if angle 1 is 57 degrees then whats angle 6

The distance it will reach to  x, = 46.6 feet

acc to our question-

hence,The distance it will reach to  x, = 46.6 feet

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The final answer is s(t) = -cos(5x)/2 + sin(8x) + 20.

The function is: dt/ds = 5sin5t + 8cos8tThe antiderivative is the inverse of the derivative.

We must integrate both sides with respect to t.

s (t) = ∫(5sin5t + 8cos8t)dt

= -cos5t + (8/5)sin5t + C

There is a constant C in the expression that can be found by using the initial condition that

s(2π) = 20.s(2π)

= -cos(5 * 2π) + (8/5)sin(5 * 2π) + C20

= 1 + C + 0C = 19

The antiderivative that satisfies the given condition is s(t) = -cos5t + (8/5)sin5t + 19.

The final answer is s(t) = -cos(5x)/2 + sin(8x) + 20.

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Step-by-step explanation:

\( \frac{ {6}^{x} }{6} \times ({ \frac{3}{18} })^{x - 2} = {6}^{x - 1} \times {6}^{2 - x} = {6}^{(x - 1 + 2 - x)} = {6}^{1} = 6\)

Answer:

(2x−1)(x+4)

Step-by-step explanation:

2x2+7x−4=(2x−1)(x+4)

The function y(x) = c₁ cos 2x + c₂ sin 2x is a valid solution to the differential equation y'' + 4y = 0. The solution is valid for all values of x, unless specific initial conditions or constraints are given that limit its interval.

To verify if the given function y(x) = c₁ cos 2x + c₂ sin 2x is a solution to the differential equation y'' + 4y = 0, we need to substitute the function into the differential equation and check if it satisfies the equation for all values of x.

First, let's find the first and second derivatives of y(x):

y'(x) = -2c₁ sin 2x + 2c₂ cos 2x

y''(x) = -4c₁ cos 2x - 4c₂ sin 2x

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

y''(x) + 4y(x) = (-4c₁ cos 2x - 4c₂ sin 2x) + 4(c₁ cos 2x + c₂ sin 2x)

= -4c₁ cos 2x - 4c₂ sin 2x + 4c₁ cos 2x + 4c₂ sin 2x

= 0

As we can see, the expression simplifies to zero, which means that y(x) = c₁ cos 2x + c₂ sin 2x is indeed a solution to the differential equation y'' + 4y = 0.

The maximum interval over which this solution is valid depends on the initial conditions or any other constraints provided in the problem. In general, since the given solution contains periodic functions (cosine and sine), it can be defined for all real values of x.

The complete question is:

For Problems 7-21, verify that the given function is a solu- tion to the given differential equation c₁ and c₂ are arbitrary constants), and state the maximum interval over which the solution is valid.

8. y(x) = c₁ cos 2x + c₂ sin 2x,  y'' + 4y = 0

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The value of the rate constant (k) ≈ \(\(2.63 \times 10^{3} \, \mathrm{M}^{-1.99} \, \mathrm{s}^{-1}\)\)

To calculate the value of the rate constant (k) for the provided reaction rate law, we'll rearrange the rate law equation and substitute the provided values:

Rate = \(k[A]^B\)

Provided values:

\(Rate = $2.63 \times 10^{-5} \, \text{Ms}^{-1}$$[A] = 5.04 \times 10^{-3} \, \text{M}$$[B] = 2.99 \times 10^{-3} \, \text{M}$\)

Rearrange the rate law equation:

\(\[ k = \frac{\text{Rate}}{[A]^B} \]\)

Substitute the provided values:

\(\[ k = \frac{{2.63 \times 10^{-5} \, \text{Ms}^{-1}}}{{(5.04 \times 10^{-3} \, \text{M})^{2.99}}} \]\)

Now, let's calculate the value of k:

\(\[k \approx \frac{{2.63 \times 10^{-5} \, \text{M} \, \text{s}^{-1}}}{{(5.04 \times 10^{-3})^{2.99} \, \text{M}^{2.99}}} \approx \frac{{2.63 \times 10^{-5} \, \text{M} \, \text{s}^{-1}}}{{1.55796 \times 10^{-8} \, \text{M}^{2.99}}} \]\)

To simplify the units, we can rewrite \(Ms^(^-^1^)\) as \(s^(^-^1^)M^(^-^1^)\):

\(\[ k \approx \frac{{2.63 \times 10^{-5} \, \text{{s}}^{-1} \text{{M}}^{-1}}}{{1.55796 \times 10^{-8} \, \text{{M}}^{2.99}}} \]\)

Now, we can simplify the units using negative exponents:

\(\[ k \approx 2.63 \times 10^{(-5 - (-8))} \, \text{M}^{(1 - 2.99)} \, \text{s}^{-1} \approx 2.63 \times 10^{3} \, \text{M}^{-1.99} \, \text{s}^{-1} \]\)

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The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer:

7.5 cups of sugar

Step-by-step explanation:

3 cups /12 cupcakes    *   30 cupcakes = 7.5 cups

Answer:

t ≥ 2

Step-by-step explanation:

3t ≥ 15-9

3t ≥ 6

t ≥ 6/3

t ≥ 2

The function value is as follows:

A function relates an input to an output.

A function relates each element of a set with exactly one element of another set (possibly the same set).

Therefore, let's solve the function as follows;

f(x) = x + 6 / 2x - 1

let's find

f(4) = 4 + 6 / 2(4) - 1

f(4) = 10 / 8 - 1

f(4) = 10  / 7

f(0) = 0 + 6 / 2(0) - 1

f(0) = 6 / -1

f(0) = - 6

f(-5) = -5 + 6 / 2(-5) - 1

f(-5) = 1 / -10 - 1

f(-5) = 1 / - 11

f(-5) = - 1  /11

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Answer: The person paid $396.

Step-by-step explanation:

1. Since we need to find 60% of 360, we can do 360 x 60/100.

2. We are now left with 216.

3. Now we have to add the total together.

4. 216 + (15x12) = 396.

5. The person paid $396.

Answer: C. 242

Step-by-step explanation:

So first you need to know the formulas for the shapes (trapezoid and rectangle) to solve it.

Trapezoid- A= 1/2(b1+b2)h

Rectangle- L x W.

So to plug in numbers for trapezoid should look like: 1/2(13+24) (4)

1/2 (37) (4)

(18.5) (4)

=74.

For rectangle: 7 x 24= 168.

So add them together and you should have your answer. 168+74=242 in.

I hope this helped!!! :)

If the class has a mean (μ) of 60 and a standard deviation (σ) of 10, and your score is 65, then you would be above the mean but still within one standard deviation. In this case, the set of parameters μ = 60 and σ = 10 would likely give you a relatively good grade.

To determine which set of parameters would give you the best grade on the exam, we need to understand the grading scheme and how your score is compared to the rest of the class. Specifically, we need to know the mean (μ) and standard deviation (σ) of the exam scores for the entire class.

If the grading scheme involves a curve, where your score is compared to the mean and standard deviation of the class, then the set of parameters that would give you the best grade would depend on the distribution of scores in the class.

If the class has a mean (μ) of 60 and a standard deviation (σ) of 10, and your score is 65, then you would be above the mean but still within one standard deviation. In this case, the set of parameters μ = 60 and σ = 10 would likely give you a relatively good grade.

However, if the class has a different mean and standard deviation, or if the grading scheme does not involve a curve, then a different set of parameters might give you the best grade.

Without more specific information about the grading scheme and the distribution of scores in the class, it is difficult to determine the exact set of parameters that would result in the best grade for you.

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Answer:

b = 3

Step-by-step explanation:

All angles in a triangle always equal 180*

so 180 - 100 + 41 = 39

39/13 = b

3 = b

Have a nice day! :-)

Yes, they do form a triangle. This is because the sum of any two sides in a triangle must be greater than the third side. In this case, 4 + 8 is greater than 10, so it meets the criteria for a triangle.

Yes, the side lengths 4 8 and 10 can form a triangle. This is because the sum of any two sides in a triangle must be greater than the third side. In this case, 4 + 8 is greater than 10, so it meets the criteria for a triangle. A triangle is defined as a polygon with three sides and three angles, and is one of the basic shapes in geometry. It is also one of the most studied shapes in mathematics due to its wide range of applications. The three angles of a triangle must add up to 180 degrees, and the three sides must satisfy the triangle inequality, meaning that the sum of any two sides must be greater than the third side. Additionally, the interior angles of a triangle are always equal to the sum of two exterior angles. Knowing this, it can be seen that the side lengths 4 8 and 10 can form a triangle, as the sum of any two sides is greater than the third side.

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Answer:

a. 700

b. 1000

c. 80

d. 700

e.

Answer:

Since point C is located at (3, 2), we know that the x-coordinate of point B must be the same as the x-coordinate of point C, since AB is on a vertical line. Therefore, we can write the coordinates of point B as (3, y), where y is some unknown value.

We also know that point C is a right angle, which means that the slope of line segment AC is the negative reciprocal of the slope of line segment BC. Since we're given that the slope of AC is 5, we can find the slope of BC as follows:

slope of AC * slope of BC = -1

5 * slope of BC = -1

slope of BC = -1/5

Now we can use the point-slope form of a line to find the equation of line BC. We know that point B has coordinates (3, y) and the slope of BC is -1/5, so we have:

y - 2 = (-1/5)(3 - 3)

y - 2 = 0

y = 2

Therefore, the coordinates of point B are (3, 2).

To find possible coordinates for point A, we can use the fact that the slope of line segment AB is infinity, since AB is a vertical line. This means that the x-coordinate of point A must be the same as the x-coordinate of point B, which is 3. The y-coordinate of point A can be any value, as long as it's not equal to 2 (the y-coordinate of point B). For example, we could choose point A to have coordinates (3, 1).

Therefore, possible coordinates for points A and B are (3, 1) and (3, 2), respectively, and the coordinates of point C are (3, 2).

The coordinates of points A and B in triangle ABC are (0, 5) and (3, 17), respectively.

For this triangle, we can use the slope of AC (5) and the coordinates of C (3, 2) to find the coordinates of A.

We know that C is a right angle, so the change in x-coordinates must be 3 and the change in y-coordinates must be 5.

Therefore, the coordinates of A must be (0, 5).

We can also use the vertical line that AB is on to find the coordinates of B. Since AB is on a vertical line, the x-coordinate of B must be 3 (the same as the x-coordinate of C).

The y-coordinate of B can be found by plugging the coordinates of A and C into the equation of a line: y = mx + b, where m is the slope of AC (5) and b is the y-intercept.

In this case, the y-intercept is the y-coordinate of C (2). Therefore, the equation is y = 5x + 2, and when x = 3, we get y = 17, so the coordinates of B are (3, 17).

Therefore, the coordinates of points A and B in triangle ABC are (0, 5) and (3, 17), respectively.

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The probability that exactly one of the coins is a 10p piece is 1/2.

To find the probability that exactly one of the coins is a 10p piece, we can consider the possible outcomes.

There are two coins, and each coin can be either a 10p piece or a non-10p piece. Let's consider the four possible outcomes:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece.

3. Both Erin's and Jack's coins are 10p pieces.

4. Both Erin's and Jack's coins are non-10p pieces.

Since the total amount of the two coins is less than 50p, we can eliminate the third possibility (both coins being 10p pieces).

Now, let's calculate the probability for each of the remaining possibilities:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece:

The probability of Erin having a 10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece:

This is the same as the previous case, so the probability is also 1/4.

3. Both Erin's and Jack's coins are non-10p pieces:

The probability of Erin having a non-10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

Now, we sum up the probabilities of the two cases where exactly one of the coins is a 10p piece:

1/4 + 1/4 = 2/4 = 1/2.

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Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

The probability of dart landing on yellow region =  = 56.31%

Step 1; We need to determine the area of the blue region and the yellow region. To calculate the different areas we must use the areas of the shapes surrounding the particular shape.

First, we find the areas of all the shapes in the dartboard.

The area of the square with a side length 18 inches = 18 × 18 = 324 square inches.

The area of a circle with radius of 9 inches = π × 9 × 9 = 254.469 square inches.

The area of 2 triangles with a base 6 inches and height 6 inches = 2 × ( × 6 × 6) = 2 × 18 = 36 square inches.

The area of the inner square = 6 × 6 = 36 square inches.

The area of the inner circle with a radius 3 inches = π × 3 × 3 = 28.274 square inches.

Step 2; Now we calculate the areas of the blue and yellow regions.

The area of the blue region = Area of the outer square - Area of the outer circle =   324 - 254.469 = 69.531 square inches.

The area of the yellow region = Area of the outer circle - Area of 2 triangles - Area of the inner square = 254.469 - 36 - 36 = 182.469 square inches.

The area of the entire board is the same as the outer square area.

Step 3; To find any event's probability we divide the number of favorable outcomes by the total number of outcomes. Here, the favorable outcome is the area of the yellow region and the total number of outcomes is the total area of the dartboard.

The probability of the dart landing on the yellow region =  = 0.5631 = 56.31%.

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The length of the model car based on the information is 0.8 feet.

It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.

From the information, the model car is constructed with a scale of 1:15.

When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:

= 1/15 = x / 12

Cross multiply

15x = 1 × 12

15x = 12

Divide

x = 12 / 15

x = 0.8

The length is 0.8 feet.

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This may be incorrect, so sorry if it is! The answer I got is 2760y.

Answer: 5 cm

Step-by-step explanation:

B = \(\sqrt{13^{2} -12^{2} } = 5\)

Answer:

OPTION C, 5

Step-by-step explanation:

Using the formula, substitute the hypotenuse and the other leg of the right triangle.

13²=12²+b²

Rearrange appropriately.

13²-12²=c²

Convert.

13²=169

12²=144

Apply and work out.

169-144= 25

c²=25

c=√25

c=5

OPTION C is therefore the answer.

Please comment below if you need more help! :)

Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

Step-by-step explanation:

\((A-B) = ( - 2, \: - 2, \: - 2, \: - 2)\)

The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3).

To determine the x-intercept, let y = 0 and solve for x in the equation y = 3x - 1.

Substitute 0 for y in the equation.0 = 3x - 1

Add 1 to both sides1 = 3x

Divide both sides by 3x = 1/3

The x-intercept of the line is (1/3, 0).

To find the y-intercept, let x = 0 and solve for y in the equation y = 3x - 1.

Substitute 0 for x in the equation.y = 3(0) - 1y = -1

The y-intercept of the line is (0, -1).

Therefore, the x-intercept is (1/3, 0), and the y-intercept is (0, -1).

Therefore, The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3). The calculation above supports the conclusion.

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Answer: b would be the answer

Step-by-step explanation:

Answer:

$36.000

Step-by-step explanation:

Beca total = 60.000

1/5 parte = 12.000

Gasta 2/5 partes lo que son 24.000

Le quedan 36.000 para otros gastos