I've been struggling a lot with interpreting what this problem wants me to find.

The plane departs an airport at 9:00 AM and flies 200 mph southwest. A second plane ldeparts the same airport at 9:30 AM and flies 320 mph northwest. Find the bearing of the second plane from the first one at 10:00 AM.

The reason: I've heard some people say a bearing has to be in one direction (north). I've also heard that a bearing has to be an acute angle and some insist there is an answer to this greater than 90º.

I drew out a diagram with a right triangle, legs of 200 and 160 (320 ÷ 2 for the half hour), separated my right triangle into two triangles with 45º angles, and went from there.

Where the hypotenuse and the 160 side meet, the angle is 51.34º. The 200 side makes a 38.66º angle (both came from arctan). I know for a fact there is an 83.66º angle that can be found.

Trouble is, I'm not sure if that's the actual bearing or not. Everything SEEMS correct there, but I've just heard so many other answers on this that I'm not sure who or what to believe!

Figured I'd see what everyone else thought. It's the "second from the first" that I'm struggling with semantically too. I can do the math just fine here.

The velocity of the rock as a function of time is given by:

[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]

where 4.9 is the value of mg in SI units.

The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.

The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:

[tex]m(dv/dt) = -mg - 0.5v[/tex]

where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.

We can simplify this differential equation by dividing both sides by m:

[tex]dv/dt = (-g - 0.5v/m)v[/tex]

This is a separable differential equation, which we can solve using the separation of variables:

[tex](1/(-g - 0.5v/m)) dv = dt[/tex]

Integrating both sides gives:

[tex]-2ln(-g - 0.5v/m) = t + C[/tex]

where C is a constant of integration.

Solving for v gives:

[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]

where C' = exp(C).

We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:

[tex]v(0) = -0.5mg + C' = 3[/tex]

[tex]C' = 0.5mg + 3[/tex]

Substituting this into the equation for v(t) gives:

[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]

Therefore, the velocity of the rock as a function of time is given by:

[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]

where 4.9 is the value of mg in SI units.

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Answer:

Parallels lines:
y = 8x - 43

Perpendicular line:

y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]

Step-by-step explanation:

y = 8x -7

Parallel lines have the same slope.

The slope will be 8.  We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept  (b)

y = mx + b  Substitute in -3 for y, 8 for m, and 5 for x.

-3 = 8(5) + b

-3 = 40 + b  Subtract 40 from both sides

-3 - 40 = 40 - 40 + b

-43 = b

Substitute in 8 for m and -43 for b to write the equation

y = mx + b

y = 8x - 43

Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]

Substitute  [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.

y = mx + b

-3 = [tex]\frac{-1}{8}[/tex](5) + b

-3 = [tex]\frac{-5}{8}[/tex] + b   add [tex]\frac{5}{8}[/tex] from both sides

-3 +  [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] +  [tex]\frac{5}{8}[/tex] + b

[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b

[tex]\frac{-19}{8}[/tex] = b

Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b

y = mx + b

y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]

Helping in the name of Jesus.

Answer:

Put your calculator in degree mode.

[tex] \cos(x) = \frac{12}{13} [/tex]

[tex]x = {cos}^{ - 1} \frac{12}{13} = 22.6[/tex]

Angle x measures 22.6°.

Answer:

t⁴+5t³-3t²-2

Step-by-step explanation:

You can't subtract a variable with a different exponent:

Example:

CAN'T BE SUBTRACTED - 3x²-3x⁴

CAN BE SUBTRACTED - 4x²-2x²=2x²

[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]

[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]

Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.

[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]

Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².

• Note: All natural numbers not being multiplied by any variables are like terms.

So now let's identify those like terms:

From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]

Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:

[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]

So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:

[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]

Answer:

Step-by-step explanation:

You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.

If you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...

  C = πd

so the total circumference is ...

  C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units

The perimeter of the figure is about 47.12 units.

The area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...

  A = (π/4)d²

The total area of the circles of diameters 4 and 11 is ...

  A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)

The area of the central rectangle is added to the areas of the semicircles. Its area is ...

  A = LW

  A = (11)(4)

The area of the entire figure is the sum of the circle areas and the rectangle area:

  total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units

The area of the figure is about 151.60 square units.

__

Additional comment

You usually see the formula for the area of a circle as ...

  A = πr²

Since r = d/2, we can express this using d as ...

  A = π(d/2)² = π(d²)/(2²) = (π/4)d²

You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.

The mathematical induction has been used to prove that the statement is true for all positive integers: 30 + 138 + 318.

In mathematics, mathematical induction is a way of proving propositions. The method entails demonstrating that a statement is true for a base case, usually the smallest feasible value, and then demonstrating that if the statement is true for some value, it is likewise true for the next value.

The key to the proof is the inductive step. It is typically accomplished by assuming that the statement is true for some value and then utilizing that assumption to establish that the statement is true for the following value.

Check the attachment.

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The total surface area of the composite figure is: 288.62 mm²

From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:

Formula for area of rectangle is:

A = Length * Width

Formula for area of triangle is:

A = ¹/₂ * base * height

Using Pythagoras theorem, length of rectangle is:

L = √(10.4² + 15.3²)

L = 18.5 mm

Thus:

TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)

TSA = 129.5 + 159.12

TSA = 288.62 mm²

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The surface area of the triangular prism is 70.2 yd²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as ;

SA = 2B +ph

where h is the height,

B is the base area and

p is the perimeter of the base

Base area = 1/2 bh( since the base Is a triangle)

Base area = 1/2 × 3 ×3 = 4.5yd²

The other side of the triangle is calculated as;

x= √ 3²+3²

x = √9+9

x = √18

x = 4.2

Therefore perimeter = 4.2 + 3+3 = 10.2yds

SA = 2× 4.5 + 10.2 × 6

SA = 9 + 61.2

SA = 70.2 yd²

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Answer:

The answer should be 1,260

Answer:

75

Step-by-step explanation:

.

The answers to the given questions about annual interest are given below:

a.

A = 4,000 (1 + 0.05/2)^(2 x 2)

  = $4,415.25

b.

A = 4,000 x e^(0.045 x 2)

  = $4,376.70

c. $100 more than option 2 = 4,376.70 + 100

                                             = $4,476.70

t (in years) = ln(4,476.70/4,000) /  ln(1 + 0.05/2)

                = 2.27986 years

Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.

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Financial aid letters display aid and attendance costs for one year only. Some schools offer a financial aid letter for four years of undergrad, aiding in budget planning for the program.

A few schools may give a budgetary help letter that ventures aid and costs for all four a long time of an undergrad program. This could offer assistance understudies arrange and budget for their whole undergrad instruction.

In a few cases, Financial aid letters  may show aid and costs for a single semester, instead of the complete scholarly year. This could be valuable for understudies who are as it were going to part-time or who got to take a semester off.

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The equation for g(x) in vertex form is g(x) = (x - 2)^ + 3

From the question, we have the following parameters that can be used in our computation:

The graph of g(x)

Also, we have

The graph of g(x) is a translation of f(x)=x^2

From the graph, we can see that

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

g(x) = f(x - 2) + 3

Substitute the known values in the above equation, so, we have the following representation

g(x) = (x - 2)^ + 3

Hence, the equation for g(x) in vertex form is g(x) = (x - 2)^ + 3

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Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.

3) The coordinates after dilation are: (5.4, 27)

2) The coordinates transformed points after dilation are completed as:

B(2, 4) → B'(3, 6)

K(4, -4) → K'(6, -6)

N(-6, 0) →N'(-9, 0)

The scale factor is same because using the ratio of the x coordinates gives:

3/2 = 1.5

6/4 = 1.5

-9/-6 = 1.5

3) The point W of the vertex of the polygon has coordinates as (2, 10)

Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:

(2*2.7, 10*2.7) = (5.4, 27)

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Answer:

1.5

Step-by-step explanation:

its a decimal number

Answer: the number 15/10 is a fraction.

Step-by-step explanation:

any two numbers that have a slash in the middle are fractons. :)

The multiplying integers -2x24= -48

Here is some rules of multiplication of integers:

1. Positive integer × negative integer = negative.

2. Positive integers × Positive integers =  positive.

3.  Negative integers × Negative integers = positive.

Here, To find the  the multiplying integers

-2x24 = -48

When you multiply integers :

Negative x Positive = Negative

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Answer:

-13

Step-by-step explanation:

We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.

We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.

We can see here that it shows that a is an element of the subgroup of H.

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The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = -2x² - 4x + 12, we have:

Axis of symmetry, Xmax = -(-4)/2(-2)

Axis of symmetry, Xmax = 4/-4 = -1.

For the vertex of f(x) = -2x² - 4x + 12, we have:

f(-1) = -2(-1)² - 4(-1) + 12 = 14.

For the given quadratic function f(x) = x²-4x+3, we have:

Axis of symmetry, Xmax = -(-4)/2(1)

Axis of symmetry, Xmax = 4/2 = 2.

For the vertex of f(x) = x²-4x+3, we have:

f(2) = (2)²-4(2) +3 = -1.

Therefore, 2 is greater than -1.

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Answer: √35/6

Step-by-step explanation:

see image for explanation

Answer:

Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:

Let r be the continuous shrinkage rate of the quantity

The effective shrinkage rate of the quantity is given by the expression (1 - r).

From the given information , r = 33% = 0.33.

Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.

Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.

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Step-by-step explanation:

The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.

The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.

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The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).

Given that,

We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.

We know that any point on the unit circle can be defined as,

(cos θ, sin θ)

where θ is the angle formed with the X axis.

-5π/4 will be the point the corresponds to -225°.

Cos(-5π/4) = cos (5π/4)

                  = cos (π + π/4)

                  = -cos (π/4)

                  = -1/√2

sin (-5π/4) = -sin (5π/4)

                  = -sin (π + π/4)

                  = sin (π/4)

                  = 1/√2

Hence the coordinate of the unit circle is (-1/√2, 1/√2).

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If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.

A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.

If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.

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Answer: 24 minutes and 30 seconds after the meeting as started

Step-by-step explanation:

110 minutes into 2 equal parts = 55 minutes in each section.

In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.

Total session minutes - 110

Two equal parts of session: 55 minutes in each session

10 minute break in each session: 55-10 =45.

24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds

After 50 minutes the break will start.

The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.

so, duration of metting without the break=100 minutes

                                 duration of each part=50 minutes

Now, the break should be after First part which is of 50 minutes.

=> The break should 50 minutes after the starting of metting.

Answer:

8.) is D

9.) is B

10.) is A

Step-by-step explanation:

mark brainliest

Answer: D, B, A

Step-by-step explanation:

When multiplying or dividing - and + numbers, rules are as follows:

If the signs are the same, your answer will be +

[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]

[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]

If the signs are different, your answer will be -

[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]

[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]

If there is no sign in front of number, it is positive

8.

a. 18 / -9 = -2   negative because signs are diff

b. -35 / -7  +5   signs same so +

c.  -12 / -6 = +2          same signs so +

d. 70 / -10 = -7        diff signs so -

Order from least to greatest:

-7    -2   2   5

Answer: D

9.  Follow rules from above:

Be careful with fractions  1/5  is not the same as 5/1.

With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.

a.  +1/5

b.  -1/5

c.  +1/10

d.  +1/10

Order from least to greatest:

-1/5    1/5   1/10    1/10

Answer: B

10.

a. -2/3

b.  +1/25

c.  +3/25

d.  +1/50

The smallest number is the negative number

Answer A