Those who have guts and really think themselves math kings/queens , solve it

ANSWER

[tex]g(x) = \sqrt{x + 4} [/tex]

EXPLANATION

The parent square root function is

[tex]f(x) = \sqrt{x} [/tex]

The translation

[tex]g(x ) = \sqrt{x + k} [/tex]

Will shift the graph of f(x) k units to left.

The translation

[tex]g(x) = \sqrt{x -k} [/tex]

will shift the graph of f(x) to the right by k units.

Therefore if f(x) is shifted 4 units to the left its new equation is:

[tex]g(x) = \sqrt{x + 4} [/tex]

Shifting a function left involves adding a value to the x-component. Hence, shifting the square root parent function, F(x) = √x, to the left by 4 units results in a new function F(x) = √(x+4).

When a function is shifted horizontally, it impacts the input or the x-values. A shift to the left is represented by the addition of a value to the x-component of the function. Hence, to shift the square root parent function, F(x) = √x, to the left by 4 units, you would add 4 to 'x' in the function, which results in a new function F(x) = √(x+4). "This function represents the original square root parent function shifted 4 units to the left".

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Answer:

6:45

Step-by-step explain if she has to leave 45 minutes before you take away 45 from 7:30 giving you the time she would have to leave

Answer:

  646 child tickets are sold

Step-by-step explanation:

Let c represent the number of child tickets sold. Then (c-186) is the number of student tickets sold, and (c+234) is the number of adult tickets sold. The total number sold is ...

  (c -186) + c + (c+234) = 1986

  3c +48 = 1986 . . . simplify

  c + 16 = 662 . . . . divide by 3

  c = 646 . . . . . . . . . subtract 16

The number of child tickets sold is 646.

The number of child tickets sold is 646.

To find the number of child tickets sold at the theatre, we can define some variables and set up equations based on the information provided.

Let:

From the information given, we have the following relationships:

The total number of tickets sold is 1986:
x + y + z = 1986

There are 234 more adult tickets sold than child tickets:
z = y + 234

There are 186 more child tickets sold than student tickets:
y = x + 186

Now we can substitute the equations for z and y into the first equation:

This simplifies to:
x + 2y + 234 = 1986

Now, we substitute y using the equation y=x+186:

Replace y in the equation:
x + 2(x + 186) = 1752

This simplifies to:
x + 2x + 372 = 1752
3x + 372 = 1752

Now isolate x:
3x = 1752 − 372
3x = 1380
x = 31380​
x = 460

Now that we have the value for x, we can find y:

Finally, we calculate z to confirm:  

Now we can verify:
x + y + z = 460 + 646 + 880 = 1986

So the number of child tickets sold is y = 646.

Answer:

[tex] y^2 + 8y + 16 [/tex]

Step-by-step explanation:

[tex] (6y^2 + 2y + 5) - (5y^2 - 6y - 11) = [/tex]

The first set of parentheses is unnecessary, so it can just be removed.

[tex] = 6y^2 + 2y + 5 - (5y^2 - 6y - 11) [/tex]

To remove the second set of parentheses, you must distribute the negative sign that is to its left. It changes every sign inside the parentheses.

[tex] = 6y^2 + 2y + 5 - 5y^2 + 6y + 11 [/tex]

Now you combine like terms.

[tex] = 6y^2 - 5y^2 + 2y + 6y + 5 + 11 [/tex]

[tex] = y^2 + 8y + 16 [/tex]

Answer:

C

Step-by-step explanation:

Since y will have same value, y doesn't really matter. Thus,

We can solve for y in the 2nd equation as:

-3x - y = 4

-3x - 4 = y

Now we can plug it into the first and solve for x:

-9x + 4y = 8

-9x + 4(-3x - 4) = 8

-9x - 12x - 16 = 8

-21x = 8 + 16

-21x = 24

x = 24/-21

x = -8/7

Correct answer is C.

Answer: Option C

C-8/7

Step-by-step explanation:

We have the following equations

 [tex]-9x + 4y = 8[/tex] and [tex]-3x - y = 4[/tex]

We want to find a value of x that satisfies both equations and obtains the same value of y.

To find the value of x, clear the value of y in both equations

[tex]-9x + 4y = 8\\\\-9x + 4y -8 = 0\\\\-9x -8 = -4y\\\\y = \frac{9}{4}x +2[/tex]

------------------------------

[tex]-3x - y = 4\\\\\-3x -y - 4 = 0\\\\y = -3x -4[/tex]

Now solve both equations and solve for x.

[tex]\frac{9}{4}x +2 = -3x -4\\\\\frac{21}{4}x = -4-2\\\\\frac{21}{4}x = -6\\\\21x = -24\\\\x = -\frac{24}{21}\\\\x = -\frac{8}{7}[/tex]

The answer is [tex]x = -\frac{8}{7}[/tex]

Answer:

I believe it is C

Hope This Helps!     Have A Nice Day!!

Answer:

its

B.The graph of W(x) is 7 units to the right of the graph of f(x)

Answer:

Use combinations because order does not matter, 1001, 0.36

Step-by-step explanation:

Answer: Combination method is used for counting.  There are 1001 possible outcomes and there is probability of 0.36 of getting two girls and two boys are on the committee.

Step-by-step explanation:

Since we have given that

Total number of members = 14

Number of girls = 9

Number of boys = 5

We will use "Combination method " to count the compound probability.

So, the total number of possible outcomes is given by

[tex]^{14}C_4\\\\=1001[/tex]

The probability that two girls and two boys are on the committee is given by

[tex]\dfrac{^9C_2\times ^5C_2}{^{14}C_4}\\\\=\dfrac{360}{1001}\\\\=0.3596\\\\=0.36[/tex]

Hence, there are 1001 possible outcomes and there is probability of 0.36 of getting two girls and two boys are on the committee.

Answer:

24 girls.

Step-by-step explanation:

If the number of boys is x then:

x + 4/7 x = 66

x = 66  / 1 4/7

x = 66 *  7/11

= 6 * 7

= 42.

So the number of  girls is 66 - 42

= 24.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

The number of girls students is 24.

In the fifth grade at Lenape Elementary School, there are 4/7 as many girls as there are boys.

There are 66 students in the fifth grade.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

There are 66 students in fifth grade, and there is a 4:7 girl to boy ratio.

[tex]= \dfrac{66}{11}\\\\= 6[/tex]

Then,

the number of girls is = [tex]6 \times 4=24[/tex]

The number of boys is = [tex]6 \times 7 = 42[/tex]

Hence, the number of girls students is 24.

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Answer:

B

Step-by-step explanation:

Given a function of a parabola (quadratic) in the form f(x) = x^2, we have a translated function as:

g(x) = a(x-b)^2

Where

The function given is p(x) = 3(x-8)^2

So it means that it is a vertical stretch with a factor 3 and the graph is shifted horizontally 8 units right

the correct answer is B

Answer:

D

Step-by-step explanation:

√(-49)

Let's rewrite this as:

√(-1) √(49)

√49 is 7, and √-1 is i.  Therefore:

7i

Answer D.

The expression √(-49) can be rewritten using the Imaginary unit "i" as follows:

[tex]\sqrt(-49) = \sqrt(49 \times (-1)) = \sqrt49 \times \sqrt(-1) = 7i[/tex]

So, the correct answer is option D) 7i.

Here, rewrite the expression √(-49) using the imaginary unit "i," you can express it as the square root of (-1) multiplied by the square root of 49. This is because the square root of -1 is represented as "i."

[tex]\sqrt(-49) = \sqrt((-1) \times 49)[/tex]

Now, we can factor out the square root of 49, which is 7:

[tex]\sqrt(-1 \times 49) = \sqrt(-1) \times \sqrt(49) = i \times 7[/tex]

So, √(-49) can be expressed as 7i.

The correct answer is:

D) 7i

Thus, √(-49) is equal to 7i, indicating that it is a complex number with a real part of 0 and an imaginary part of 7. option D) 7i is correct choice .

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Answer:

the graph of y=4 x+3 is a straight line that passes through the point (0,3) and (\frac{-3}{4},0)

Step-by-step explanation:

The graph of the exponential function y = 4ˣ + 3 is attached below.

An exponential function is in the form:

y = abˣ

Where y, x are variables, a is the initial value of y and b is the multiplication factor.

Given an exponential function of y = 4ˣ + 3

The graph of the exponential function y = 4ˣ + 3 is attached below.

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Answer:

Any number between 36-49

Step-by-step explanation:

The number has to be higher then 35. It has to be less then 50 because any number 50 or above would be more then/equal to 35

Answer: x < 50

Explination:

The given equation is x - 15 < 35.

To solve you add 15 to both sides:

x - 15 + 15 < 35 + 15

And you are left with a simplified answer of x < 50.

Answer:

(C) 1 : 511

Step-by-step explanation:

Possible outcome for every throw = 2 (head or tail)

Total possible outcome for 9 throws

= 2⁹

= 512

Odd of getting all head

= 1 : 511

The odds in favor of getting all heads on nine coin tosses is 1 to 512.

The odds in favor of getting all heads on nine coin tosses can be calculated as the number of favorable outcomes divided by the number of possible outcomes. In this case, we want all nine coin tosses to result in heads, which is only 1 favorable outcome. The total number of possible outcomes for nine coin tosses is 2^9 = 512.

Therefore, the odds in favor of getting all heads on nine coin tosses is 1 to 512. Comparing this to the options given, the correct answer is A. 1 to 508.

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Answer:

[tex]f(x)=\dfrac{2x-1}{x+2}\\ \\f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]

[tex]f(x)=\dfrac{x-1}{2x+1}\\ \\f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]

[tex]f(x)=\dfrac{x+2}{-2x+1}\\ \\f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]

[tex]f(x)=\dfrac{2x+1}{2x-1}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]

[tex]f(x)=\dfrac{x+2}{x-1}\\ \\f^{-1}(x)=\dfrac{x+2}{x-1}[/tex] - extra

Step-by-step explanation:

1.

[tex]f(x)=y=\dfrac{2x-1}{x+2}\\ \\y(x+2)=2x-1\\ \\yx+2y=2x-1\\ \\yx-2x=-1-2y\\ \\x(y-2)=-1-2y\\ \\x=\dfrac{-1-2y}{y-2}\\ \\y=f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]

2.

[tex]f(x)=y=\dfrac{x-1}{2x+1}\\ \\y(2x+1)=x-1\\ \\2xy+y=x-1\\ \\2xy-x=-1-y\\ \\x(2y-1)=-1-y\\ \\x=\dfrac{-1-y}{2y-1}\\ \\y=f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]

3.

[tex]f(x)=y=\dfrac{x+2}{-2x+1}\\ \\y(-2x+1)=x+2\\ \\-2xy+y=x+2\\ \\-2xy-x=2-y\\ \\x(-2y-1)=2-y\\ \\x=\dfrac{2-y}{-2y-1}\\ \\y=f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]

4.

[tex]f(x)=y=\dfrac{2x+1}{2x-1}\\ \\y(2x-1)=2x+1\\ \\2xy-y=2x+1\\ \\2xy-2x=1+y\\ \\x(2y-2)=1+y\\ \\x=\dfrac{1+y}{2y-2}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]

5.

[tex]f(x)=y=\dfrac{x+2}{x-1}\\ \\y(x-1)=x+2\\ \\xy-y=x+2\\ \\xy-x=2+y\\ \\x(y-1)=2+y\\ \\x=\dfrac{2+y}{y-1}\\ \\y=f^{-1}(x)=\dfrac{x+2}{x-1}[/tex]

For this case we have by definition that the volume of the pyramid is given by:

[tex]V = \frac {A_ {b} * h} {3}[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

We have, according to the figure shown:

[tex]A_ {b} = 8 ^ 2 = 64 \ units ^ 2\\h = 6 \ units[/tex]

Then, replacing:

[tex]V = \frac {64 * 6} {3}\\V = \frac {384} {3}\\V = 128 \ units ^ 3[/tex]

Answer:

Option D

Answer:

The correct answer is option D.  128 units²

Step-by-step explanation:

Formula:-

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

To find the volume of pyramid

Here base side = 8 units and h = 6 units

Volume = (a²h)/3

 = (8² * 6)/3 = 8100/3 = 2700  units²

Therefore the correct answer is option D.  128 units²

Answer:

Option C: 90+90 Sq. Root of 2

Step-by-step explanation:

First we find the distance from second base to home plate.  This is the diagonal of the square, which splits it into two right triangles.

Each right triangle will have legs of 90 feet.  We use the  Pythagorean theorem to find the length of the diagonal (the hypotenuse of the right triangle):

a² + b² = c²

90² + 90² = c²

8100 + 8100 = c²

16200 = c²

Take the square root of each side:

√(16200) = √(c²)

Simplifying √16200, we find the prime factorization:

16200 = 162(100)

162 = 2(81)

81 = 9(9) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

100 = 10(10) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

√16200 = √(9²×10²×2) = 9×10√2 = 90√2

This means the distance from 1st to 2nd and then from 2nd to home would be

90 + 90√2

Answer:

d. ≈ 37,106 ft

Step-by-step explanation:

The angle of depression to the plane to the airport is the same as the angle of elevation from the airport to the plane. Therefore, the angle of elevation form the airport to the plane is 6°.

Notice that the height of the plane is the opposite side of the angle of elevation and the ground distance is the adjacent side of the angle of elevation. To find ground distance we need to use a trig function to relate the opposite side and the adjacent side; that trig function is tangent:

[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(6)=\frac{3900ft}{ground-distance}[/tex]

[tex]ground-distance=\frac{3900ft}{tan(6)}[/tex]

[tex]ground-distance=37106ft[/tex]

We can conclude that the plane's ground distance to the airport is approximately 37,106 feet

Answer:

216 degrees

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of the circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

Find the measure of the arc if the length of the arc is 12π in

Remember that

The circumference of a circle subtends a central angle of 360 degrees

so

by proportion

[tex]\frac{360}{20\pi}=\frac{x}{12\pi}\\ \\x=360*12/20\\ \\x= 216\°[/tex]

To find out how many apple pieces are in the bowl when 1/4 of 12 fruit pieces are apples, divide 12 by 4, which equals 3. So, there would be 3 apples in the bowl.

Understanding fractions is an important part of mathematics. In this scenario, we have a total of 12 pieces of fruit in a bowl and we want to find out how many of those are apple pieces if 1/4 of the fruit pieces are apples.

Since there's a total of 12 pieces, we divide this number into 4 equal parts (fractions strips) to determine what one quarter (1/4) of the bowl would contain.

To visualize this, you can draw a rectangle and divide it into 4 equal horizontal sections (fractions strips), because 1/4 means one part out of four equal parts. When you divide 12 by 4, you get 3. So, each section of your fraction strip would represent 3 pieces of fruit. This means that if 1/4 of the pieces are apples, there are 3 apples in the bowl.

Answer:

B. 13.26

Step-by-step explanation:

To go from the Degree-Minute-Second (DMS) system to a numeric one, we simply use this formula:

numeric = d + (min/60) + (sec/3600)

Where you take the degree number as is (13 in our case), then you divide the number of minutes by 60 (15 in our case) and the number of seconds by 3600 (36 in our case) and you add everything together.

So, if we plug in our numbers, we have

numeric = 13 + (15/60) + (36/3600)

numeric = 13 + 0.25 + 0.01

numeric = 13.26

Answer:

$3.55/workout

Step-by-step explanation:

Total cost:  $39 + ($27.50/month)(12 months) = $369

Number of visits per year:  (2 visits/week)(52 weeks/year) = 104 visits/year

Dividing the total cost by 104 visits/year results in:

 $369

--------------- = 3.55

104 visits

Each workout cost him $3.55. Each workout cost is obtained by the total cost and the number of the visit per year.

It is the sum of the variable cost and the fixed cost. The total cost is the minimum dollar cost of producing some quantity of output.

Registration fee = $39

Monthly fee = $27.50

No of visit a week for a year= 2

Total cost is found as;

Total cost = registration fee+monthly fee ×no of month

Total cost =  $39 + ($27.50/month)(12 months)

Total cost =$369

Number of visits per year= visits/week×no of week

Number of visits per year= (2 visits/week)(52 weeks/year)

Number of visits per year = 104 visits/year

When you divide the entire cost by 104 visits per year, you get:

Each workout cost = $369/104

Each workout cost =$3.55

Hence, each workout cost him $3.55

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Answer:

Step-by-step explanation:

1 heads

1 tails

2 heads

2 tails.

That's all you can write given the constraint.

Answer:

  11 m by 18 m

Step-by-step explanation:

The area is the product of two adjacent sides of a rectangle. The perimeter is twice the sum of two adjacent sides, so that sum is (58 m)/2 = 29 m.

We want to find two factors of 198 that sum to 29.

  198 = 1·198 = 2·99 = 3·66 = 6·33 = 9·22 = 11·18

Of these factor pairs, only the last one has a sum of 29.

The dimensions of the pool are 11 meter by 18 meters.

Answer:

240

Step-by-step explanation:

Volume of the cylinder

= π(4)²(10)

= 160π in³

Volume of the cone

= 1/3 π(1)²(2)

= 2/3 π in³

Number of cones

= 160π ÷ 2/3 π

= 240

By calculating the volumes of both the original cylinder and one of the cones, we can determine that 80 solid right circular cones can be formed from the melted cylinder.

The question involves calculating the number of solid right circular cones that can be formed from melting and recasting a solid metal cylinder with given dimensions. First, we need to calculate the volume of the original cylinder and then the volume of one of the right circular cones, followed by dividing the volume of the cylinder by the volume of a cone to determine how many cones can be formed.

Step 1: Calculate the Volume of the Cylinder

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height (altitude). For the cylinder with a 4-inch radius and 10-inch altitude, the volume is V = π(4²)(10) = 160π cubic inches.

Step 2: Calculate the Volume of a Cone

The formula for the volume of a cone is V = ⅓πr²h, where r is the radius and h is the height. For a cone with a 1-inch radius and 2-inch altitude, the volume is V = ⅓π(1²)(2) = ⅓π cubic inches.

Step 3: Determine the Number of Cones Formed

To find the number of cones that can be formed, divide the volume of the cylinder by the volume of a cone: Number of cones = (160π) / (⅓π) = 80. Therefore, 80 solid right circular cones can be formed from the melted cylinder.

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° × (n - 2) ← n is the number of sides

Here n = 8 ( octagon ), hence

sum = 180° × 6 = 1080°

let the measure of 1 congruent angle be x

Then sum the 8 angles and equate to 1080

100 + 120 + 140 + 5x = 1080

360 + 5x = 1080 ( subtract 360 from both sides )

5x = 720 ( divide both sides by 5 )

x = 144

Thus each of the 5 congruent angles is 144°

Answer:

Step-by-step explanation:

The information given in the problem statement lets you write two equations relating box weights (L for the large box weight; S for the small box weight).

  2L +3S = 78 . . . . . . weight of the first collection of boxes

  6L +5S = 180 . . . . . weight of the second collection of boxes

We can subtract 3S from the first equation and multiply it by 3 and we have ...

  2L = 78 -3S . . . . . . subtract 3S [eq3]

  6L = 234 -9S . . . . . multiply by 3

Now we have an expression for 6L that can substitute into the second equation:

  (234 -9S) +5S = 180

  234 -4S = 180 . . . . . . . . simplify

  54 -4S = 0 . . . . . . . . . . . subtract 180

  13.5 -S = 0 . . . . . . . . . . . divide by 4

  13.5 = S . . . . . . . . . . . . . add S

From [eq3] above, we can now find L.

  2L = 78 -3(13.5) = 37.5

  L = 37.5/2 = 18.75

The weight of the large box is 18.75 kg; the small box is 13.5 kg.

_____

A graphing calculator can provide an alternate means o finding the solution.

Answer:

There's a lot of them.

There are many different ways to calculate [tex]\pi[/tex]. The ones used by computers to generate tons of digits are usually infinite series.

The series that has been prominent in recent records for the most digits of pi is the Chudnovsky algorithm.

The algorithm is this:

[tex]\frac{1}{\pi}=12\sum_{k=0}^{\infty}\frac{\left(6k\right)!\left(545140134k+13591409\right)}{\left(3k\right)!\left(k!\right)^3\left(640320\right)^{3k+\frac{3}{2}}}[/tex]

For faster performance, it can be simplified to this:

[tex]\frac{426880\sqrt{10005}}{\pi}=12\sum_{k=0}^{\infty}\frac{\left(6k\right)!\left(545140134k+13591409\right)}{\left(3k\right)!\left(k!\right)^3\left(-262537412640768000\right)^k}[/tex]

Other algorithms have been used, but right now this is the one that is being used to set the recent records.

There are also some approximations that are used because they are very easy to calculate.

first, [tex]\frac{22}{7}[/tex] can be used to calculate a fairly accurate pi, but a better rational approximation is [tex]\frac{355}{113}[/tex] This fraction is actually accurate to 6 digits and it is the best approximation of [tex]\pi[/tex] in simplest form and with a denominator below 30,000.

There are several other approximations and if you want to learn more I would recommend looking at the Wikipedia page which has tons of algorithms for pi.

Answer:

36

Step-by-step explanation:

The 5 part of the ratio represents 60 girls.

Divide 60 by 5 to find the value of one part of the ratio

60 ÷ 5 = 12 ← value of 1 part of the ratio

The 3 part of the ratio represents the number of boys, hence

3 × 12 = 36 ← number of boys

I took the test, (for this particular graph) it was -1.5.

Answer:

The correct option is 1.

Step-by-step explanation:

The formula for residual value is

[tex]\text{Residual Value = Observed Value - Estimated value}[/tex]

In the given graph points represents the observed value and the line represents the expected or estimated value.

From the given graph it is clear that the observed value at x=5 is 5.5 and the estimated value at x=5 is 7.

[tex]\text{Residual Value}=5.5-7[/tex]

[tex]\text{Residual Value}=-1.5[/tex]

The residual value is -1.5, therefore the correct option is 1.

Start with

[tex]\vec v=x\,\vec\imath+y\,\vec\jmath[/tex]

as a template for the vector [tex]\vec v[/tex]. Its magnitude is 4, so

[tex]\|\vec v\|=\sqrt{x^2+y^2}=4[/tex]

Its component in the [tex]\vec\imath[/tex] direction is twice the component in the [tex]\vec\jmath[/tex] direction, which means

[tex]x=2y[/tex]

So we have

[tex]\sqrt{(2y)^2+y^2}=\sqrt{5y^2}=4\implies y^2=\dfrac{16}5\implies y=\pm\dfrac4{\sqrt5}[/tex]

and

[tex]x=\pm\dfrac8{\sqrt5}[/tex]

Lastly, rationalize the denominator:

[tex]\dfrac1{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{\sqrt5}5[/tex]

So we end up with two possible answers,

[tex]\vec v=\pm\left(\dfrac{8\sqrt5}5\,\vec\imath+\dfrac{4\sqrt5}5\,\vec\jmath\right)[/tex]

Final answer:

The vector v with a magnitude of 4 and i-component being twice the j-component can be found by solving for y in the equation of magnitude based on the given conditions and then determining the i and j components accordingly. The result is the vector v = (8√5 i + 4√5 j) / 5.

Explanation:

To find a vector v whose magnitude is 4, and whose i-component is twice its j-component, we can let the i-component be 2y and the j-component be y. Using the Pythagorean theorem for two-dimensional vectors, we can write the equation for magnitude as v = √((2y)^2 + y^2). Given that the magnitude is 4, the equation becomes:

4 = √(4y^2 + y^2)

4 = √(5y^2)

16 = 5y^2

y^2 = ⅔

y = √(⅔)

y = √(⅔)

y = √(⅔)

y = √(⅔)

y = √(⅔)

y = √(⅔)

(2.0 s) gives us the direction in unit vector notation. The magnitude of the acceleration is à(2.0 s)| = √√5.0² + 4.0² + (24.0)² = 24.8 m/s².

Using the value of y we calculated, the components of vector v are:

i-component = 2y = 2(⅔) = 8√5 / 5

j-component = y = ⅔ = 4√5 / 5

So the vector v can be expressed as v = (8√5 i + 4√5 j) / 5.