A vector F of magnitude 50 lb acts at an angle of 55° and another vector G of magnitude 60 lb acts at an angle of 310°. Find the sum of the two vectors. (Round the magnitude to the nearest whole number and the angle to the nearest degree.

Comparing both given functions, we can state that: B. Function 1 has the greater rate of change; the slope is 2.

Another name for the rate of change of a function is the slope. It is calculated using the formula:

Slope / rate of change = change in y / change in x.

If the equation of a linear function is given in slope-intercept form as y = mx + b, the rate of change or the slope is represented by "m".

Given the first function as an equation, y = 2x - 6, the slope of this function is represented as 2. This means, the rate of change is m = 2.

To find the rate of change of function 2, use two points from the table, (1, -4) and (2, -5):

Rate of change / slope (m) = (-5 - (-4)) / (2 - 1) = -1/1

m = -1.

The slope value of 2 is greater than the slope value of -1, therefore, we can conclude that: B. Function 1 has the greater rate of change; the slope is 2.

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Answer:

\(785in^3\)

Step-by-step explanation:

\(V=\pi r^2h=\pi *5^2*10=785.39816\\=785.4\\=785in^3\)

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Explanation:

For this problem, we can make a lattice multiplication diagram. Place the digits of 124 across the top of the lattice multiplication box. Then place the digits along the right hand side of the box. Refer to figure 1 in the diagram below. I've color-coded the alternating bands of diagonals to help be able to add the values we need.

In figure 2, I multiplied all of the outer header single-digit values to get two-digit results. For instance, in the bottom right corner we have 4*3 = 12. Note how the 1 and the 2 of "12" is broken up like you see in figure 2. It's important to separate out the digits like this.

This is because we'll be adding along the diagonal color bands. The 2 in the white triangle in the very bottom right corner is the last digit of the product. This matches with 64086e2 having 2 as the last digit.

Then we add along the diagonal pink color band getting 6+1+2 = 9. This is the digit e. So e = 9 (refer to figure 3). The number 64086e2 updates to 6408692

We could keep going with the lattice process, but I'll stop here and move onto the next section below.

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

Let m = 6408692

We can do trial and error to determine what d must be equal to. The list of choices we have are {0,1,2,3,4,5,6,7,8,9}

So let's go through those possible values of d

Since d = 6 and e = 9, this means d+e = 6+9 = 15.

Answer:

1000 cm2

Step-by-step explanation:

Pretty sure

Answer:

Your answer is: 1000\(cm^{2}\)

Step-by-step explanation:

The second description is not suitable.

It should be "simplify the terms" sice you are just adding 36 and -20.

Consider the given expression,

Apply the distributive property,

Combine like terms,

Subtract 20 from both sides,

Divide both sides by 27,

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

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Answer:

A. 5

Step-by-step explanation:

Based on the secant and tangent theorem, (4 + x)*4 = 6²

We can solve for x using the equation which describes the relationship between secant and tangents.

Thus,

\( (4 + x)*4 = 6^2 \)

\( 4*4 + x*4 = 36 \)

\( 16 + 4x = 36 \)

Subtract 16 from both sides

\( 4x = 36 - 16 \)

\( 4x = 20 \)

Divide both sides by 4

\( \frac{4x}{4} = \frac{20}{4} \)

\( x = 5 \)

Given the inequality

Re-arranging

If we make x the subject of the formula

Answer:

6:10

Step-by-step explanation:

3:5 is equivalent to 6:10 because you multiply both 3 and 5 by 2 and you get 6:10. every thing else is wrong

Answer:

6:10 is the only ratio equivalent to 3:5

Step-by-step explanation:

its not the first one because 5 goes into 30 6 times and 3*6=18 not 13

4:15 isn't possible either because 5 goes into 15 3 times and 3*3=9 not 4

the last one is correct because 3*2=6 and 5*2=10

The given statement "The probability of winning a lottery is .0000000012. The Law of Large Numbers says that because this probability is so small, no one should ever win a lottery." is False because the Law of Large Numbers does not state that an event with a small probability will never occur.

In fact, the law states that as the number of trials increases, the observed frequency of an event will approach the theoretical probability of that event. So, while the probability of winning a lottery may be very small, if enough people play the lottery over a large number of trials, it is expected that some people will win.

Additionally, the Law of Large Numbers does not apply to a single event but rather to the long-term frequency of an event over a large number of trials. Therefore, it is not accurate to use the Law of Large Numbers to make predictions about individual lottery outcomes.

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The curvature of the function y = x^3 at x = 1 is 2√10 / 9. A graph of the curve and the osculating circle can be visualized using GeoGebra.

a. Find the equation of the line of intersection between x+y+z=3 and 2x-y+z=10.For the line of intersection between the two given planes, let's solve the two given equations to find the two unknowns, y and z:    x + y + z = 3    2x - y + z = 10Multiplying the first equation by 2 and subtracting the second from the first gives:    2x + 2y + 2z - 2x + y - z = 6 - 10 which simplifies to:    3y + z = -4We can now choose any two of the variables to solve for the third. Since we are interested in the line of intersection, we will solve for y and z in terms of x:    y = (-1/3)x - (4/3)    z = (-3/3)y - (4/3)x + (9/3) which simplifies to:    z = (-1/3)x + (5/3)The equation of the line of intersection is therefore:    r = (x,(-1/3)x - (4/3),(-1/3)x + (5/3)) = (1, -1, 2) + t(3, -1, -1) b. Derive the formula for a plane, wrote the vector equation first and then derive the equation involving x, y, and z.The general form of the equation of a plane is: ax + by + cz = dThe vector equation of a plane is:    r • n = pwhere r is the position vector of a general point on the plane, n is the normal vector of the plane, and p is the perpendicular distance from the origin to the plane. To derive the formula involving x, y, and z, let's rewrite the vector equation as a scalar equation:    r • n = p    (x,y,z) • (a,b,c) = d    ax + by + cz = d The formula for a plane can be derived by knowing a point on the plane and a normal vector to the plane. If we know that the plane contains the point (x1,y1,z1) and has a normal vector of (a,b,c), then the equation of the plane can be written as:    a(x - x1) + b(y - y1) + c(z - z1) = 0    ax - ax1 + by - by1 + cz - cz1 = 0    ax + by + cz = ax1 + by1 + cz1The right-hand side of the equation, ax1 + by1 + cz1, is simply the dot product of the position vector of the given point on the plane and the normal vector of the plane. c. Write the equation of a line in 3D, explain the idea behind this equation (2-3 sentences).In 3D, a line can be represented by a vector equation:    r = a + tbwhere r is the position vector of a general point on the line, a is the position vector of a known point on the line, t is a scalar parameter, and b is the direction vector of the line. The direction vector is obtained by subtracting the position vectors of any two points on the line. This equation gives us the coordinates of all points on the line. d. Calculate the curvature of y = x3 at x=1. Graph the curve and the osculating circle using GeoGebra.The curvature of a function y = f(x) is given by the formula:    k = |f''(x)| / [1 + (f'(x))2]3/2The second derivative of y = x3 is:    y'' = 6The first derivative of y = x3 is:    y' = 3xSubstituting x = 1, we get:    k = |6| / [1 + (3)2]3/2    k = 2√10 / 9The graph of y = x3 and the osculating circle at x = 1 using GeoGebra are shown below:

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(a)  The equation of the line of intersection is given by x = 7 + 2t, y = t and z = -10 - 3t.

(b)  The vector equation is ⟨x, y, z⟩ = ⟨x₀, y₀, z₀⟩ + s⟨a, b, c⟩ + t⟨d, e, f⟩

and the equation of a plane involving x, y, and z is (x - x₀)/a = (y - y₀)/b = (z - z₀)/c.

(c)  The equation of a line in 3D is r = r₀ + t⋅v

(d) The curvature of y = x³ at x=1 is 6.

(a) To find the equation of the line of intersection between the planes x+y+z=3 and 2x-y+z=10, we can set up a system of equations by equating the two plane equations:

x + y + z = 3 ...(1)

2x - y + z = 10 ...(2)

We can solve this system of equations to find the values of x, y, and z that satisfy both equations.

Subtracting equation (1) from equation (2) eliminates z:

2x - y + z - (x + y + z) = 10 - 3

x - 2y = 7

We now have a new equation that represents the line of intersection in terms of x and y.

To find the equation of the line, we can parameterize x and y in terms of a parameter t:

x = 7 + 2t

y = t

Substituting these expressions for x and y back into equation (1), we can solve for z:

7 + 2t + t + z = 3

z = -10 - 3t

b)

The vector equation of a plane is given by:

r = r₀ + su + tv

where r is a position vector pointing to a point on the plane, r₀ is a known position vector on the plane, u and v are direction vectors parallel to the plane, and s and t are scalar parameters.

To derive the equation of a plane in terms of x, y, and z, we can express the position vector r and the direction vectors u and v in terms of their components.

Let's say r₀ has components (x₀, y₀, z₀), u has components (a, b, c), and v has components (d, e, f).

Then, the vector equation can be written as:

⟨x, y, z⟩ = ⟨x₀, y₀, z₀⟩ + s⟨a, b, c⟩ + t⟨d, e, f⟩

Expanding this equation gives us the equation of a plane involving x, y, and z:

(x - x₀)/a = (y - y₀)/b = (z - z₀)/c

(c) The equation of a line in 3D can be written as:

r = r₀ + t⋅v

The idea behind this equation is that by varying the parameter t, we can trace the entire line in 3D space.

The vector v determines the direction of the line, and r₀ specifies a specific point on the line from which we can start tracing it.

By multiplying the direction vector v by t, we can extend or retract the line in that direction.

(d)  To calculate the curvature of y = x³ at x = 1, we need to find the second derivative and evaluate it at x = 1.

Taking the derivative of y = x³ twice, we get:

y' = 3x²

y'' = 6x

Now, substitute x = 1 into the second derivative:

y''(1) = 6(1) = 6

Therefore, the curvature of y = x^3 at x = 1 is 6.

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When changing the sign of the constant a from positive to negative, the domain remains the same. But the range changes.

A function's range is the set of all values it can accept, whereas its domain is the set of all values for which it is defined.

Consider the given function f(x)=a|x|. Let us consider "a" takes positive values that is \(a\geq0\). Then, the given function is defined as follows,

\(f(x)=\begin{cases}a(x)=ax}\; &x\geq0\\{a(-x)=-ax\;&x < 0\end{cases}\)

Then, the domain will be \(\text{domain}=\mathbb{R}\{(-\infty, \infty)\) and the range will be given as \(\text{Range} = \text{only non-negative real numbers} = \mathbb{R}^++\{0\}\).

Now let us consider "a" takes negative values that is a<0. Then, the given function is defined the same and the domain will remain the same. But the range will be given as \(\text{Range} = \text{only negative real numbers} = \mathbb{R}^-+\{0\}\).

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Answer:

Hello!!...

I hope its helpful to you...

Answer:

Zero

Step-by-step explanation:

Given: 3x+13=3(x+6)+1

Step 1: Expand

3x+13=3x+19

Step 2: Subtract 3 from both sides

3x+13-13=3x+19-13

Step 3: Simplify

3x=3x+6

Step 4: Subtract 3x from both sides

3x-3x=3x-3x+6

Step 5: Simplify

0=6

NO REAL SOLUTIONS

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

zero

Step-by-step explanation:

3x + 13 = 3(x + 6) + 1

3x + 13 = 3x + 18 + 1

3x - 3x = 18 + 1 - 13

0 = 18 + 1 - 13

0 = 6

NO SOLUTION

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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Answer:

reflection over axis switch coradinate

Step-by-step explanation:

Answer:

AP : PQ = 4 : 7

Step-by-step explanation:

A, P and Q lie on a straight vertical line with

AP = 4 units and AQ = 7 units, then

AP : PQ = 4 : 7

Answer:

i dont think that this is all of the information.

Step-by-step explanation:

Answer:

5y+11

Step-by-step explanation:

y+3+4(y+2)

Use the distributive property to multiply 4 by y+2.

y+3+4y+8

Combine y and 4y to get 5y.

5y+3+8

Add 3 and 8 to get 11.

Answer:

C. A condition in which a quantity increases at a rate that is

proportional to the current value of the quantity

Step-by-step explanation:

Exponential growth is increasing, but not at a steady rate. On a graph, it has a curve instead of being a straight line.

The sample consists of three scores: 7, 8, and 9. The mean is 8, the median is 8, there is no mode, and the range is 2.

In statistics and probability, a sample refers to a subset of a population that is used to make inferences or draw conclusions about the entire population. In this case, the sample consists of the scores you obtained in 5 quizzes. The scores are as follows: 7, 8, and 9.
To analyze this sample, there are several key measures that can be calculated:
1. Mean: The mean, also known as the average, is calculated by summing up all the scores and dividing it by the number of scores. In this case, the mean can be calculated as (7 + 8 + 9) / 3 = 8.
2. Median: The median is the middle value when the scores are arranged in ascending order. In this case, since there are three scores, the median is the middle score, which is 8.
3. Mode: The mode is the score that appears most frequently in the sample. In this case, none of the scores repeat, so there is no mode.
4. Range: The range is the difference between the highest and lowest scores in the sample. In this case, the highest score is 9 and the lowest score is 7, so the range is 9 - 7 = 2.
5. Standard Deviation: The standard deviation is a measure of how spread out the scores are from the mean. It quantifies the amount of variation or dispersion in the sample. To calculate the standard deviation, you would need the full set of scores, not just the three provided.

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As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by \(ax² + bx + c = 0\).

To solve the quadratic equation, we can use the quadratic formula given by\(x = (-b ± sqrt(b² - 4ac)) / 2a\) Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.

Substituting these values in the quadratic formula, we get

\(x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2\)

Hence, the exact solutions to the given equation are \((-3 + i√15) / 2 and (-3 - i√15) / 2.\)

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The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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Answer:

x = 5

Step-by-step explanation:

f(x) = -17.1 means that the number you inputted for x gave an output of -17.1.  We see from the table that when x = 5, f(x) = -17.1.  

The correct force equilibrium equation along the y direction is ∑Fy = Cy + 450sin40° - 300 = 0.

The force equilibrium equation is used to find the unknown forces or force components that keep an object stationary, i.e. in equilibrium.

A force is defined as the push or pull on an object that results from its interaction with another object. The force equilibrium equation is based on the principle that for an object to be in equilibrium, the sum of all the forces acting on it must be equal to zero.

This equation is a vector equation that can be resolved into its x and y components. The correct force equilibrium equation along the y direction is ∑Fy = Cy + 450sin40° - 300 = 0.

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