OAB is a sector of a circle as shown below.
Work out the length of the arc AB.
Give your answer in millimetres (mm) to
1 d.p.
IMPORTANT

The coordinates of the two points that intersect with the y-axis are (2, 3) and (-2, 4)

Represent the points with P and Q

A vertical line is a line whose endpoints have the same x-coordinate

i.e. (x, y1) and (x, y2)

Using the above as a guide, we have the following:

We can make use of the coordinates (x1, y1) and (x2, y2), where the values of x's and y's are not the same

An instance of these points is (2, 3) and (-2, 4)

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The secx equivalent of the two expressions are

tan²x = sec²x - 1

tan x =sec x * sin x

Generally, Equalities that utilize trigonometry functions and are true no matter what the values of the variables that are specified in the equation are what are referred to as trigonometric identities. There are many different trigonometric identities that may be found using the length of a triangle's side as well as the angle of the triangle.

a) Using the identity:

tan²x + 1 = sec²x

We can rearrange it to get:

tan²x = sec²x - 1

Therefore, in terms of secx:

tan²x = sec²x - 1

b) Using the identity:

tan x = sin x / cos x

We can rewrite it in terms of sec x as follows:

tan x = sin x / cos x

= (1/cos x) * sin x

= sec x * sin x

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The requried, possible solution sets of the inequality ax + b < cx + d is x < (d - b)/(a-c).

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
To describe the possible solution sets of the inequality ax + b < cx + d, we need to isolate the variable x on one side of the inequality and simplify.

ax + b < cx + d

ax - cx < d - b

x(a-c) < d - b

x < (d - b)/(a-c)

So the solution set for the inequality is all values of x that are less than the quotient of (d - b) divided by (a-c).

Therefore, the possible solution sets of the inequality ax + b < cx + d is x < (d - b)/(a-c).

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123

Step-by-step explanation:

As per the given distance, Martin was 79 kilometers from the hole when he started.

Let's call the initial distance between Martin and the hole "x". According to the problem statement, on Martin's first stroke, the golf ball traveled 4/5 of this distance. This means that the distance the ball traveled on the first stroke was:

distance traveled on first stroke = (4/5)x

After the first stroke, Martin was left with a distance of:

distance left after first stroke = x - (4/5)x = (1/5)x

On Martin's second stroke, the ball traveled 79 meters and went into the hole. This means that the total distance the ball traveled was:

total distance traveled = distance traveled on first stroke + distance left after first stroke + distance traveled on second stroke

total distance traveled = (4/5)x + (1/5)x + 79

total distance traveled = x + 79

Since the ball went into the hole after the second stroke, the total distance traveled is equal to the initial distance between Martin and the hole:

x + 79 = initial distance between Martin and the hole

Therefore, the initial distance between Martin and the hole was:

x = initial distance between Martin and the hole = (79 km)

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The length of CE is 16 units.

Since ΔCDE ~ ΔCBA, we know that their corresponding sides are proportional. This means that CD/CA = DE/BA = CE/AB. We are given that CD = 10, DA = 8, and CE = 6. We can use the Pythagorean theorem to find CA:

CA^2 = CD^2 + DA^2
CA^2 = 10^2 + 8^2
CA^2 = 100 + 64
CA^2 = 164
CA = √164

Now we can use the proportion CD/CA = DE/BA to find EB:

10/√164 = DE/(8 + EB)
10(8 + EB) = DE√164
80 + 10EB = DE√164
10EB = DE√164 - 80
EB = (DE√164 - 80)/10

We can use the Pythagorean theorem to find DE:

DE^2 = CE^2 + CD^2
DE^2 = 6^2 + 10^2
DE^2 = 36 + 100
DE^2 = 136
DE = √136

Now we can plug DE back into the equation for EB:

EB = (√136√164 - 80)/10
EB = (12√164 - 80)/10
EB = 1.2√164 - 8
EB ≈ 4.26

So the length of EB is approximately 4.26 units.

30. Since ΔCDE ~ ΔCBA, we know that their corresponding sides are proportional. This means that CD/CA = DE/BA = CE/AB. We are given that CD = 10, CA = 16, and EB = 12. We can use the proportion CD/CA = DE/BA to find DE:

10/16 = DE/(8 + 12)
10/16 = DE/20
DE = 20(10/16)
DE = 12.5

Now we can use the Pythagorean theorem to find CE:

CE^2 = CD^2 + DE^2
CE^2 = 10^2 + 12.5^2
CE^2 = 100 + 156.25
CE^2 = 256.25
CE = √256.25
CE = 16

So the length of CE is 16 units.

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Answer:

[tex]x \leqslant - 27[/tex]

Step-by-step explanation:

[tex]1. \: - \frac{x}{9} \geqslant 3 \\ 2. \: - x \geqslant 3 \times 9 \\ 3. \: - x \geqslant 27 \\ 4. \: x \leqslant - 27[/tex]

The final answer is 2x^3 +x^2 +3x+5 = (2x^2 + 3x + 6)(x−1) + 11.

(2) To solve the inequality |2x − 5| ≤ 9, we need to split it into two separate inequalities and solve for x:
2x − 5 ≤ 9 and 2x − 5 ≥ −9
2x ≤ 14 and 2x ≥ 4
x ≤ 7 and x ≥ 2
The solution in interval notation is [2, 7].

(3) To find the inverse of the function f(x) = 5/(6x−1), we need to switch the x and y values and solve for y:
x = 5/(6y−1)
6y−1 = 5/x
6y = 5/x + 1
y = (5/x + 1)/6
The inverse function is f^(-1)(x) = (5/x + 1)/6.

(4) To find fg and fg, we need to plug in the functions for x and simplify:
fg(x) = f(g(x)) = √(x^2−11x+30−4) = √(x^2−11x+26)
fg(x) = g(f(x)) = (√x−4)^2−11(√x−4)+30 = x−8√x+16−11√x+44+30 = x−19√x+90
The domain of fg is all real numbers greater than or equal to 26, and the domain of fg is all real numbers greater than or equal to 0.

(5) To find the equation of the line perpendicular to y = 35 x − 4 and passing through the point (1, 2), we need to find the slope of the perpendicular line and use the point-slope form:
The slope of the original line is 35, so the slope of the perpendicular line is -1/35.
Using the point-slope form, y − y1 = m(x − x1), we get:
y − 2 = −1/35(x − 1)
y = −1/35x + 2 + 1/35
y = −1/35x + 71/35
The equation of the line in slope-intercept form is y = −1/35x + 71/35.

(6) To divide 2x^3 +x^2 +3x+5 by x−1 using long division, we need to divide each term of the dividend by the divisor and find the remainder:
2x^3 ÷ x = 2x^2
2x^2(x−1) = 2x^3−2x^2
(x^2 +3x+5) − (2x^3−2x^2) = 3x^2 +3x+5
3x^2 ÷ x = 3x
3x(x−1) = 3x^2−3x
(3x+5) − (3x^2−3x) = 6x+5
6x ÷ x = 6
6(x−1) = 6x−6
5 − (6x−6) = 11
The final answer is 2x^3 +x^2 +3x+5 = (2x^2 + 3x + 6)(x−1) + 11.

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A majority of the consumers in the sample prefer pepsi over coke.

Based on the given information, a random sample of 100 soft drink consumers tasted an unmarked cup of pepsi and an unmarked cup of coke. Fifty-nine out of the 100 consumers stated that they prefer pepsi over coke.

This means that the majority of the consumers in the sample, or 59%, preferred pepsi over coke. It is important to note that this is only a sample of consumers and may not necessarily reflect the preferences of the entire population of soft drink consumers. However, it does provide some insight into the preferences of a portion of the population.

In conclusion, the results of the taste test indicate that a majority of the consumers in the sample prefer pepsi over coke.

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a)

i)  The function is not harmonic.

ii). The function is harmonic.

b) v is also harmonic in D

a) A function is harmonic if it satisfies the Laplace equation:

∂²u/∂x² + ∂²u/∂y² = 0

i) For the function u = x² + 2x - 4², we can take the partial derivatives with respect to x and y:

∂u/∂x = 2x + 2

∂u/∂y = 0

∂²u/∂x² = 2

∂²u/∂y² = 0

Plugging these into the Laplace equation, we get:

2 + 0 = 0

This is not true, so the function is not harmonic.

ii) For the function u = 2e* cos(y), we can take the partial derivatives with respect to x and y:

∂u/∂x = 0

∂u/∂y = -2e* sin(y)

∂²u/∂x² = 0

∂²u/∂y² = -2e* cos(y)

Plugging these into the Laplace equation, we get:

0 + (-2e* cos(y)) = 0

-2e* cos(y) = 0

This is true for all values of y, so the function is harmonic.

The harmonic conjugate of a function u(x,y) is a function v(x,y) such that f(z) = u(x,y) + i*v(x,y) is analytic. To find the harmonic conjugate of u = 2e* cos(y), we can use the Cauchy-Riemann equations:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

Plugging in the partial derivatives of u, we get:

0 = ∂v/∂y

-2e* sin(y) = -∂v/∂x

Integrating both equations with respect to x and y, we get:

v = C₁

v = 2e* cos(y) + C₂

Setting these equal to each other and solving for v, we get:

v = 2e* cos(y) + C

So the harmonic conjugate of u = 2e* cos(y) is v = 2e* cos(y) + C, where C is a constant.

b) If u is the harmonic conjugate of v in a domain D, then f(z) = u(x,y) + i*v(x,y) is analytic in D. This means that f(z) satisfies the Cauchy-Riemann equations:

∂u/∂x = ∂v/∂y

∂u/∂y = -∂v/∂x

If we take the partial derivatives of these equations with respect to x and y, we get:

∂²u/∂x² = ∂²v/∂x∂y

∂²u/∂x∂y = -∂²v/∂x²

∂²u/∂y∂x = -∂²v/∂y²

∂²u/∂y² = ∂²v/∂y∂x

Adding the first and last equations, we get:

∂²u/∂x² + ∂²u/∂y² = ∂²v/∂x∂y + ∂²v/∂y∂x

Since the mixed partial derivatives are equal, this simplifies to:

∂²u/∂x² + ∂²u/∂y² = 0

So u is harmonic in D. Similarly, we can add the second and third equations to get:

∂²v/∂x² + ∂²v/∂y² = 0

So v is also harmonic in D. Therefore, if u is the harmonic conjugate of v in a domain D, then both u and v are harmonic in D.

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The ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.

To write the ratio as a fraction in simplest form, we will follow the steps below:

Step 1: Write the ratio as a fraction. In this case, we have 3.5cm:1.4cm, which can be written as 3.5cm/1.4cm.

Step 2: Simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF). In this case, the GCF of 3.5 and 1.4 is 0.7. So we will divide both the numerator and denominator by 0.7 to get:

(3.5cm/0.7) / (1.4cm/0.7) = 5/2

Step 3: Convert the fraction to simplest form with whole numbers in the numerator and denominator. In this case, we can multiply both the numerator and denominator by 10 to get:

(5*10)/(2*10) = 50/20

Step 4: Simplify the fraction by dividing both the numerator and denominator by the GCF. In this case, the GCF of 50 and 20 is 10. So we will divide both the numerator and denominator by 10 to get:

(50/10)/(20/10) = 5/2

Therefore, the ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.

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Answer:

4

Step-by-step explanation:

compare the coordinates of each point:

G: (1,2)    x4→   G': (4,8)

H: (3,0)   x4→   H': (12,0)

I:  (2,-2)   x4→    I':  (8,-8)

As you can see the scale factor is 4

Each x and each y coordinate of the small triangle GHI is multiplied by 4 to get the image triangle G'H'I'

The number of copies sold in total is 586,301

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, a book sold 42800 copies in its first month of release, this represents 7.3 of the number of copies sold to date, we need to find the number of the copies have been sold to date,

Let the number of copies sold in total be x,

Using the concept of percentage,

7.3 % of x = 42800

7.3 / 100 of x = 42800

x = 100/7.3 (42800)

x = 586,301

Hence, the number of copies sold in total is 586,301

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Answer:

x-coordinate is 3

Step-by-step explanation:

Q has y-coordinate of -4 => the distance from origin to y-coordinate is 4 units, which is one leg of the right triangle

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

with c = 5, a = 4

5^2 = 4^2 + b^2

b^2 = 25 - 16 = 9

b = √9 = 3

so Q has coordinates (3,-4)

Answer:

Step-by-step explanation:

31 degreese

add 59 with 90 you get 149 then you subtract 149 with 180 a

nd then get 31

We can conclude that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, as shown in the diagram.

What are the attributes of a good conclusion?

The key argument raised throughout the argument's discussion must be summarized in the good conclusion.

a. In below diagram, each city is represented by a point, and the distances between the cities are shown as line segments with the distance in miles labeled above the segment. The distances are labeled in the order in which they appear in the diagram, so for example, the distance between Kadoka and Rapid City is labeled as 96 because that is the distance between the two cities as you move from Kadoka to Rapid City.

b. To support the conclusion that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, we can use the distances given in the problem to show that it is possible to travel from any one city to any other city using only Interstate 90.

First, we note that Kadoka is connected to Rapid City by Interstate 90, because the distance between them is given as 96 miles and no other route is mentioned. Similarly, Rapid City is connected to Alexandria by Interstate 90, because the distance between them is given as 292 miles and no other route is mentioned.

Finally, to show that Alexandria is connected to all the other cities by Interstate 90, we note that the distance between Alexandria and Rapid City is given as 292 miles, and the only way to travel between the two cities is on Interstate 90. Also, since Kadoka is connected to Rapid City by Interstate 90 and Rapid City is connected to Alexandria by Interstate 90, it follows that Kadoka is connected to Alexandria by Interstate 90.

Therefore, we can conclude that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, as shown in the diagram.

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Answer: internal systolic blood pressure (100,110).

Step-by-step explanation:

Given the systolic blood pressure is normally distributed with a

mean G 105  and a standard leviation 5 .

to find : using empirical rule determines  the interval

dyslolie blood pressure that represent the middle 68% malen

solution 68% value  lie within 1 standard deviation the mean .

            { using empirical rule 2

we cab express this range as :

= (x -s , x +s)

= (105 -5, 105+5)

= (100 , 110)

1. 1920 Beetle Population

Beetle Type #Beetles #Beetle % Frequency

BB 22 22/86 ≈ 0.26

bb 14 14/86 ≈ 0.16

Bb 50 50/86 ≈ 0.58

2. 2020 Beetle Population

Beetle Type #Beetle % Frequency

BB 0 0/14 = 0

bb 14 14/14 = 1

Bb 0 0/14 = 0

3. Gene pool for the beetle population: The gene pool for the beetle population consists of the two alleles for the coloration gene, which are represented by "B" (dominant allele) and "b" (recessive allele).

4. Allele frequency for the 1920 Homozygote dominant Beetle population:

5. The allele frequency for the heterozygote population in 2020 is B = 0 and b = 1.

6. Yes, the beetle population experienced evolution because the allele frequencies changed from 1920 to 2020.

For question 1 and 2 above, The % frequency for each beetle type was calculated by dividing the number of beetles of that type by the total number of beetles in the population, and then multiplying the result by 100 to get a percentage.

For example, in the 1920 beetle population, the frequency of BB beetles was calculated as follows:

% Frequency of BB = (# of BB beetles / Total # of beetles) x 100

% Frequency of BB = (22 / 86) x 100

% Frequency of BB ≈ 25.58 or 26% (rounded to the nearest whole number)

Similarly, the % frequency for bb and Bb beetles in the 1920 population were calculated as:

% Frequency of bb = (14 / 86) x 100 ≈ 16%

% Frequency of Bb = (50 / 86) x 100 ≈ 58%

The same process was used to calculate the % frequency for the 2020 beetle population.

4. The frequency of the dominant allele (B) in the 1920 population is the sum of the number of copies of B (from BB and Bb beetles) divided by the total number of alleles (2x the total number of beetles).

Frequency of B = (22 + 50/2) / (86x2) ≈ 0.55

5. Allele frequency for the 2020 heterozygote beetle population:

Since only the frequency of the heterozygote (Bb) is given, the frequency of both alleles (B and b) can be calculated as follows:

Frequency of b = 1 - Frequency of B = 1 - 0 = 1

Frequency of B = frequency of Bb / 2 = 0 / 2 = 0

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The probability of being dealt 5 cards from a standard 52-card deck and getting a four of a kind is 0.00024.

To find the probability of being dealt 5 cards from a standard 52-card deck and getting a four of a kind, first find the total number of ways to get a four of a kind and then dividing that by the total number of possible 5-card hands.

Total number of 5-card hands:

52C5 = 52! / (5!)(47!) = 2,598,960

Total number of ways to get a four of a kind:

There are 13 different ranks in a standard deck, so there are 13 ways to choose the rank of the four of a kind. There are also 48 remaining cards in the deck after the four of a kind has been chosen, so there are 48 ways to choose the fifth card.

13(48) = 624

So the probability of getting a four of a kind is 624 / 2,598,960 = 0.00024.

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Answer:

nonlinear

Step-by-step explanation:

If that's a fraction with an x on the bottom, it is non-linear.

Linear (graph is a line) has y = mx + b format or similar, with x having only a power of 1 (just plain x)

You get curves and other graphs when x is squared or higher exponent, or x inside a squareroot is also not a line. And, like your problem if x is on the bottom of a fraction it is nonlinear.

Answer: 30 millimeters

Step-by-step explanation:

Diameter = Circumference / π

Plug in values:

d = 94.2 / 3.14

d = 30

The diameter is 30 millimeters.

Answer: Okay, so it's $8 per day to feed all of them. So one way you could answer it could be to say; "It costs $8 per day to feed all of the meerkats,..." then pick a number of days to multiply $8 by.

I hope this helps some!

When we evaluate f(3) in the function f(x)=3x^2+9/x+1, we get the result 31.

The function f(x) = 3x^2 + 9/x + 1 is a quadratic function with a variable x. To find the value of f(3), we need to plug in the value of x = 3 into the function and simplify.
f(3) = 3(3)^2 + 9/3 + 1
f(3) = 3(9) + 3 + 1
f(3) = 27 + 3 + 1
f(3) = 31

Therefore, the value of f(3) is 31.

A quadratic term is any expression that has in its unknowns (in which letters are used) one that is squared (or two), these terms are part of a quadratic function.

For a term to be quadratic it must be multiplied by itself (twice), for example:

a² + a + 1

We can see that it is a quadratic function and that its literal term is a while the quadratic term is a², i.e. a*a.

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The coordinate of the other endpoint of the line segment is (-1, 2).

In geometry, a line segment is a part of a line that has two endpoints. It is the shortest distance between two points on a line. A line segment can be straight or curved, and can be vertical, horizontal, or diagonal.

The length of a line segment can be measured using units such as centimeters, inches, or feet. The midpoint of a line segment is the point that is exactly halfway between its endpoints, and it is located at the average of the x-coordinates and the y-coordinates of the endpoints.

Let (x, y) be the coordinate of the other endpoint of the line segment. Then, we know that the midpoint of the line segment is given by the formula:

midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the given values, we have:

(1, -2) = ((3 + x)/2, (-6 + y)/2)

Multiplying both sides by 2, we get:

(2, -4) = (3 + x, -6 + y)

Separating the x and y terms, we have:

2 = 3 + x -> x = -1

-4 = -6 + y -> y = 2

Therefore, the coordinate of the other endpoint of the line segment is (-1, 2).

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I'm not 100%

sure

:))))))))))))))))))))))))

Look at the picture.

<, > - dotted line

≤, ≥ - solid line

x > a, x ≥ a - to the right of a

x < a, x ≤ a - to the left of a

y > a, y ≥ a - up from a

y < a, y ≤ a - down from a

The perimeter of this rectangle is equal to 14 units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

For the width, we would determine the distance between the vertices (5, 6) and (5, 1)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(5 - 5)² + (1 - 6)²]

Distance = √[(0² + (-5)²]

Distance = √25

Distance = 5 units.

For the length, we have:

Distance = √[(7 - 5)² + (6 - 6)²]

Distance = √[(2² + 0²]

Distance = √4

Length = 2 units.

Perimeter of this rectangle, P = 2(5 + 2)

Perimeter of this rectangle, P = 14 units.

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Complete Question:

Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5,1). B(7,1), C(7,6), and D(5,6). What is the perimeter of rectangle ABCD?

use the slope formula

5 - 9/4-2 = -4/2 = -2

slope = -2

The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Each triangle has three medians, one from each vertex, and they are concurrent at a point called the centroid. The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.

Therefore, the median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.

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Answer:

1. 2430 feet

2. 1.8 m/s^2

Step-by-step explanation:

See the attached worksheet.

A time versus speed graph contains a small treasure of mathematical rewards. The area under the graph is equal to the distance travelled. The slope of the line segments represents acceleration.

For total distance: If we break the graph into three sections (2 triangles and a rectangle) we can calculate the areas for each. Each area is the distance travelled for that segment. As shown on the workseet, the total area is 2430 miles, the distance travelled by the train for this question.

The slope of the line in the first 10 seconds is 1.8 meters/sec^2, the acceleration of the train over that period.