speed of the car in centimeters per second based on the information given would be 2,145.8

A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)

Solution:

We have 48 [tex] \frac{miles}{hour} [/tex]

To convert, miles to centimeters.

Let us convert miles to feet and then inches and then centimeters.

1miles=5280feet

And, 1 foot=12inches

So, 5280 feet or 1 miles =12*5280inches

So, 1miles=63360inches

Now, Let us convert inches to centimeters

1centimeter=0.39inches

Or, 1 inch= [tex] \frac{1}{0.39} [/tex] centimeter

So, 63360inches (or 1 mile)= [tex] \frac{63360}{0.39} [/tex] centimeter

1mile or 63360inches=162461.54centimeter

1mile=162461.54 centimeter

We have, 48 [tex] \frac{miles}{hour} [/tex]

We have, 48 *[tex] \frac{162461.54 centimeter}{60minutes} [/tex]

We have, 48* [tex] \frac{162461.54 centimeter}{60*60seconds} [/tex]

So, We have, 48* [tex] \frac{162461.54 centimeter}{3600seconds} [/tex]

=48*[tex] \frac{162461.54}{3600} [/tex][tex] \frac{centimeters}{second} [/tex]

=48*45.13[tex] \frac{centimeters}{second} [/tex]

=2166.15[tex] \frac{centimeters}{second} [/tex]

Answer:= Speed of the car in centimeters per second is 2166.15 centimeters/second

The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?

Answers

the complete question in the attached figure

we know that
The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so

the answer is the option
A. the remote interior angles

The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.

the answer is the option

A. the remote interior angles

fatima wants to find the value of sin theta, given cot theta equals 4/7. which identity would be best for fatima to use?

Answers

we know that
1+cot ²∅=csc² ∅
cot ∅=4/7
so
1+(4/7)²=csc² ∅
csc² ∅=1+(16/49)
csc² ∅=(65/49)
csc ∅=(√65)/7

remember that
csc ∅=1/sin ∅
sin ∅=1/csc ∅------> sin ∅=7/√65-----> sin ∅=(7√65)/65

the answer is
the best identity to find sin ∅ is
1+cot ²∅=csc² ∅

Answer:

D edge

Step-by-step explanation:

Subtract.

(x + 1) − (−2x − 5)

Answers

3x+6, you have to distribute the negative to get the parentheses away and simplify

Answer:

3x+6

Step-by-step explanation:

you have to distribute the negative to get the parentheses away and simplify

Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?

Answers

Sum of angles of regular polygon = 180*(n-2), n - number of sides, or angles.

120n=180*(n-2)

120n=180n-360
180n-120n=360
60n =360
n=6

It is hexagon.

Find the variable of each pair

Answers

A. X=4
B. Y= 24, X= 6

Will give brainliest! Which are simplified forms of the expression sec^2theta sin2theta
Which is the second answer? I already got the first one

Answers

[tex]\bf \cfrac{sin(2\theta )}{cos^2(\theta )}\implies \cfrac{1}{cos^2(\theta )}\cdot sin(2\theta )\implies sec^2(\theta )sin(2\theta )\\\\ -------------------------------\\\\ 2tan(\theta )\implies \cfrac{2sin(\theta )}{cos(\theta )}\implies \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )cos(\theta )}\implies \cfrac{2sin(2\theta )}{cos^2(\theta )} \\\\\\ \cfrac{1}{cos^2(\theta )}\cdot sin(2\theta )\implies sec^2(\theta )sin(2\theta )[/tex]

Answer:

C) 2 tan θ

E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)

Step-by-step explanation:

This is essentially what the other person said, but in a better format.

A fair dice is rolled 5 times in sequence. what is the probability that you will get exactly the same number for all 5 rollings

Answers

1/7776. The probability of you getting any one number when rolling a dice is 1/6. Since you are rolling the dice 5 times and you are trying to get the same number each time. You would multiply 1/6 5-times. 1/6*1/6*1/6*1/6*1/6=1/7776.

HELP!! Drag values to complete each equation.

Answers

(12²)³ x 12^-4 = 144 which means it is 12² = 144.

12^7 x 12^-5 / 12² which equals 1.

Hope this Helps!!

Answer:

a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

Step-by-step explanation:

We have to complete each equation

We are given that

[tex]((12)^2)^3\cdot (12)^{-4}[/tex]

[tex](12)^6\cdot (12)^{-4}[/tex]

Using identity

[tex](a^x)^y=a^{xy}[/tex]

[tex](12)^{6-4}=(12)^2[/tex]

Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]

[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]

b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]

[tex]\frac{(12)^2}{(12)^2}[/tex]

[tex](12)^{2-2}=(12)^0=1[/tex]

Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]

[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]

Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. What is the speed of the train, if it is 5 km/h greater than the speed of the car?

Answers

Speed of the car = 255 ÷ 4 = 63.75 km/h

Speed of the train = 63.75 + 5 = 68.75 km/h

Answer: 68.75 km/h

[tex]\\ \text{Let the speed of the car is x km/h}\\ \text{Then, the speed of the train is x+5 km/hr}\\ \text{Now, 4 hr is the time of the car}\\ \text{and 7 hour is the time of the train}\\ \text{We know the formula}\\ \text{Distance }= \text{Velocity }\times \text{ time}\\ \text{Distance travelled by car is 4x}\\ \text{Distance travelled by train is }7(x+5)\\ \text{The total distance is given by 255 km. Hence, we have}\\ 4x+7(x+5)=255\\ 4x+7x+35=255\\ 11x=220\\ x=20[/tex]

The speed of the car is 20 km/hr and hence the speed of the train is 2+5=25 km/hr.

The speed of the train is given by 25 km/hr.

what expression is equivalent to the division expression 3/4 divided by 4/5

Answers

3/4 ÷ 4/5 =

3/4 times 5/4 =

15/16 = .9375

Answer:

3/4 ÷ 4/5 = .75 ÷ .80

Step-by-step explanation:

3/4 ÷ 4/5

= .75 ÷ .80

= 0.9375

Can someone help me in this trig question, please? thanks
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12

Answers

[tex]\bf \textit{the position of the rider is clearly }20cos\left( \frac{5\pi }{12} \right)~~,~~20sin\left( \frac{5\pi }{12} \right)\\\\ -------------------------------\\\\ \cfrac{5}{12}\implies \cfrac{2+3}{12}\implies \cfrac{2}{12}+\cfrac{3}{12}\implies \cfrac{1}{6}+\cfrac{1}{4} \\\\\\ \textit{therefore then }\qquad \cfrac{5\pi }{12}\implies \cfrac{1\pi }{6}+\cfrac{1\pi }{4}\implies \cfrac{\pi }{6}+\cfrac{\pi }{4}\\\\ -------------------------------[/tex]

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ -------------------------------\\\\ cos\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=cos\left( \frac{\pi }{6}\right)cos\left(\frac{\pi }{4} \right)-sin\left( \frac{\pi }{6}\right)sin\left(\frac{\pi }{4} \right)[/tex]

[tex]\bf cos\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}-\cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{6}}{4}-\cfrac{\sqrt{2}}{4}\implies \boxed{\cfrac{\sqrt{6}-\sqrt{2}}{4}} \\\\\\ sin\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=sin\left( \frac{\pi }{6}\right)cos\left( \frac{\pi }{4} \right)+cos\left( \frac{\pi }{6}\right)sin\left(\frac{\pi }{4} \right)[/tex]

[tex]\bf sin\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=\cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}+\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}+\cfrac{\sqrt{6}}{4}\implies \boxed{\cfrac{\sqrt{2}+\sqrt{6}}{4}}\\\\ -------------------------------\\\\ 20\left( \cfrac{\sqrt{6}-\sqrt{2}}{4} \right)\implies 5(-\sqrt{2}+\sqrt{6}) \\\\\\ 20\left( \cfrac{\sqrt{2}+\sqrt{6}}{4} \right)\implies 5(\sqrt{2}+\sqrt{6})[/tex]

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

The position

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

The value of 20cos75°

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

The value of 20sin75°

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Learn more about position here:

https://brainly.com/question/11001232

Other Questions

April bradley's arguments in favor of solar power are hardly worth listening to. after all, look where she graduated fromnortheast texas state. that's hardly ivy league. and look at how she dresses. yuck! For local travel addresses and street names should be The measure of arc QS is (4x 18).What is the value of x?40.549.594.5180ANSWER IS 49.5 Needing English 9th GradeHelp! :CRead the poem.excerpt from I Explain a Few Things by Pablo NerudaAnd one morning all was aflameand one morning the firescame out of the earthdevouring people,and from then on fire,gunpowder from then on,and from then on blood.Bandits with airplanes and with Moors,bandits with rings and duchesses,bandits with black-robed friars blessingcame through the air to kill children,and through the streets the blood of childrenran simply, like childrens blood.Jackals that the jackal would spurn,stones that the dry thistle would bite spitting,vipers that vipers would abhor!Facing you I have seen the bloodof Spain rise upto drown you in a single waveof pride and knives!Question:Refer to Explorations in Literature for a complete version of this poem.Which explanation about I Explain a Few Things best develops the speakers viewpoint that adversity only makes his compatriots stronger?A.) By describing the Bandits with airplanes and with Moors, the speaker demonstrates that these aggressors will not be tolerated.B.) By stating that citizens will rise up / to drown you in a single wave, the speaker indicates they are determined to overcome their opponents.C.) The image of jackals and vipers illustrates that the opponents are savage and will fight viciously in order to win the war.D.) The image of flames coming out of the earth to devour people shows the level of suffering the war causes citizens to endure. Discuss, in detail, martin luther king jr.'s "militant nonviolence." how did this philosophy inspire others to challenge segregation in the south? how did some civil rights leaders oppose this philosophy? A tree's root is 9 feet below ground and spans a radius of 6 feet. If the total length of the tree from root tip to top is 23 feet, what is the tree's elevation above ground? a. 14 feet b. 17 feet c. 26 feet d. 32 feet The more kinetic energy there is an a sample of matter, the-A.more energy is absorbed as heatB.more energy is given off as heatC.Lower the temperatureD.higher the temperature Which visual aid is best for representing the steps needed to publish the school yearbook?a table of contents for the yearbooka graph showing the circulation of the yearbooka diagram showing each stepa picture of the yearbook staff Lucia is not yet 80 years old. each of her sons has as many sons as brothers. the combined number of lucias sons and grandsons equals her age, and her oldest grandson is 29. how old is lucia? place your numerical answer in the corresponding answer blank. In Richard Connell's short story "The Most Dangerous Game," the main character, Sanger Rainsford, is a former war hero. Which sentence from this excerpt hints at his time serving in the war? He had not been entirely clearheaded when the chateau gates snapped shut behind him. His whole idea at first was to put distance between himself and General Zaroff; and, to this end, he had plunged along, spurred on by the sharp rowers of something very like panic. Now he had got a grip on himself, had stopped, and was taking stock of himself and the situation. He saw that straight flight was futile; inevitably it would bring him face to face with the sea. He was in a picture with a frame of water, and his operations, clearly, must take place within that frame. Rainsford had dug himself in in France when a second's delay meant death. That had been a placid pastime compared to his digging now. The pit grew deeper; when it was above his shoulders, he climbed out and from some hard saplings cut stakes and sharpened them to a fine point. These stakes he planted in the bottom of the pit with the points sticking up. With flying fingers he wove a rough carpet of weeds and branches and with it he covered the mouth of the pit. Then, wet with sweat and aching with tiredness, he crouched behind the stump of a lightning-charred tree. In cognitive therapy, a therapist pays attention to the patients perception,___,reason, attention, and judgment. *FILL IN THE BLANK ... PLEASE HELPP* Which statements identify potential effects of accessing an unreliable mental health resource? CHECK ALL THAT APPLY. Health insurance might be fraudulently billed. Providers might not include certified professionals. Providers might charge a lot of money for services. Individuals might be taken advantage of for financial gain. Individuals might offer false help in the form of cures and treatment. please help me :))))) Suppose two companies own adjacent oil fields. under the two fields is a common pool of oil worth $60 million. for each well that is drilled, the company that drills the well incurs a cost of $4 million. each company can drill up to two wells. what is the likely outcome of this game if each company pursues its own self-interest?a. each company drills one well and experiences a profit of $26 million.b. each company drills one well and experiences a profit of $22 million.c. each company drills two wells and experiences a profit of $22 million.d. one company drills two wells and experiences a profit of $32 million; the other company drills one well and experiences a profit of $16 million. 2 parents with the gg have what percentage of producing offspring with that trait Why did Native Americans have to renegotiate treaties with the U.S. government after the Civil War?a) Many of them had fought for the Confederate Army, so they were perceived as an enemy of the nation. b) Because they had lost so many tribal members, they wanted to make new arrangements with the government.c) They had established new tribal leaders after the war and wanted the U.S. government to recognize them. d) They had challenged the old terms in court and had permission from the Supreme Court to make adjustments. Qu busc ella?Ella busqu el tesoro.Ella busc el tesoro.Ella buscaron el tesoro.Ella busca el tesoro. a man made lake is stocked with 10,000 fish. This population is expected to decline by an annual rate of 15%. Predict the fish population 5 years after the lake is stocked What happens during the first trimester?a.the fetus develops fully working eyes.b.the major organ systems have started developing.c.rhythmic breathing movements begin.d.contractions begin in the womb? This plot shows the number of cakes sold each day in aunt Alices cake shop last month.What number of cakes sold is an outlier?