Problem 9 ……….!.!,!,!!,!,

Trigonometry is an important branch of mathematics that deals with the relationships between the sides and angles of triangles. It has many real-world applications in fields such as physics, engineering, and architecture. In this answer, I will provide a brief overview of some key concepts in trigonometry that are typically covered in a high school junior-level course.

One of the most important concepts in trigonometry is the unit circle. This is a circle with a radius of 1 unit that is centered at the origin of a coordinate plane. The unit circle is used to define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.

To understand the trigonometric functions, we must first define some key terms. The hypotenuse of a right triangle is the side opposite the right angle. The opposite side is the side opposite the angle of interest, and the adjacent side is the side that is adjacent to both the angle of interest and the right angle.

Using the unit circle, we can define the sine and cosine of an angle as the y- and x-coordinates of the point on the unit circle that corresponds to the angle. The tangent of an angle is the ratio of the opposite side to the adjacent side. The cosecant, secant, and cotangent functions are simply the reciprocals of the sine, cosine, and tangent functions, respectively.

Trigonometric functions can be used to solve problems involving right triangles, such as finding missing side lengths or angles. They can also be used to model periodic phenomena, such as waves or oscillations.

In summary, trigonometry is a fascinating and useful branch of mathematics that has many applications in the real world. By understanding the key concepts of the unit circle and the trigonometric functions, students can develop a deeper appreciation for the beauty and utility of mathematics.

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Answer:

see explanation

Step-by-step explanation:

3x and 144 are adjacent angles on a straight line and sum to 180°

3x + 144 = 180 ( subtract 144 from both sides )

3x = 36 ← value of 3x

divide both sides by 3

x = 12

and

2y - 5 and 95 are vertically opposite angles and are congruent, so

2y - 5 = 95 ← value of 2y - 5

add 5 to both sides

2y = 100 ( divide both sides by 2 )

y = 50

Then

x + y = 12 + 50 = 62

Answer:

3x = 36; 2y - 5 = 95; x + y = 62

Step-by-step explanation:

Supplementary angles add up to 180

180 = 3x + 144

36 = 3x

x = 12

Vertically opposite angles are equal

95 = 2y - 5

100 = 2y

y = 50

x + y = 12 + 50 = 62

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."

When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.

Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.

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When any angle bisects with other angle then both the angles are equal.

Then, m of angle ABD = angle CBD

ABD = 70

ABD = CBD = 70°

ABC = 70 + 70 = 140°

Answer:

Step-by-step explanation:

because both equations add up to equal abc

we can solve for x

8x+35=11x+23

subtract 8x from boths sides

35=3x+23

subtract 23 from both

12=3x

x=4

Now we can solve for Abd

8(4)+35=67degrees =ABD

11(4) +23=67degrees=CBD

67+67=134=abc

I hope this made since sorry if it doesn't

Have a wonderful day

Answer: 1.7×10*4×8.5×10*-2= 1445

Step-by-step explanation:

The question must be written as follows:

1.7×10∧4×8.5×10∧-2=

(1.7×10000×8.5)÷100

=144500÷100=1445

The points that has same quadrant as (2, –10) could Tamara use a number line to find the distance are (2, -9), (10, -10) and (7, -10)

The coordinates of the first point = (2, -10)

Using the number line we can only find the distance when the y coordinates or the x coordinates of the lines are equal

Here the first point is (2, -10)

The next point should be same quadrant, then the x coordinate will be positive and y coordinate will be negative

The points with same x coordinates = (2, -9)

The points with same y coordinates = (10, -10) and (7, -10)

Hence, the points that has same quadrant as (2, –10) could Tamara use a number line to find the distance are (2, -9), (10, -10) and (7, -10)

The complete question is

Tamara wants to find the distance from (2, –10) to other points. For which points in the same quadrant as (2, –10) could Tamara use a number line to find the distance? Check all that apply. (10, –10) (3, –2) (2, –9) (7, –10) (9, –2) (10, –2) (12, –1)

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The flow rate of water in each steel pipe at 25°C is as follows:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

To calculate the flow rate of water in each steel pipe, we need to consider the properties of the pipes and the lengths of the sections through which the water flows. The schedule 40 pipes mentioned in the question are commonly used for various applications, including plumbing.

Given the lengths of each pipe section, we can calculate the total equivalent length (sum of all lengths) to determine the pressure drop across each pipe. Since the question mentions ignoring minor losses, we assume that the flow is fully developed and there are no significant changes in diameter or fittings that would cause additional pressure drop.

Using the flow rate formula Q = ΔP * A / √(ρ * (2 * g)), where Q is the flow rate, ΔP is the pressure drop, A is the cross-sectional area of the pipe, ρ is the density of water, and g is the acceleration due to gravity, we can calculate the flow rates.

Considering the given data, we can directly assign the flow rates to each pipe:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

The flow rate of water in each steel pipe at 25°C is determined based on the given information. Pipe 1 has a flow rate of 1.2 ft³/s, Pipe 2 and Pipe 3 have flow rates of 0.3 ft³/s each, and Pipe 4 has a flow rate of 0.6 ft³/s. These values represent the volumetric flow rate of water through each pipe under the specified conditions.

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Answer:

127

Step-by-step explanation:

Angle u is 32°.

A line can go on forever. The line continues forever in both directions. There are no endpoints on the lines. The following are the angles of lines: Equal angles are those that are vertically opposed, such as a = d and b = c. As an example, the angles a + b and a + c add up to 180 degrees. Angles that correspond to one other are equal, such as a = e, b = f, c = g, and d = h. A line is a geometric form with only one dimension. There is no thickness to the line; it merely has length. Lines that cross at an angle will do so only once.

Given that angle Y at the q line is 32°. Since line p and line q are parallel. From properties of a line. angle made by the same cross line with two parallel lines will be the same.

Therefore, Angle u will be the same as angle y which is 32°.

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Answer:

7x = 7

with solution of x = 1

This is the first choice

Step-by-step explanation:

Choice 1
7x = 7 => x = 7/7 = 1

Choice 2
7x = 7x provides no additional info and therefore there are an infinite number of solutions; any value of  will satisfy

Choice 3
x + 1 = x + 1; infinite solutions for reasons cited under choice 2

Choice 4
x + 1 = x + 2
Eliminating x from both sides gives 1 = 2
Such an equation will have no solution; no value of x can satisfy the equation

Correct answer: Choice 1: 7x = 7

Answer:

$3,300

Step-by-step explanation:

$60,000 falls into the $50,001 - $100,000 range, so 5.5% is owed on it.

5.5% → 0.055

60,000 * 0.055 = $3,300

Answer:

it's 7, right?

Step-by-step explanation:

if you do it backwards it's 33÷3 which is 11 (only whole number that goes into 33)

then 11-4 is 7

Answer:

7

Step-by-step explanation:

1. Translate the statement into an equation:

2. Simplify both sides of the equation.

3. Subtract 12 from both sides.

4. Divide both sides by 3.

The parametric equations for the line passing through the point (1,2) are: x = t and y = 2

To find the parametric equations of a line with a rectangular equation, we can first convert the rectangular equation into slope-intercept form and then use the slope and y-intercept to create the parametric equations.

Since we don't have a specific rectangular equation given in the question, I'll assume a general form of:

y = mx + b

where m is the slope and b is the y-intercept.

To find the slope, we can use the fact that the line passes through the point (1,2). We can choose any other point on the line to calculate the slope, but using the given point simplifies the calculation. We'll substitute x=1 and y=2 into the equation:

2 = m(1) + b

Simplifying:

2 = m + b

To find the y-intercept, we can substitute x=0 into the equation and use the fact that y=0 (since the line passes through the x-axis):

0 = m(0) + b

Simplifying:

b = 0

Now we have both m and b, so we can write the slope-intercept equation for the line:

y = mx

Substituting the value of b:

y = mx + 0

Simplifying:

y = mx

Finally, we can create the parametric equations using the parameter t:

x = t
y = mt

Substituting the value of m:

x = t
y = (2/t) * t

Simplifying:

x = t
y = 2

So the parametric equations for the line passing through the point (1,2) are:

x = t
y = 2

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Answer:

150m

Step-by-step explanation:

work = force x distance

w=fd

d=w/f

d= 4500/30 = 150

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

L(x) if x is 4.12 inches per second is $21.

To estimate the tolerance for the firm to minimize its quality-related cost (loss), we need to determine the range of acceptable speeds that minimize the cost. The tolerance can be calculated as the difference between the upper and lower limits of the acceptable speed range.

Given that the desired speed is 4 inches per second and the quality specification allows a deviation of 0.17 inches per second, we can calculate the upper and lower limits as follows:

Upper Limit = Desired Speed + Tolerance

Lower Limit = Desired Speed - Tolerance

Let's assume the tolerance is represented by 't'.

Upper Limit = 4 + t

Lower Limit = 4 - t

To minimize the quality-related cost, we want to find the smallest value of 't' that satisfies the condition.

The cost can be minimized when the difference between the upper and lower limits is equal to twice the return cost of $28.

Upper Limit - Lower Limit = 2 * $28

(4 + t) - (4 - t) = 2 * $28

2t = 2 * $28

t = $28

Therefore, the estimated tolerance for the firm to minimize its quality-related cost is 0.28 inches per second (rounded to 4 decimal places).

Note: In this scenario, the tolerance is set to 0.28 inches per second to ensure that the cost of returns is minimized for the company.

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Answer:

4/ 3 = 7

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

first add two to each side

Simplify  7+2 to 9

3x=9

divide both sides by 3.

x=9/3

simplify 9/3 to 3

​

Answer: Rs 1469

Step-by-step explanation:

Coat of item = RS 1300

Value added tax = 13%

The price of the item will then be calculated as:

= 1300 + (1300 × 13%)

= 1300 + (1300 × 0.13)

= 1300 + 169

= Rs 1469

A composite function to find the area of the region at time t is written as-

A(r(t)) = π(0.25 + 2t + 4t²)

f(g(x)) or (f ∘ g)(x) represents the composition of functions f(x) & g(x), where g(x) acts first (x). It integrates a number of functions to produce another.

The output of one function inside the parenthesis is becoming the input of the other function in a function composition. i.e.,

Now, as per the given question;

To create a composite function, we pertain one function to another. In this scenario, we would like to find area in terms of time, so we apply the function A(r) to the function r. (t).

To accomplish this, we substitute r with r(t).

Since we know that r(t) = 0.5 + 2t, we can replace r to 0.5 + 2t:

A(r(t)) = π(0.5+2t)²

To make things easier, we'll simplify this same squared term:

A(r(t)) = π(0.5 + 2t)(0.5 + 2t)

A(r(t)) = π[(0.5×0.5) + (0.5×2t) + (2t×0.5) + (2t×2t)]

A(r(t)) = π(0.25 + t + t + 4t²)

A(r(t)) = π(0.25 + 2t + 4t²)

Therefore, the composite function to find the area of the region at time t is written as A(r(t)) = π(0.25 + 2t + 4t²).

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The complete question is-

A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t. Explain how to write a composite function to find the area of the region at time t.

Answer:

it would be 210 feet but u can't put feet into hours

Step-by-step explanation:

If the rest of the ribbon will be cut up into equal-sized sections, and each section will be 8 inches long, the length of the remaining ribbon can be calculated by subtracting the length already used from the total length:

The length of the ribbon is 8 feet, which is equivalent to 96 inches.

Shyanne has already used 32.5 inches of the ribbon.    

Remaining ribbon length = Total length - Length already used

Remaining ribbon length = 96 inches - 32.5 inches

Remaining ribbon length = 63.5 inches

We want to find the length of each individual section, denoted by "l."

Now, we can set up the equation:

8l = 63.5

To solve for "l," we divide both sides of the equation by 8:

l = 63.5 / 8

l = 7.9375

Therefore, the correct answer is:

C) The length of each individual section will be 7.9375 inches.

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Answer:

1,800/7,200 as a percentage is 1/4 which is 25%.

Answer: 25%.

Step-by-step explanation:

because 1,800/7,200 as a simplyfly fraction

will be 1/4 and if you make it in persant it will be 25%

Hope this helps :)

Answer:

x=-16

Step-by-step explanation:

−2(x+14)+1=5

Step 1: Simplify both sides of the equation.

−2(x+14)+1=5

(−2)(x)+(−2)(14)+1=5(Distribute)

−2x+−28+1=5

(−2x)+(−28+1)=5(Combine Like Terms)

−2x+−27=5

−2x−27=5

Step 2: Add 27 to both sides.

−2x−27+27=5+27

−2x=32

Step 3: Divide both sides by -2.

−2x

−2

=

32

−2

x=−16

Answer:

x=−16

Answer:

-2(x + 14) + 1 = 5

-2x - 28 + 1 = 5

-2x - 27 = 5

-2x = 32

x = -16

Answer:3 symmetrical lines

Step-by-step explanation: just look in the middle and draw a line