MATHS GCSE VECTORS
PLS HELP!!!! URGENT

The length of the shortest path is 44.69cm.

To find the length of the shortest path, we need to calculate the distance between the two points on the rim of the conical cup where the spider and the fly are located. Since the cone is symmetric, we can find the distance by considering a cross-section of the cone through the center of the cup.

In this cross-section, the spider and the fly are located on a circumference of radius 18 cm (half of the diameter of the cone). The distance between the spider and the fly is one-third of this circumference, or (2pi18 cm)/3 = 12*pi cm.

However, since the cone is 24 cm deep, the shortest path between the spider and the fly is not a straight line, but a curved path along the surface of the cone. To find the length of this path, we need to use the Pythagorean theorem to find the distance between the two points on the surface of the cone.

The height of the cone is 24cm, and the distance between the two points on the circumference is 12pi cm. Using the Pythagorean theorem, we can calculate the length of the shortest path as the square root of (12pi)^2 + 24^2 = 12pi cm + 576 = √(144π^2+ 576)cm=44.69 cm.

So, the length of the shortest path is √(144*π^2+ 576)cm = 44.69cm

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The data points to use is based on two companies knowledge to accomplice.

Here in this question we have been given an example of our time in a school team in which you have to realize on data to convince a group about the recommendation.

Here we also know that when we were making any recommendation to convince a group we have to keep its positive wherever we response to a question about the time you had to convince someone to do something your way.

Here we have also know that you may be tempted so may be tempted to put a negative spin on situation.

So, in order to accomplish the we have to accomplice and will have knowledge two companies knowledge to accomplice

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0.168 is the probability that exactly 1 of the 4 players has exactly one ace and one king.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

a)

Given that,

each player gets 13 cards.

So, n = total no. of ways = ⁵²C₁₃ = 6.350× 10¹¹

As we know, there are 2 black aces and 4 kings in a deck of 52 cards. Since, one black ace out of 2 black aces can be chosen in ²C₁ ways, next one king out of 4 kings in ⁴C₁ ways and the remaining 11 cards from the remaining 46 cards in ⁴⁶C₁₁ ways.

So, m = ²C₁ × ⁴C₁ × ⁴⁶C₁₁

m = 1.067 × 10¹¹

Therefore, Required probability p =  m/n

p = (1.067 × 10¹¹) / (6.350× 10¹¹)

p = 0.168

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By using a trigonometric relation, we will see that the value of x on the right triangle is x = 53.4

We want to find the value of x on the given right triangle, which is one of the cathetus of the triangle (the adjacent cathetus of the shown angle).

We know one angle of 51°, and the opposite cathetus of that angle, which has a measure of 66 units.

Here we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the known values, we will get:

tan(51°) = 66/x

Solving that for x, we will get:

x = 66/tan(51°) = 53.4

The measure of the adjacent cathetus is 53.4 units.

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Line is not parallel to line because no scaling from point can transform triangle into triangle.

Line is not parallel to line because there is no transformation that can send triangle to triangle. A transformation is a function that changes the location, size, or orientation of an object. A dilation of a shape is a transformation that changes its size, either making it larger or smaller, but does not change its orientation. To determine if two lines are parallel, one must consider if a dilation from a point can send one line to the other. In this case, there is no dilation from point that can send triangle to triangle, so line is not parallel to line.

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Answer: Hello how are you doing?

Step-by-step explanation: How may I help you?

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~10(\sqrt[7]{x}+9)\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~10(\sqrt[7]{y}+9)} \\\\\\ \cfrac{x}{10}=\sqrt[7]{y}+9\implies \cfrac{x}{10}-9=\sqrt[7]{y} \\\\\\ \left( \cfrac{x}{10}-9 \right)^7=(\sqrt[7]{y})^7 \implies \left( \cfrac{x}{10}-9 \right)^7=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

first get one odd No, again more odd number than even, Lastly two or more odd number

Applying the area of the parallelogram formula, it can be concluded that the area is 56 square units.

The area of the parallelogram is the magnitude of the cross-product of the adjacent edges (base and height).

Given information:

A parallelogram is made up of 4 vertices: A(−3, 0), B(−1, 6), C(8, 5), and D(6, −1).

So first we find the adjacent edges as follows:

AB = B - A

     = ( (-1-(-3)) , (6-0) )

     = (2,6)

AD = D - A

     = ((6-(-3)) , (-1-0))

     = (9,-1)

We want to find the area of the parallelogram, we do the following step:

[tex]AB x AD = \left[\begin{array}{ccc}i&j&k\\2&6&0\\9&-1&0\end{array}\right][/tex]

               = i(0 - 0) + j(0 - 0) + k(-2 - 54)

               = -56k

The area of the parallelogram = | AB x AD |

                                                  = √(-56)²

                                                  = 56 square unit

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Answer:

1 5/12 (One whole number five over twelve)

Step-by-step explanation:

Recipe calls for 2 3/4 cups

No of cups available are 1 1/3 cups

To get the number of cups needed to fulfill the recipe well say:

1 1/3 + X = 2 3/4

X = 2 3/4 - 1 1/3 = 1 5/12

a) The solution that is in the interval -2≤rs - 1 is x=0.5, which is the approximation of the solution correct to two decimal places.

b) The remaining zeros of f(x) are -8i.

a) Generally, One way to approximate the solution of this equation is to use the method of bisection. The bisection method starts by finding the midpoint of the interval in which the solution is known to exist, and then determining which half of the interval the solution must lie in. This process is repeated until a sufficiently accurate approximation of the solution is found.

Another way to approximate the solution is to use a numerical method like the Newton-Raphson method. The Newton-Raphson method starts with an initial approximation of the solution and then uses the derivative of the function to find a better approximation.

However, for the given polynomial equation, the solution can be directly found by factoring it, which will give the roots of the polynomial equation.

By factoring 8x³+3x²-7x+6=0, we can get (2x-3)(4x+1)(x-2) = 0

so the roots are x = -0.25, 0.5, and 2

b)

The remaining zeros of f(x) are -8i.

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The ice cream costs $3 for a small serving and $4 for a large serving.

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Since 3 small servings of ice cream and 1 large serving of ice cream for $13, and 2 small servings of ice cream and 1 large serving of ice cream for $10. We can set up two equations to represent the situation:

Let S and L represent the cost of small servings and large servings respectively

3S + L = 13 --- (1)

2S + L = 10 --- (2)

From (1):
L = 13 - 3S  --- (3)

Put (3) in (2):

2S + L = 10

2S + 13-3S = 10

-S + 13 = 10

S = 13-10

S = $3

Put S = 3 into (3):

L = 13 - 3S

L = 13 - 3(3)

L = 13 - 9

L = $4

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All the values after squares are,

a) 2.3

b) 22.1

c) 65.6

d) 176.9

e) 396

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The numbers are,

a) 1.5

b) 4.7

c) 8.1

d) 13.3

e) 19.9

Now, Find all the squares as;

a) 1.5

⇒ 1.5² = 1.5 × 1.5

          = 2.25

          = 2.3

b) 4.7

⇒ 4.7² = 4.7 × 4.7

           = 22.09

           = 22.1

c) 8.1

⇒ 8.1²= 8.1 × 8.1

         = 65.61

         = 65.6

d) 13.3

⇒ 13.3² = 13.3 × 13.3

            = 176.89

            = 176.9

e) 19.9

⇒ 19.9² = 19.9 × 19.9

             = 396.01

             = 396

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As a result, the automobile will go 90 miles to the location where we will stop for food before beginning our 720-mile journey.

The amount or magnitude of the difference between two points is what is referred to as distance. It should be noted that the distance traveled between two positions and the distance between them are not the same. The total length of a path connecting two points is known as the distance traveled. A body's actual journey distance is referred to as distance. A different name for it is path length. For instance, the length of the path if an object is going from point O to point P will be equal to OP = 360 m. A scalar quantity is the distance. Only magnitude exists.

given

We will stop for food at after traveling 8 miles from Point B, or 90 miles total.

= 760 miles 

As a result, the automobile will go 90 miles to the location where we will stop for food before beginning our 720-mile journey.

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The complete question is " . Diagram of a car traveling 90 miles . Our food stop will be at what miles after we start our trip from Point B. "

Salut/Hello!

Answer: 3120 cubic cm

Step-by-step explanation:
cm - centimeters
=> - results

We know the area is 156 square cm
And the height is 20 cm

We know the area formula is A = L x l
where L - length
and l - latitude

We also know the volume formula is V = L x l x h
where h - height

So we can replace the length and latitude with the area and we have
V = A x h     and we know the area and height

So we calculate:
V = 156 x 20 => V = 3120 cubic cm


I hope it was helpful! :]

The area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

Let w be the width of rectangular pen.

We have been given that a farmer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.

Since the perimeter is 2 times the length and width of rectangle.

Perimeter of a rectangle = 2 (Width + Length)

Upon substituting our given values in above formula we will get,

[tex]100 = 2(w + length)\\50 = w + length\\50-w = Length[/tex]

Area of a rectangle = Width x Length

[tex]Area of a rectangle = w (50-w)\\= 50w - w^{2}[/tex]

Let us represent area in terms of width of rectangle as:

[tex]A(w) = 50w - w^{2}[/tex]

Therefore, the area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

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The transition that was applied to the triangle ABC to create triangle A’B’C’ is (x, y) ⇒ (x - 4, y - 3)

Transformation is the movement of a point from its initial location to a new location. Rigid transformations are transformations on the coordinate plane that preserves the shape and size of the figure. Types of rigid transformations are reflection, translation and rotation.

Rigid transformations are translation, reflection and rotation since they preserve the size.

Translation is the movement of a point up, left, right or down in the coordinate plane.

Triangle ABC was translated 4 units to the left and 3 units down using the rule (x, y) ⇒ (x - 4, y - 3)

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The last customer will be in the book store for 3.22 seconds.

The solution can be calculated using Little's Law, which states that the average number of people in a system equals the average arrival rate multiplied by the average time spent in the system.

Using this formula, we can calculate the time that the last customer will spend in the book store.

Little's Law: Average number in system = Average arrival rate x Average time in system

Average number in system = 29 customers/second x 3 seconds = 87 customers

Average time in system = 87 customers/27 customers/second = 3.22 seconds

Therefore, the last customer will be in the book store for 3.22 seconds.

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The initial force between the two charges is given by:

[tex]F=k\frac{q_{1} q_{2} }{d^2}[/tex]

where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:

1. F

In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.

So, we have:

q'₁=q₁/2

q'₂=2q₂

d'=d

So, the new force is:

[tex]F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F[/tex]

So the force has not changed.

2. F/4

In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.

So, we have:

q'₁=q₁

q'₂=q₂

d'=2d

So, the new force is:

[tex]\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}[/tex]

So the force has decreased by a factor of 4.

3. 6F

In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.

So, we have:

q'₁=2q₁

q'₂=3q₂

d'=d

So, the new force is:

[tex]F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F[/tex]

So the force has increased by a factor of 6.

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Answer:

1. F

2. F/4

3. 6F

Answer:

2 3/4 square yd

Step-by-step explanation:

3/1 x 11/12 = 2 3/4

The product of x and y is: "1"

Step-by-step Solution:

Given: 16/9, x, 1, y  are in Geometric Progression (G.P)

Let the general terms of a Geometric Progression are: a, ar, ar², ar³

So, On comparing we get; a=16/9,

⇒ar² = 1

⇒ 16/9*r² = 1

⇒ r² = 9/16

⇒ r = 3/4

x = ar

⇒ (16/9)(3/4)

⇒x=4/3.

y = ar³

⇒(r)(ar^2) = (3/4)(1)

⇒y=3/4.

Now, to find the product of "x" and "y":

⇒x*y = 4/3 x 3/4

⇒1

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Step-by-step explanation:

1.

equilateral triangle. all sides and also all angles are equal.

the sum of all angles in a triangle is always 180°.

so,

6x = 180/3 = 60°

x = 10

2.

all 3 angles are equal, so, also all 3 sides are equal.

6x - 5 = 5x

x - 5 = 0

x = 5

3.

again, all 3 angles are equal.

3x = 180/3 = 60

x = 20

4.

the 2 sides are marked as equally long.

4x = 40

x = 10

5.

isoceles triangle with 60° angle in top, that means it is again an equilateral triangle.

3x + 8 = 4x - 4

8 = x - 4

12 = x

6.

again all angles are equal.

4x = 60

x = 15

In accordance with the above assertion, the offered differential equation by variable separation is P = 1/ (k*e^t +1).

A differential equation in mathematics is one that has one or more negatively influencing variables. Dy/dx provides the function's derivative. The phrase describes an equation with several ways to connect the dependent variable to one or more regressors.

dP/dt = P - P^2

1/(P - P^2)dP = dt

∫1/(P - P^2)dP = ∫dt

t + c = 1/(P - P2)dP, where c would be a constant

Use the partial fractions method to calculate the integrated on the left. We wish to rewrite 1/(P-P2) in the pattern A/P+B/(1-P) for those constants A and B since P-P2 factors to P(1-P). We therefore have:

1/[P(1-P)] = A/P + B/(1-P)

A(1-P) + BP = 1

When P is 1, we have A(1-1)+B(1)=1, or B=1.

When P is 0, we have A(1-0)+B(0)=1, or A=1.

So, we can rewrite 1/(P-P^2) as 1/P+1/(1-P).

Whilst doing the entire on the ODE's left side, we have:

∫1/(P - P^2)dP

∫[1/P + 1/(1-P)]dP

∫(1/P)dP + ∫1/(1-P)dP

ln(P) + ∫1/(1-P)dP

Make a u-substitution to perform the second integral:

u = 1-P, du = -dP

ln(P) - ∫(1/u)du

ln(P) - ln(u)

ln(P) - ln(1-P)

ln[P/(1-P)]

Reconnecting that to the ODE yields the following:

ln[P/(1-P)] = t + c

e^ln[P/(1-P)] = e^(t + c)

P/(1-P) = e^t * e^c

P/(1-P) = ke^t, where k is a constant equal to e^c

P = (1-P)ke^t

P = ke^t - Pke^t

P + Pke^t = ke^t

P(1 + ke^t) = ke^t

P = ke^t / (1 + ke^t)

P = e^t / (1/k + e^t)

P = e^t / (d + e^t), where d is a constant equal to 1/k

So, the general solution to the ODE is P = e^t / (d + e^t), where d is a constant.

p*(1-p) = k*e^t ( we say that e^k is a constant)

1-p/p = k*e^t

P = 1/ (k*e^t +1)

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The complete question is-

Solve the given differential equation by separation of variables.

dP/dt = P - P²

Number of seats allocated to state A = 12

Number of seats allocated to state B = 18

Number of seats allocated to state C =22

Number of seats allocated to state D = 38

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Percentage of Population of state A = 258/1858 x 100 = 13.88%

Now, Number of seats allocated to state A = 13.88% of 45

                                                                       = 12.492 = 12 (whole number)

Percentage of Population of state B = 377/1858 x 100 = 20.29%

Now, Number of seats allocated to state A = 20.29% of 90

                                                                       = 18.261 = 18 (whole number)

Percentage of Population of state C = 456/1858 x 100 = 24.54%

Now, Number of seats allocated to state A = 13.88% of 90

                                                                       = 22

Number of seats allocated to state D = 90-(12+18+22) = 38

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We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.

The initial value is b.

A linear function is a graph with straight lines.

A unit rate exists for all linear functions (b).

Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.

Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.

Paul's idea has a linear function as its equation.

This leads us to the conclusion that linear functions can be used to represent each of the ideas.

Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

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Correct Question:

x = 60° - 35°

x = 25°

The measure of angle FGJ is 25°

Answer:

9.919742348374221

Step-by-step explanation:

(x+5)(x)=x^2+5x. (x^2+5x)/2; x=

9.919742348374221

Answer:

71.4°F

Step-by-step explanation:

The maximum is when [tex]\sin(0.24x-1.88)=1[/tex], yielding a maximum of [tex]8.6+62.8=71.4[/tex].

50

I attached a pic of my work.

so what I did was find the amount of the other sides of the triangle using their opposite congruent sides. aka, the bottom is 90, which means the top should also be 90. and 90-50 is 40, so the rest of that side (which is one side of the triangle) should be 40.

and then I used the pythagorean theorem, since it is a right triangle (indicated by the squares in the corners).

the theorem states that a^2 + b^2 = c^2

so just plug in the legs (a and b), and you should get the amount of segment AB (which is c)