What is the value of f(3) ?

Answer:

The correct option is;

[tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]

Step-by-step explanation:

The given parameters are

The equation of motion of one (the first) object is r = 4·cos(θ)

The equation of motion of the other (the second) object is r = -1 + 2·cos(θ)

Equating both equations gives;

4·cos(θ) = -1 + 2·cos(θ)

4·cos(θ) - 2·cos(θ) = -1

2·cos(θ) = -1

cos(θ) = -1/2

θ = Arccos(-1/2) = 120° = 2·π/3

Therefore, the two equations are equal when θ = 2·π/3 for which we have;

r = 4·cos(2π/3) = -2 and r = -1 + 2·cos(2π/3) = -2

∴ r = 4·cos(2π/3) = -1 + 2·cos(2π/3) = -2

The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore [tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]

Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex])

Given that ,

The first object is moving around the screen r = 4 cos(0)

The second object is moving around the screen r = -1 + 2cos(0)

We have to find ,

The coordinates represent a possible collision point of the objects.

According to the question,

Coordinate represent collision points to object ,

Equating both equations ;

4·cos(θ) = -1 + 2·cos(θ)

4·cos(θ) - 2·cos(θ) = -1

2·cos(θ) = -1

cos(θ) = -[tex]\frac{1}{2}[/tex]

θ = [tex]cos^{-1} (\frac{1}{2} )[/tex] = 120°

[tex]\theta[/tex] = [tex]\frac{-2\pi }{3}[/tex]

Therefore, the two equations are equal when θ = [tex]\frac{2\pi }{3}[/tex]

We have;

r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -2

And r = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex]) =

r = -2

r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex])

r = -2

The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore r = -2 and [tex]\theta = \frac{2\pi }{3}[/tex] .

Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex]) .

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Answer:

61

Step-by-step explanation:

first we set <B and <E equal to each other to find x (they are equal because it is a given in the phrase below the pics)

5x + 8 = 7x - 12

5x + 20 = 7x

20 = 2x

10 = x

now we know x is 10, so substitute it into an equation to find the measure of the vertex of the triangles

5(10) + 8 = 58

subtract 58 from 180 to find what the base angles are combined

180 - 58 = 122

since there are two congruent base angles (the base angles of isosceles triangles are always congruent), we have to divide 122 by 2 to find the measure of a base angle

122 ÷ 2 = 61

<F is a base angle, so <F is 61

Answer:

31

Step-by-step explanation:

y=kx

Answer:

The slope is 1/2

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=2-1/4-2

m=1/2

Answer:

The tens digit = 5

The units digit = 9

The two digit number is 59

Step-by-step explanation:

Let the tens digit be represented by x

The units digits be represented by y

In a two-digit number, the units digit is six less than three times the tens digit.

y = 3(x) - 6

y = 3x - 6

Four times the units digit minus five times the tens digit equals 11.

4(y) - 5(x) = 11

4y - 5x = 11

We substitute

4(3x - 6) - 5x = 11

12x - 24 - 5x = 11

Collect like terms

12x - 5x = 11 + 24

7x = 35

x = 35/7

x = 5

y = 3x - 6

y = 3(5) - 6

y = 15 - 6

y = 9

Hence,

The tens digit = 5

The units digit = 9

The two digit number is 59

Answer:

5=tens 9=units

Step-by-step explanation:

I think its this

Answer:

b = 1/4

Step-by-step explanation:

We will use 4 as a common denominator.

3 × 2 = 6        2 × 2 = 4

Now we have the equation 6/4 + b = 7/4

Asia is a chef in a restaurant. To prepare for dinner service, she chops 7 1/2 onions in 1/6 of an hour. Asia's rate of chopping onions is 30 onions per hour.

From the information given;

So, the onion is given in mixed fraction which can be converted to an improper fraction as: [tex]\mathbf{\dfrac{15}{2}\ onions}[/tex]

Now,

We can cross multiply the above two equations to determine the number of onions Asia will chop per hour as follows:

[tex]\mathbf{(x) \times \dfrac{1}{6} \ hours = \dfrac{15}{2} \ onions \times 1 \ hour}}[/tex]

Making (x) the subject of the formula:

[tex]\mathbf{(x)=\dfrac{ \dfrac{15}{2} \ onions \times 1 \ hour}{ \dfrac{1}{6} \ hours }}}[/tex]

[tex]\mathbf{(x)={ \dfrac{15}{2} \ onions } \times { \dfrac{6}{1} }}}[/tex]

(x) = 15 onions × 3

(x) = 30 onions per hour.

Therefore, Asia's rate of chopping onion is 30 onions per hour.

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If Asia chops 7 1/2 onions in 1/6 hour, therefore, using proportion, the rate of chopping onions per hour is: 45 onions per hour.

Applying the knowledge of proportion and fractions, we can determine Asia's chopping rate of onions per hour.

Given:

Using proportion, we have the following:

[tex]7\frac{1}{2} = \frac{1}{6} \\\\x = 1[/tex]

[tex]\frac{1}{6} \times x = 7\frac{1}{2} \times 1\\\\\frac{x}{6} = \frac{15}{2}[/tex]

[tex]\frac{x}{6} = \frac{15}{2}\\\\x = \frac{15}{2} \times 6\\\\x = 45[/tex]

Therefore, if Asia chops 7 1/2 onions in 1/6 hour, therefore, using proportion, the rate of chopping onions per hour is: 45 onions per hour.

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Answer:

P = 7/3 and q = 0

Step-by-step explanation:

The given parameters are;

The endpoints of the segment are, (3, -4) and (1, 2)

The points that trisect the given points are P and Q with coordinates (p, -2) and (5/3, q) respectively

Therefore, we have;

The first point of the trisection cuts 1/3 of the length from one point and the second point of the trisection cuts 2/3 of the length from the same point

The coordinates of P or Q = (3 - (3 - 1)/3, -4 - (-4 - 2)/3) = (7/3 , -2)

Therefore, given that the y-coordinate value of the derived point coincides with the y-coordinate value of the point P, (p, -2) and there is only one point with x = -2 on the line, we have that the coordinate of the point P is (p, -2) = (7/3 , -2)

∴ P = 7/3

Similarly we have the second point of the trisection, Q, given as follows;

We are already given the x-coordinate value of the point Q as the 5/3 in (5/3, q)

Point Q = (5/3, q) = (3 - 2×(3 - 1)/3, -4 - 2×(-4 - 2)/3) = (5/3 , 0)

Point Q = (5/3, q) = (5/3 , 0)

∴ q = 0.

Answer:

8x+(-27)=y

Step-by-step explanation:

To find an equation of a line, you use the formula mx+b=y

M=slope

x=x cooridnates

y=y coordinates

b=y intercept

Slope:

You use the formula y2-y1/x2/x1 to find slope.

5-(-3)/2-5

5+3/-3

8/-3

8

Y intercept:

8(5)+b==3

40+b=-3

b=-37

Equation: 8x+-37=y

The equation of the line that passes through each pair of points (5,-3), (2,5) is 3y = -8x+31

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a line passes through each pair of points (5,-3), (2,5)

We know that, the equation of a line passing through two points (x1, y1) and (x2, y2) is given by,

(y-y1) = (y2-y1)/(x2-x1)(x-x1)

Where, (y2-y1)/(x2-x1) is, representing the slope of the line.

Here, x1 = 5, x2 = 2 and y1 = -3, y2 = 5

Equation of the line =

(y+3) = (5+3)/(2-5)(x-5)

y+3 = -8/3(x-5)

3y+9 = -8x+40

3y = -8x+31

Hence, The equation of the line that passes through each pair of points (5,-3), (2,5) is 3y = -8x+31

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Answer:

X represents the value you can multiply with the slope to get the answer.

y = 0.007x

  = 0.007(6)

  = 0.042

Therefore, 0.042 inches of rain falls in 6 minutes.

Answer: [tex]2x+y^2[/tex]

Step-by-step explanation:

[tex]x\:+\:x\:+\:y\:\cdot \:y[/tex]

[tex]x+x+yy[/tex]

[tex]2x+yy[/tex]

[tex]2x+y^2[/tex]

Answer:

2(x)+[tex]y^{2}[/tex]

Answer:

You just do

Step-by-step explanation:

Answer:

just click the thing that says "Ask blah blah about this question..."

Step-by-step explanation:

Answer:

- 1.2+15.45=14.43

Step-by-step explanation:

Answer:

1/3x

Step-by-step explanation:

Subtract x by x and y by y to find the distance/difference

36            163

24,          127

= 12/36 = rise/run

Now reduce to find the slope, reduce until you can't anymore.

12/36

6/18

3/9

1/3 (that's your slope)

Answer:

$20,232.75

Step-by-step explanation:

I hope it helped

Answer:

is it multiple choice

Step-by-step explanation:

Answer:

x is 10 y is 5.8

Step-by-step explanation:

x=y+4.2=10

Answer:

c.

Step-by-step explanation:

$4 a ticket

12÷3=4

I hope this was helpful

Answer:

150

Step-by-step explanation:

maybe it could be like this

0.40x = 240

we could get x = 600

then 0.25x = 600 × 0.25 = 150

Answer:

what is a crown

Step-by-step explanation:

they should stop eating out

you need 10 8' planks of wood because 15x3= 45+9x4= 77, then 77÷8= 9.625, but you can't get .625 of a plank, so 10. hope you get a good grade!

Answer:

710 is the answer.

Step-by-step explanation:

7.1 x 10^2

10^2= 10 x 10 = 100

so,

7.1 x 100 = 710

Answer:

[tex]y=x+0.2x[/tex]

Step-by-step explanation:

Step one:

given data

we are told that Dillon paid $x for a haircut.

and gave a tip of 20% of the amount he paid, this is expressed as

=20/100*x

=0.2x

Let the total amount he paid, that is haircut plus tip be y

the expression for the total amount is

[tex]y=x+0.2x[/tex]

     here x represents the amount he paid

              0.2 represents 20% of the haircut

Answer:

Step-by-step explanation:

The answer is 64 because If you multiply 2x2x2x2x2x2 It equals 64

Answer:

12 beats per minute after 30minutes

Step-by-step explanation:

Since we are told by how much his heartrate increased in 20 minutes, we can simply calculate how much it increased in 10 minutes and add that amount to the current heart rate to know how much his heartrate increased after 30 minutes of working out. Since 10minutes would be half of the 20minutes we simply divide the beats per minute by 2.

8 / 2 = 4 beats per minute after 10 minutes

Now we simply add this to the beats per minute at the 20minute mark to calculate the beats per minute at 30minutes

8 + 4 = 12 beats per minute after 30minutes

Answer:

yes, correct me if im wrong

Step-by-step explanation:

No it is not a direct variation or A

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The equation can be used to find, x, the number of baskets Derek made on Saturday.

3x = 15

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of baskets made = 15

This was triple the number of baskets he made on Saturday.
This means,

3x = 15

Number of baskets made on Saturday = x

Now,

3x = 15

Divide both sides by 3.

x = 5

The number of baskets made on Saturday is 5.

Thus,

The equation can be used to find, x, the number of baskets Derek made on Saturday.

3x = 15

Option D is the correct answer.

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Answer:

A

Step-by-step explanation:

not sure.................pero tama sagot ko