Normalize the following vectors.a) u=15i-6j +8k, v= pi i +7j-kb) u=5j-i , v= -j + ic) u= 7i- j+ 4k , v= i+j-k

Answers

Answer 1

The normalized vector is:

V[tex]_{hat}[/tex] = v / |v| = (1/√3)i + (1/√3)j - (1/√3)k

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

a) To normalize the vector u = 15i - 6j + 8k, we need to divide it by its magnitude:

|u| = sqrt(15² + (-6)² + 8²) = sqrt(325)

So, the normalized vector is:

[tex]u_{hat}[/tex] = u / |u| = (15/√325)i - (6/√325)j + (8/√325)k

Similarly, to normalize the vector v = pi i + 7j - kb, we need to divide it by its magnitude:

|v| = √(π)² + 7² + (-1)²) = √(p² + 50)

So, the normalized vector is:

[tex]V_{hat}[/tex] = v / |v| = (π/√(p² + 50))i + (7/√(p² + 50))j - (1/√(p² + 50))k

b) To normalize the vector u = 5j - i, we need to divide it by its magnitude:

|u| = √(5² + (-1)²) = √(26)

So, the normalized vector is:

[tex]u_{hat}[/tex] = u / |u| = (5/√(26))j - (1/√(26))i

Similarly, to normalize the vector v = -j + ic, we need to divide it by its magnitude:

|v| = √(-1)² + c²) = √(c² + 1)

So, the normalized vector is:

[tex]V_{hat}[/tex] = v / |v| = - (1/√(c² + 1))j + (c/√(c² + 1))i

c) To normalize the vector u = 7i - j + 4k, we need to divide it by its magnitude:

|u| = √(7² + (-1)² + 4²) = √(66)

So, the normalized vector is:

[tex]u_{hat}[/tex] = u / |u| = (7/√(66))i - (1/√(66))j + (4/√(66))k

Similarly, to normalize the vector v = i + j - k, we need to divide it by its magnitude:

|v| = √(1² + 1² + (-1)²) = √(3)

So, the normalized vector is:

[tex]V_{hat}[/tex] = v / |v| = (1/√(3))i + (1/√(3))j - (1/√(3))k

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Related Questions

Find the surface area of the prism. Round to the nearest tenth if necessary.

Answers

Answer:

480

Step-by-step explanation:

First, lets solve for the area of the 3 rectangles in the prism

One can be found by doing 17*9. The other, 8*9, the last 15*9

Next, lets solve for the 2 triangles. This is found with...

1/2(8)(15). This turns out to be 60, and we multiply that by 2 since there are 2 of those triangles.

Add everything up:

72+153+135+120 = 480

Line ab passes through points a(-6,6) and b(12,3). if the equation of the line is written in slope-intercept form, y=mx+b, then m= -1/6. what is the value of b?

Answers

Answer: 5

Step-by-step explanation:

We have the equation of the line is of the form [tex]y=-\frac{1}{6}x+b[/tex].

Substituting in the coordinates (12,3), we get that:

[tex]3=-\frac{1}{6}(12)+b\\\\3=-2+b\\\\b=5[/tex]

Which of the following is an arithmetic sequence where a₁ = 9 and d= 7?

A) 9, 16, 23, 30, 37, ...
B) 0, 9, 18, 27, 36,...
C) 7, 16, 25, 34, 43,...
D) 0, 7, 14, 21, 28, ...

Answers

Answer:

Option A

Step-by-step explanation:

Arithmetic sequence:

  In a arithmetic sequence, difference between any two consecutive term is constant.

  a₁ = 9  & d = 7

         t₁ = 9

         t₂ = a₁ + d

             = 9 + 7

             = 16

         t₃ = t₂ + d = 16+ 7

            = 23

        t₄ = t₃ + d

            = 23 + 7

            = 30

        t₅ = t₄ + d

           = 30 + 7

           = 37

9,16,23,30,37,.......

Katelynn is excited about her trip to Chicago with her orchestra. She needs to raise $500 in order to go. She decides to make and sell scarves in order to fund her trip. In order to make each scarf, she will need $3 worth of yarn. If she plans on making 100 scarves, how much must she charge for each scarf in order to be able to pay for her trip?

Answers

Answer:

$8 each scarf

Explanation:

Let the selling price for each scarf be x,

Formula:

unit amount(selling price - cost price) = total profit

Stepwise:

100(x - 3) = 500

100(x) - 100(3) = 500

100x - 300 = 500

100x = 500 + 300

100x = 800

x = 8

which of the following can be used to support the idea that the set of polynomials is closed under multiplication?

A) (5x-1)(3x^2+4x)
B) (9x^-3-5)(2x-17)
C) (10x^0.5)(5x^0.5+4)
D) (2x^-1-5x^4)(7x-2^-5)

Answers

The polynomial which can be used to support the idea that the set of polynomials is closed under multiplication is: A. (5x - 1)(3x² + 4x).

What is a polynomial?

A polynomial can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:

AdditionSubtractionMultiplication

In Mathematics, a set is considered as closed under a multiplication operation, if the multiplication performed on two (2) elements of the set produces an element of the same set.

Note: The exponents of the variables are added when multiplying polynomials in accordance to the rules of exponents.

For option A, we have:

P = (5x - 1)(3x² + 4x)

P = 15x³ - 3x² + 20x² - 4x

P = 15x³ - 23x² - 4x.

For option B, we have:

P = (9x⁻³ - 5)(3x - 17)

P = 27x⁻² - 15x - 153x⁻³ + 85.

In conclusion, we can infer and logically deduce that the polynomial (5x - 1)(3x² + 4x) can be used to support the idea that the set of polynomials is closed under multiplication.

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What is the factored form of 27 - 530?
(2 - 10 ) ( - 590) (9 - 510)
( 20 + 1820م + 18 ) ( 10 - 2) -
O
O
0
(2 - 10) ( 9 + 9 10 + 510)
(2 - 10 ) ( 18 + 2 510 + 20 )

Answers

It’s the last choice

PLEASE HELP!!! THIS IS TIMED!!! PLEASE HELP ASAP!! How many solutions does this system have?

2 x minus 3 y = 10. Negative 4 x + 6 y = negative 20.

one

two

an infinite number

no solution

Answers

Answer:

No solution

Step-by-step explanation:

The equations:

2x – 3y = 10 → equ(1)

–4x + 6y = 20 → equ(2)

Using elimination method, and solving with y, we have:

3( –4x + 6y = 20) → equ(3)

6( 2x – 3y = 10) → equ(4)

Opening the bracket, we have:

–12x + 18y = 60

+12x – 18y = 60

From the above, we can see that both x and y are now eliminated, thereby giving us: 0 = 120 which makes no sense to me as it looks incorrect.

Therefore, there is no solution to the given equation.

I hope this helps

Answer:

One

Step-by-step explanation:

The probability of correctly rejecting the null hypothesis when the null hypothesis is false is the _____.

Answers

The probability of correctly rejecting the null hypothesis when the null hypothesis is false is the power

How to complete statement?

From the question, we have the following highlights

Null hypothesis is falseNull hypothesis is correctly rejected

The statement that represents the probability of the above highlights is power

Hence, the statement that completes the blank is power

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There is a number that if you subtract 9 from it first, and then divide that total by 6, you get 7. What's the number?​

Answers

Answer:

51

Step-by-step explanation:

Translate the problem into an equation and solve the equation.

(x - 9)/6 = 7

x - 9 = 42

x = 51

Answer: 51

Answer:

51

Step-by-step explanation:

Create an equation.

[tex]\frac{(x-9)}{6} = 7[/tex]

Multiply 6 to both sides.

x-9 = 42

Add 9 to both sides.

x=51

To check if this is correct follow the steps given in the question.

51-9=42

42÷6=7

It is correct.

Hope this helps!

If joe travels 434 miles in 7 hours, how far will he travel in 10 hours at the same speed?

Answers

He travels 620miles at the same speed.

Given that joe travels 434 miles in 7 hours.

An object's speed is determined by how quickly it moves. It is the distance a body travels in one unit of time.

Firstly, we will find the speed when the distance is 434 miles and the time is 7 hours by using the formula

Speed=Distance/Time

Substitute the values in the formula, we get

Speed=434miles/7 hours

Speed=62 miles/hour

Now, we will find the distance when time is 10 hours, we get

62=distance/10

Multiply both sides by 10, and we get

62×10=(distance/10)×10

620miles=distance.

Hence, in 10 hours at the same speed, he travels when joe travels 434 miles in 7 hours is 620miles.

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A)x=45
B)x=90
C)x=20
D)x=4.5

Answers

Answer:

x=4.5

Step-by-step explanation:

We know that if all sides are congruent then all angles must also be congruent, therefore you can solve for x with the following equation:

[tex]20x=90[/tex]

Solve

[tex]x=4.5[/tex]

Complete the following conversions. i) 1 mm = m ii) mm = 1 m iii) 1 cm = m iv) cm = 1 m v) 1 km = m vi) km = 1 m vii) 1 cm = mm viii) cm = 1 mm

Answers

The unit conversion for the given values are explained below.

What is unit conversion?

Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

The following measurements: length, weight, capacity, temperature, and speed are all measured in units.

Some basic unit conversions are-

1 Km = 1000 m1 m = 100 cm1 m = 1000 mm1 cm = 10 mm

There are two methods to convert the units

To convert smaller unit into larger divide the number by conversion factor.To convert larger value into smaller value multiply by the conversion factor.

The unit conversion for the following factors are-

i) 1 mm = _ m

Here, conversion is from smaller to larger. So, divide by conversion factor.

  1 mm = (1/100)m

ii) _ mm = 1 m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  1000 mm = 1 m

iii) 1 cm = _ m

Here, conversion is from smaller to larger. So, divide by conversion factor.

   1 cm = (1/100)m

iv) _ cm = 1 m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  100 cm = 1 m

v) 1 km = _m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  1 km = 1000 m.

vi) _ km = 1 m

Here, conversion is from smaller to larger. So, divide by conversion factor.

(1/1000) km = 1 m.

vii) 1 cm = _mm

Here, conversion is from larger to smaller. So, multiply with conversion factor.

   1 cm = 10 mm

viii) _cm = 1 mm

Here, conversion is from smaller to larger. So, divide by conversion factor.

   (1/10) cm = 1 mm.

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FIRST PERSON TO ANSWER GETS BRAINLIEST OR FIVE STARS Define the domain and range of the function.

Domain:

Range:

Answers

Answer:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

The domain are the x-values included in the function (the horizontal axis).

The range are the y-values included in the function (the vertical axis).

The two arrows on the ends of the line (pointing upwards and downwards respectively) indicate that the function goes in those direction for infinity. Therefore, if there are an infinite amount of y-values, the range is (-∞, ∞).

While the slope is quite steep, there is still a slope and slowly "expands" the line on the horizontal axis. Because there is no limit to the y-values, the domain will also expand infinitely. Therefore, the domain is also (-∞, ∞).

Answer:

Domain: All real numbers (interval notation: [tex](-[/tex]∞, ∞[tex])[/tex]

Range: All real numbers (interval notation: [tex](-[/tex]∞, ∞[tex])[/tex].

Step-by-step explanation: The domain of a graph is all the x-values where the line touches or will eventually touch.

The range of a graph is like the domain, but it is all the y-values where the line touches or will touch.

In a linear function in the form y = mx + b or ax + by = c, the domain and range will always be "all real numbers" and the interval will always be (-∞,  ∞). This makes sense since a line always goes on forever (unless it's piecewise or an inequality.) So the line will eventually meet every single x and y value on the xy graph.

A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.

The constant of proportionality is
.
The equation that represents this proportional relationship is
.

Answers

The equation of constant of proportionality will be y = 2.5x.

Given A 2-column table with 3 rows. Column 1 has entries 2, 4, 5. Column 2 has entries 5, 10, 12.5.

Equation of two variables look like ax+by=c. It can be a linear equation,quadratic equation,cubic equation.

Equation from two points can be found out by putting the values of points in the formula given below:

[tex](y-y_{1})=(y_{2} -y_{1} /x_{2} -x_{1} )*(x-x_{1} )[/tex] in which [tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} )[/tex] are the end points of the line.

Equation of constant proportionality looks like:

k=y/x

in which k is slope which is to be find out according to the same formula as we find in the equation of line.

Slope from (2,5),(4,10) is (10-5/4-2)

=5/2

=2.5

Put the value of k=2.5 in formula of slope.

2.5=y/x

2.5x=y

y=2.5x.

Hence the equation of constant of proportionality is y=2.5x.

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What are the ratios for sin A and cos A? The diagram is not drawn to scale.

Answers

Answer:

C

Step-by-step explanation:

Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).

Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).

Which of the following is equivalent to 5 squareroot of 13 3

Answers

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

What is equivalent to 5 sqrt 13³ ?

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]

Hence,

[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

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Find the area of the figure

Answers

Answer:

100

Step-by-step explanation:

Lets first find the area of the greater square:

[tex]8*14=112[/tex]

And now the area of the cut inside of the square:

[tex]3*4=12[/tex]

Now subtract the area cut from the area of the greater square:

[tex]112-12=100[/tex]

Which ordered pair is a solution to the system of linear equations? 2x 3y= 6 –3x 5y = 10

Answers

The given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

In the question, we are asked for the ordered pair, which is the solution to the system of equations:

2x + 3y= 6 ... (i)

–3x + 5y = 10 ... (ii).

To solve for the solution to the system of equations, we use the elimination method.

We multiply (i) by 3, and (ii) by 2, and then add the resultant equations to eliminate x as follows:

 6x + 9y = 18 {(i) * 3}

-6x + 10y = 20 {(ii) * 2}

_____________

19y = 38,

or, y = 38/19 = 2.

Substituting, y = 2, in (i), we get:

2x + 3y = 6,

or, 2x + 3(2) = 6,

or, 2x + 6 = 6,

or, 2x = 6 - 6 = 0,

or, x = 0/2 = 0.

Thus, the given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

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The complete question is:

"Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

(0,2)

(2,0)

(3,2)

(2,3)"

If point E is the midpoint of and point D is the midpoint of , which expression represents the value of s

Answers

The length of ED is half the length of AB.

What is the length?Distance is measured by length. Length is a quantity with the dimension distance in the International System of Quantities. Most measurement systems use a base unit for length from which all other units are derived. The meter is the foundation unit of length in the International System of Units.

Reasons:

The given parameters are;

In ΔABC, point E is the midpoint of AC

The midpoint of BC is the point D

Segment ED = s

Segment CE = p

Segment EA = r

Segment CD = q

Segment DB = t

Segment ED = s

Segment AB = u

Required:

The expression that represents the value of [tex]s[/tex].

Solution:

CE = 0.5 × AC Definition of midpoint

CD = 0.5 × CB Definition of midpoint

Therefore, we have;

[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]

Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;

ΔABC is similar to ΔCDE by Side-Angle-Side similarity

Which gives;

[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]

ED = s and AB = u which gives;

[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]

[tex]\frac{s}{u} =\frac{1}{2}[/tex]

Which gives:

[tex]s=\frac{1}{2} *u[/tex]

The expression that represents the value of s is; s = one-half u

Therefore, the length of ED is half the length of AB.

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The question you are looking for is here:

If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u

Help me please 10 pts for you mark you brainliest

Answers

Answer 1: A and C

Step-by-step explanation:

Use distribution law to see which answer match the equation at the top.


Answer 2: 16q + 4

10q and 6q are like terms

10q + 6q = 16q

+

5 - 1

Answer:

Hello,

Step-by-step explanation:

page 1:

60-36j=12(5-3j) answer C
=6(10-6j) answer A

page 2:

10q+5+6q-1=16q+4=4(4q+1)

page 3:

24j-16=8(3j-2)

page 4:

10h+30+50j=10*(h+3+5j) answer B
=2*(5h+15+25j) answer C

=5(2h+6+10j) not A  nor D

Jeri finds a pile of money with at least $200. If she puts $80 of the pile in her left pocket, gives away 1/3 of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $200 of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)

Answers

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

How to solve Inequality Word Problems?

We are told that Jeri finds a pile of money with at least $200.

Now, let x be  the additional amount over the  original amount of $200.

The greater side of the  inequality will be expressed as;

Original  pile  =  (200 + x)

After  she gives away $80 and as such she has;  (120 + x)

And  she gives (1/3)  of  this away  which means she will have;

=  (1/3) (120 + x)

Thus, she  must  have  (2/3)  of this left

=  (2/3)(120 + x) = amount in her right pocket

The lesser  side of the inequality is expressed as;

(x + 200)  -  200   =   x

Thus, we now have  that;

2[120 + x ]/3  >  x

240 + 2x  >  3x

240 > 3x - 2x

240 > x

x < 240

Thus, we can conclude that the original  amount could be on the interval   (200, 440)

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

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Help me please



6. Find the LCM of 22a³b³c4 and 55abc.
O 110abc
O 77a³b³c¹
O 110a³b³c4
O 11a³b³c4

Answers

110a3b3c4 is yours answer.

What is the slope of the line represented by the values in the table?
X
10
2
3
7
20
O-2
7-7
12
02
y
14
-2
0
8
34

Answers

Answer: 2

Step-by-step explanation:

[tex]\frac{-2-14}{2-10}=\frac{-16}{-8}=\boxed{2}[/tex]

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.

Isosceles triangles K I T and K E T are connected at side K T. The length of K T is 10 inches. The length of sides K E and E T are 8 inches. The lengths of sides K I and I T are 6 inches.

Heron’s formula: Area = StartRoot s (s minus a) (s minus b) (s minus c) EndRoot

How much material is used for the entire kite, quadrilateral KITE? Round to the nearest square inch.
31 square inches
34 square inches
48 square inches
62 square inches

Answers

The amount of material needed for the entire kite is 48 square inches

How to determine the amount of material?

The given parameters:

KI =6 inches

ET = 8 inches

KT=10 inches

Area of ΔKIT = 17 square inches

Start by calculating the area of the bottom triangle using:

A = 0.5 * Base * Height

This gives

A = 0.5 * 10 * 6

Evaluate

A = 30

The amount of material is

A = 30 + 17

A = 47

Hence, 48 square inches of material is used for the entire kite,  quadrilateral KITE

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What are the missing side lengths for the triangle?

Answers

Answer:

[tex]BC=5\sqrt{2}[/tex], [tex]AC=5\sqrt{4}[/tex]

Step-by-step explanation:

In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:

[tex]BC=5\sqrt{2}[/tex]

To find the hypotenuse we must multiply the shortest side by [tex]\sqrt{2}[/tex], both sides are equal so it doesn't matter which we multiply.

[tex]AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}[/tex]

Which statement is the most appropriate comparison of the spreads?

Answers

Option D. The most appropriate comparison for the spread is that the interquartile range for town A, 15 degrees is less than that of B.

How to solve for the interquartile range

The inter quartile is solved as Q3 - Q1

This is seen as

For Town A,

30 - 15 = 15 degrees

For town B

40 - 20 = 20 degrees.

Hence we can see that 15 is less than 20, so town A is less than town B. The answer is option D.

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Arnold paid R2 599,99 for a car sound system in 1997 Assuming an average inflation rate of 7% per annum what did he pay for a sound system with the equivalent value in 2014

Answers

The value of the car in 2014 is 154709

How to determine the value?

The given parameters are:

Initial, a = 599,99

Rate, r = 7%

The value of the car in t years is

Value = a * (1 + r)^t

This gives

Value = 59999 * (1 + 7%)^t

2014 is 17 years from 1997.

So, we have:

Value = 59999 * (1 + 7%)^14

Evaluate

Value = 154709

Hence, the value of the car in 2014 is 154709

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1. The perimeter of a rectangle is 16cm, and the area of the same rectangle is 8cm^2. What is the diagonal length of the rectangle?
2. Kendrick rides his bike x miles per hour to school and it takes him x + 15 minutes to get there. If Kendrick lives 5.4 miles from school, how many minutes does it take for Kendrick to ride to school?

Answers

Answer:

Step-by-step explanation:

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d

Answers

The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).

What is the principle of pendulum?

As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.

Calculation for the cosine function-

The given function is: cosine function, d = acos(bt).

As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.

The total time 't' by the pendulum is 2 sec.

Calculate the angular speed of the pendulum by-

ω = 2[tex]\pi[/tex]f

   = 2[tex]\pi[/tex]×(1/2)

ω = [tex]\pi[/tex] which is 'b' value of the given function.

As given, the distance of the pendulum from the centre is half of the total distance.

a = 12/2

a = 6

Substitute the obtained values in the cosine function, d = acos(bt),

d(t) = 6cos([tex]\pi[/tex]t)

Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is  d(t) = 6cos([tex]\pi[/tex]t).

To know more about the basic principle of the pendulum, here

https://brainly.com/question/13868386

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The complete question is -

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).

Answer:

a=6

The period is 2 seconds.

b=pi

t=0.5

d=4.243

Step-by-step explanation:

Can someone help me

Answers

Answer:

1. y = 0

2. f(x) has a horizontal asymptote at y=3/2

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

There is a horizontal asymptote at y = 0 because the degree of the x value in the denominator is greater than the degree of the numerator (since it doesn't exist in the numerator, it counts as 0).

The second question does not have a slant asymptote.

The degree of both numerator and denominator are equal, so the horizontal asymptote is the quotient of the leading coefficients. So, it's 3 divided by 2.

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