Evaluate (18)^2-(15)^2.
Please show working

Answer:

\(\sqrt{45}\)

Step-by-step explanation:

The velocity of the ball at t = 2 is as follows: v(2) = lim t→2 (−16t14)(t − 2) /(t − 2) = -224.

A limit is a mathematical concept that represents the value a function or sequence approaches as the input or index approaches some value or approaches infinity or negative infinity. It may be a single real number or ± infinity, depending on the behavior of the function around the limit point.

Here are the steps for evaluating a limit by factoring:

1: Use algebraic techniques to simplify the expression and cancel out any common factors.

2: Substitute the limiting value of the function. Use direct substitution if possible.

3: If the denominator equals zero after substitution, factor the numerator and denominator, then cancel out any common factors.

4: Use the properties of limits to simplify the expression and evaluate it.

The velocity of the ball at t = 2 is as follows: v(2) = lim t→2 (−16t14)(t − 2) /(t − 2) = -224.

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Answer:

C  72

Step-by-step explanation:

55% close at 10

25% close at 11

55% + 25% = 80%

The "rest" means 100% - 80% = 20%

The rest is 20% of 360.

20% of 260 = 0.20 * 360 = 72

Answer:

The ratio means that for every 9 boys there are 10 girls

Step-by-step explanation:

The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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The distance from a to the line passing through b and c is 7/5.

To find the distance from a point to a line, you can use the cross product and the dot product.

First, find the vector pointing from a to b and the vector pointing from b to c:

u = b - a = (3, -5, 0) - (0, 3, -5) = (3, -8, 5)

v = c - b = (3, 0, -5) - (3, -5, 0) = (0, 5, -5)

Next, find the cross product of these two vectors, which gives a vector orthogonal to the plane defined by the line:

n = u x v = (-40, 0, 40)

Finally, find the dot product of n and a - b, which gives the magnitude of the projection of a - b onto n:

d = |n . (a - b)| / |n| = |(-40, 0, 40) . (-3, -8, -5)| / |(-40, 0, 40)| = 57 / √(40^2 + 40^2) = 57 / √1600 = 57 / 40 = 7/5

Therefore, the distance from a to the line passing through b and c is 7/5.

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Answer:

Range: 75 Median: 58 1Q: 40 3Q: 75 Interquartile: 35

Answer:

x=-1, y=2

Step-by-step explanation:

2(2x+4)=6x+10

2x=-2

x=-1

y=2(-1)+4

y=2

The direction angles of the vector v = 2i + 6j - 3k are α = 73°, β = 31°, and γ = 115°

To find the direction angles of the vector v = 2i + 6j - 3k, we need to calculate the angles α, β, and γ between the vector and the x, y, and z axes, respectively.

1. Calculate the magnitude of the vector:

|v| = \(√(2^2 + 6^2 + (-3)^2)\)

= √(4 + 36 + 9)

= √49 = 7

2. Find the cosine of each direction angle:
  cos(α) = (2) / |v| = 2/7
  cos(β) = (6) / |v| = 6/7
  cos(γ) = (-3) / |v| = -3/7

3. Calculate the direction angles by finding the inverse cosine of each cosine value:
  α = \(cos^(-1)(2/7)\) ≈ 73°
  β = \(cos^(-1)(6/7)\) ≈ 31°
  γ = \(cos^(-1)(-3/7)\)≈ 115°

Thus, the direction angles of the vector v = 2i + 6j - 3k are α = 73°, β = 31°, and γ = 115°.

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Therefore, the sides of the two triangles for x = 2 are approximately 106.099 and 22.317. After a few iterations, we get an approximate value of y for x = 2: y_1 = 9.618, y_2 = 9.614 and y_3 = 9.614

A triangle is a two-dimensional geometrical shape with three straight sides and three angles. It is one of the basic shapes in geometry and is commonly encountered in mathematics, science, and everyday life. Triangles can be classified based on the lengths of their sides and the measures of their angles. Some common types of triangles include equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), and scalene triangles (no sides or angles are equal). Triangles have many properties and relationships that are useful in solving problems involving angles, sides, and area.

Here,

Since the two triangles are similar and one triangle is inscribed in the other, the corresponding sides of the two triangles are proportional. That is,

(y² + 16) / (yx² + 9x) = (x² + 7x + y/2) / (3y/2 + 17)

Cross-multiplying and simplifying, we get:

(y² + 16)(3y/2 + 17) = (yx² + 9x)(x² + 7x + y/2)

Expanding and rearranging, we get a quadratic equation in y:

3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836 = 0

This equation is difficult to solve explicitly for y, but we can use numerical methods or algebraic software to find an approximate value of y for a given value of x.

For example, let's assume x = 2. Using a numerical method such as Newton-Raphson, we can iteratively solve for y:

Let f(y) = 3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836

Let f'(y) be the derivative of f(y): f'(y) = 9y² + 88y + 102

Let y_0 be an initial guess for y, such as y_0 = 10 (any positive value of y would work as an initial guess)

Iterate using the formula: y_n+1 = y_n - f(y_n) / f'(y_n), starting with n = 0

After a few iterations, we get an approximate value of y for x = 2:

y_1 = 9.618

y_2 = 9.614

y_3 = 9.614

Therefore, for x = 2, the positive value of y is approximately 9.614. We can then use this value to find the corresponding sides of the two triangles:

Side of big triangle: y² + 16

= 9.614² + 16

= 106.099

Side of small triangle: x² + 7x + y/2

= 2² + 7(2) + 9.614/2

= 22.317

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The angle between the vectors u and v is 126.87° and the sketch of the vector has been attached below.

To find the angle between two vectors u and v, we can use the dot product formula:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of the vectors u and v, and θ is the angle between them.

First, we need to find the magnitudes of u and v:

|u| = √(0^2 + 8^2) = 8

|v| = √((-3)^2 + (-3)^2) = 3√2

Next, we need to calculate the dot product of vectors u and v:

u · v = (0)(-3) + (8)(-3) = -24

Now we can solve for θ:

-24 = (8)(3√2) cosθ

cosθ = -24 / (8)(3√2) = -√2 / 6

Taking the inverse cosine of both sides, we get

θ = cos⁻¹(-√2 / 6) ≈ 126.87°

Therefore, the angle between u=(0,8) and v=(-3,-3) is approximately 126.87°

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Answer: -6

Step-by-step explanation:

you divide

1. 4.8y = -28.8

2. -28.8/4.8

3. y = -6

double check by multiplying 4.8 by -6

Answer:

false

Step-by-step explanation:

False

5(9)(3.2)

45*3.2=144

Hope this helps :)

Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

Answer:

8/10

Step-by-step explanation:

The rise on the y axis is eight and the run on the x axis is 10

(Hope this helped)

Answer:

The function crosses the Y axis (the up down axis) at -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

b + 2 = b + 2

Answer:

A

Step-by-step explanation:

b+2=b+2 has infinite solutions

Answer:

i don't know but I think question 1 is 64

Answer;

J is 6

Step-by-step explanation:

Answer:   j = 486

Step-by-step explanation:

So the order from left to right would be: Mode, Median, Mean.

In a positively skewed distribution, the mean is typically larger than the median, and the median is larger than the mode.

This can be illustrated in the following way:

Mean: The mean is affected by extreme values in the tail of the distribution, and will be pulled in the direction of the skew. Therefore, in a positively skewed distribution, the mean will be to the right of the median.

Median: The median is the value that separates the lower 50% of the data from the upper 50% of the data. In a positively skewed distribution, the tail of the distribution is on the right-hand side, which means that the median will be closer to the left-hand side than the mean.

Mode: The mode is the most frequent value in the distribution. In a positively skewed distribution, the mode will be the smallest value, located at the left-hand side of the distribution, while the mean and median will be to the right of it.

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My friend consumed 8 donuts in one sitting. 8 donuts is a lower bound on how many donuts he is physically capable of eating in one sitting option A.

An element of K that is bigger than or equal to each member of S is referred to as an upper limit or majorant of a subset S of some preordered set (K, ) in mathematics, notably in order theory. In addition, each element of K that is smaller than or equal to each element of S is characterised as a lower limit or minorant of S.

A set that has an upper (or lower) bound is referred to as being majorized (or minorized), bounded from above, or minorized by that bound. In the mathematical literature, sets that have upper (or lower, respectively) limits are referred to as being bounded above (or below).

Friend consumed 8 doughnuts. So it is

lower bound on how can eat in a sitting.

Many donuts he lower bound is the lowest quantity in a set, as in our.

example, we definitely know he can eat 8 of them. We don't know how many more can be eat (upper bound) or is it exact amount be can eat.

Hence option (a) is correct.

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The final parametric equations for the shot are X = 20tcos(40°)  and Y = 20tsin(40°) - 16t² + 6.

Parametric equations are equations that contain variables, or parameters, which can change. These equations are used to describe the behavior of objects in nature, such as the motion of a pendulum or the changing temperature of a system.

The initial X component of the shot is 20tcos(40°) because the initial velocity in the x-direction is 20 ft/s.
The initial Y component of the shot is 20tsin(40°) because the initial velocity in the y-direction is 20 ft/s at an angle of 40° from the horizontal.
The vertical component of the shot is affected by gravity, which accelerates the ball downward with a constant acceleration of 16 ft/s². Therefore, the equation of motion in the vertical direction is -16t².
Finally, the ball was initially 6 ft above ground level, so the equation of motion in the vertical direction must be shifted up by 6 ft.
Therefore, the final parametric equations for the shot are:
X = 20tcos(40°)

Y = 20tsin(40°) - 16t² + 6.

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In the given question the labor hours productivity using the Standard power washer was 4.5 cars per hour using unitary method.

To calculate the labor hours productivity using the Standard power washer, we need to find the number of cars washed per hour.

First, let's calculate the total number of cars washed in a month with the Standard power washer. The Students Union washed 105 cars per month.

Next, we calculate the total number of labor hours worked in a month by multiplying the number of students, days worked, and hours per day. In this case, 4 students worked 20 days a month, and each day they worked for 8 hours. So the total labor hours worked is 4 * 20 * 8 = 640 hours.

To find the labor hours productivity, we divide the total number of cars washed by the total labor hours worked. Therefore, 105 cars / 640 hours = 0.164 cars per hour.

Rounding to one decimal place, the labor hours productivity using the Standard power washer is approximately 0.2 cars per hour, which is equivalent to 4.5 cars per hour.

Therefore, the correct answer is option Ob. 4.5 cars/hr.

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Answer:

equivalent of 50En-1+n(4n+3))is4{50(50+1)(2×60+1)+3{50(51)_2}

Answer: D

Step-by-step explanation: Im from the future D is correct on edge yw :)

When x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

In the given question, we have to find what is remainder when x^3+2x^2+x+1 is divided by (x+1).

To find the remainder there are two ways. First we divide the x^3+2x^2+x+1 by (x+1). Second we find the value of from (x+1) by equating (x+1) equal to zero. The put the value of x in the expression x^3+2x^2+x+1.

In this we ca easily find the remainder.

Now we firstly find the value of x;

(x+1) = 0

Subtract 1 on both side we get;

x= −1

Now put x= -1 in the expression x^3+2x^2+x+1.

x^3+2x^2+x+1 = (−1)^3+2(−1)^2+(−1)+1

x^3+2x^2+x+1 = −1+2−1+1

x^3+2x^2+x+1 = 1

Hence, when x^3+2x^2+x+1 is divided by (x+1) then remainder is 1.

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The right question is:

What is remainder when x^3+2x^2+x+1 is divided by (x+1)?

Answer:

A \(1.3 - 5.6 = - 4.3\)

Step-by-step explanation:

\(1.3 - 5.6 = - 4.3\)

Hope this helps! Pwease mark me brainliest! Have a great day!

−xXheyoXx

Answer:

just answering so you can give the other person brainliest :D

Step-by-step explanation:

Answer:

L=9

Step-by-step explanation:

Find the length of a rectangle whose breadth is 15 cm and perimeter is 48 cm.

perimeter = 2B +2L

48 = 2X15 +2L

48 = 30+ 2L

48-30 = 30-30+2L

18= 2L

18/2 =L

L=9

A M function file 'tconvert.m', which can convert coordinates (x, y) into Polar from Cartesian coordinates. is:
"```matlab
function [theta, r] = tconvert(x, y)
```"

To create the M function file 'tconvert.m' that converts Cartesian coordinates (x, y) into Polar coordinates, follow these steps:

1. Open the MATLAB Editor or any text editor and create a new file named 'tconvert.m'.

2. In the file, start with the function declaration line: `function [theta, r] = tconvert(x, y)`.

3. Inside the function, write the conversion code using MATLAB's built-in functions:

  - Calculate the angle theta using `atan2(y, x)`, which returns the angle in radians.

  - Calculate the radius r using `sqrt(x^2 + y^2)`, which gives the distance from the origin.

4. End the function with the `end` keyword.

5. Save the file in a directory accessible by MATLAB.

The function 'tconvert' takes the Cartesian coordinates (x, y) as input and returns the corresponding Polar coordinates (theta, r). The angle theta represents the direction in radians, and the radius r represents the distance from the origin.

The function can be called from the MATLAB command window or from another script or function file.

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Complete question:

Write a M function file 'tconvert.m', which can convert from Cartesian coordinates (x,y) into Polar coordinates.