write five next terms:1;8;27;64;125​

Answer: 68

Step-by-step explanation:

By the inscribed angle theorem, arc BA measures twice of 34 degrees, which is 68 degrees.

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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The pοssible first steps tο simplify the equatiοn are:

Multiply bοth sides οf the equatiοn by -2.

Distribute Negative οne-half οver (x + 4).

Multiply bοth sides οf the equatiοn by -2, tο get rid οf the fractiοn:

-2 * Negative οne-half (x + 4) = -2 * 6

This simplifies tο: (x + 4) = -12

Distribute Negative οne-half οver (x + 4):

Negative οne-half (x + 4) = Negative οne-half * x + Negative οne-half * 4

This simplifies tο: (-1/2)x - 2 = 6

Therefοre, the pοssible first steps tο simplify the equatiοn are:

Multiply bοth sides οf the equatiοn by -2.

Distribute Negative οne-half οver (x + 4).

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Answer:

x = 5/2

Step-by-step explanation:

Answer:

x=2.5

Step-by-step explanation:

15x + 9x = 33 + 27

24x = 60

x = 60 ÷ 24

x = 5/2 = 2.5

A road map without scale is useful for providing general directions and landmarks but may not be reliable for accurate distance measurements.

A road map without scale is good purpose for individuals who are seeking general directions or landmarks. For example, if we want to take road trip and need to know which highways to take, the map without a scale is sufficient for their needs.

But, lack of scale means the map cannot provide accurate distance measurements which will make it difficult for someone who needs to know exactly how far they need to travel. The absence of scale also make it challenging to navigate in unfamiliar areas because it is hard to determine the distance between two points.

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｡☆✼★ ━━━━━━━━━━━━━━  ☾  

x - 9.9 = 2.1

+ 9.9 to both sides

x = 12

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Answer:

X = 12

Step-by-step explanation:

X - 9.9 = 2.1

Add 9.9 to both sides

X - 9.9 + 9.9 = 2.1 + 9.9

Simplify

X = 12

Answer:

x = 10.9

Step-by-step explanation:

7.2 + x = 18.1

-7.2         -7.2

x = 18.1 - 7.2

x = 10.9

Part i) Simple interest = $600,000.00.

Part ii) Selling price = $2,900,000.00.

Part i) The formula for simple interest is;

SI = PRT/ 100

P = principal amount = $2,000,000.00.

R = rate of interest  = 15%

T = time in years = 2 years.

Put the value in the formula;

SI = ( $2,000,000 × 2 × 15)/100

On simplification;

SI = 600,000

Thus, the simple interest at the end of 2 years is $600,000.oo

Part ii) the selling price

Selling price = cost price + profit

Selling price = cost price + 45%of cost price

Cost price = $2,000,000.00

45%of cost price = 45× $2,000,000.00/100

45%of cost price = 900,000.00

Selling price = $2,000,000.00 + 900,000.00

Selling price = $2,900,000.00.

The the selling price of the fridge is found as $2,900,000.00.

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To find the point(s) on the surface z = x^2 - 5y + y^2 where the tangent plane is parallel to the xy-plane, we need to determine the points where the partial derivative of z with respect to z is zero. The equation of the tangent plane parallel to the xy-plane can be obtained by substituting the coordinates of the points into the general equation of a plane.

The equation z = x^2 - 5y + y^2 represents a surface in three-dimensional space. To find the points on this surface where the tangent plane is parallel to the xy-plane, we need to consider the partial derivative of z with respect to z, which is the coefficient of z in the equation.

Taking the partial derivative of z with respect to z, we obtain ∂z/∂z = 1. For the tangent plane to be parallel to the xy-plane, this partial derivative must be zero. However, since it is always equal to 1, there are no points on the surface where the tangent plane is parallel to the xy-plane.

Therefore, there are no coordinate points (∗,∗,∗) that satisfy the condition of having a tangent plane parallel to the xy-plane for the surface z = x^2 - 5y + y^2.

Since no such points exist, there is no equation of a tangent plane parallel to the xy-plane to provide in this case.

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The fourth graph represents the functions f(x)=-3ˣ-2

We can plug in the y intercept to find which graph has the correct one.

x = 0 is y intercept

Thus function f(0)=-3⁰-2

f(0)=-1-2

f(0)=-3

At this point we known the y intercept is -3 so both graph in the left is considerable.

Notice that the base is the negative, thus the graph would goes down. Therefore the bottom right would be correct.

Hence, the fourth graph represents the functions f(x)=-3ˣ-2

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Answer:

x=22° hope it helps:)

Step-by-step explanation:

Please mark it the brainliest if you won't mind:)

(:

Answer:

x =22

Step-by-step explanation:

ABCD is a parallelogram. In parallelogram, adjacent angles are supplementary.

∠B +∠C = 180

4x + 12 + 3x + 14 = 180

Combine like terms

4x +3x + 12+ 14 = 180

  7x +  26 = 180    {Subtract 26 from both sides}

           7x = 180 -  26

           7x = 154      {Divide both sides by 7}

             x = 154/7

x = 22

Answer:

7

Step-by-step explanation:

Using the triangle midsegment theorem,

\(x+8=2(2x-5) \\ \\ x+8=4x-10 \\ \\ 8=3x-10 \\ \\ 3x=18 \\ \\ x=6 \\ \\ SR=2(6)-5=7\)

The truth value of proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], given that a and b are true and x and y are false, is TRUE.

In the provided scenario where a and b are true while x and y are false, proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], is evaluated to be true. Let's break it down to understand why.

The proposition is in the form of an implication (⊃), where the antecedent is [(x ⊃ a) • (b ⊃ ∼ y)] and the consequent is [(b ∨ y) • (a ⊃ x)]. To determine the true value, we need to examine both the antecedent and the consequent.

In the antecedent, we have two conditions connected by a conjunction (∧): (x ⊃ a) and (b ⊃ ∼ y). Since x and y are false, the condition (x ⊃ a) is vacuously true because false implies anything. Similarly, (b ⊃ ∼ y) is also true because b is true, and ∼ y (not y) is true since y is false. Therefore, the antecedent is true.

Moving on to the consequent, we have two conditions connected by a conjunction (∧): (b ∨ y) and (a ⊃ x). In this case, b is true, so (b ∨ y) is true regardless of the truth value of y. Additionally, a is true, and since x is false, (a ⊃ x) is false. Therefore, the consequence is false.

Now, when we evaluate the entire proposition, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], we find that a true antecedent implies a false consequent, which results in a true overall proposition. Hence, the truth value of proposition 2a is TRUE in the given scenario.

In conclusion, proposition 2a holds true when a and b are true, and x and y are false. Understanding the evaluation of logical propositions like these can help in reasoning and problem-solving tasks.

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Answer:

On a number line, -6 is greater than -14.

Here's how to show it: (o is a point if you were to draw it out you would color the o in)

  -14   - 13   -12   -11   -10   -9   -8   -7    -6   -5   -4   -3   -2  -1  0

<--o------------------------------------------------o------------------------------->

-6 is closer to 0

To visualize this transformation, imagine a rectangle with vertices at and (0,2). Applying the transformation (x,y) →  \((3x,3y)\) to each vertex, we get a new rectangle with vertices at   \((0,0), (3,0), (3,6),\) and \((0,6)\), which is three times the size of the original rectangle.

Algebraic representations can take many forms, including equations, inequalities, functions, and matrices. These representations provide a powerful tool for analysing complex systems and deriving meaningful insights from them.

The algebraic representation \((x,y) (3x,3y)\) describes a dilation transformation, specifically an enlargement or stretch by a scale factor of 3 in both the x and y directions.

This means that every point in the original figure is multiplied by 3 in both the x and y directions, resulting in a larger, similar figure.

To visualize this transformation, imagine a rectangle with vertices at  \((0,0), (1,0), (1,2),\)  and   \((0,2).\) Applying the transformation (x,y) → (3x,3y) to each vertex, we get a new rectangle with vertices at \((0,0), (3,0), (3,6),\)  and (0,6), which is three times the size of the original rectangle.

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Answer:

7000

Step-by-step explanation:

Thus the truck delivers 7 tons of gravel.

"A unit conversion expresses the same property as a different unit of measurement. A conversion factor is a ratio that expresses how many of one unit is equal to another unit".

For the above situation,

A truck delivers 14,000 pounds of gravel.

We know that,

1 US ton = 2000 pounds

Thus, 14000 pounds = \(\frac{14000}{2000}\)

⇒ \(7 tons\)

Hence we can conclude that the truck delivers 7 tons of gravel.

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Answer:

f(1) = 5, f(2) = 8, f(3) = 11

Step-by-step explanation:

Common difference refers to how you get from one value in the sequence to the next.

If f(0) = 2, f(1) = 2 + 3 = 5 etc

The derivatives for given functions are as follows::

a) dy/dx = (4x^3(x^2 + 1/7x - 7) + x^4(2x + 1/7)) / (x^4x^2 + 1/7x - 7)

b) dy/dx = cos(x) - xsin(x)

To find the derivative of each function, we'll use the chain rule and the product rule where necessary.

a) y = ln(x^4x^2 + 1/7x - 7)

Using the chain rule, the derivative dy/dx is given by:

dy/dx = (1 / (x^4x^2 + 1/7x - 7)) * d/dx(x^4x^2 + 1/7x - 7)

To find the derivative of x^4x^2 + 1/7x - 7, we apply the product rule:

d/dx(x^4x^2 + 1/7x - 7) = (d/dx(x^4) * (x^2 + 1/7x - 7)) + (x^4 * d/dx(x^2 + 1/7x - 7))

The derivative of x^4 is 4x^3, and the derivative of x^2 + 1/7x - 7 is 2x + 1/7.

Substituting these derivatives into the equation:

dy/dx = (1 / (x^4x^2 + 1/7x - 7)) * ((4x^3 * (x^2 + 1/7x - 7)) + (x^4 * (2x + 1/7)))

Simplifying further, we can combine like terms:

dy/dx = (4x^3(x^2 + 1/7x - 7) + x^4(2x + 1/7)) / (x^4x^2 + 1/7x - 7)

b) y = xcos(x)

Using the product rule, the derivative dy/dx is given by:

dy/dx = (d/dx(x) * cos(x)) + (x * d/dx(cos(x)))

The derivative of x is 1, and the derivative of cos(x) is -sin(x). Substituting these derivatives into the equation:

dy/dx = 1 * cos(x) + x * (-sin(x))

Simplifying:

dy/dx = cos(x) - xsin(x)

Therefore, the derivatives are:

a) dy/dx = (4x^3(x^2 + 1/7x - 7) + x^4(2x + 1/7)) / (x^4x^2 + 1/7x - 7)

b) dy/dx = cos(x) - xsin(x)

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The first 10 Pythagorean triples are: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65).

Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The first 10 Pythagorean triples, listed in ascending order of their hypotenuse lengths, are (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65). There are infinitely many Pythagorean triples, and they have important applications in mathematics, physics, and engineering.

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The number of cruise passengers must there have been in 2017 is  26.7 million.

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

\(\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}\)

Multiplying both sides by 100;

\(\begin{aligned}&\frac{106.7 x}{100} * 100=28.5 * 100 \\&106.7 x=2850\end{aligned}\)

Dividing both sides by 106.7;

\(\frac{106.7 x}{106.7}=\frac{2850}{106.7}\)

x = 26.7

Therefore, the number of cruise passengers in 2017 must have ranged from 26.7 million.

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Answer:

B (-3,3)

Step-by-step explanation:

calculate where the lines cross each other

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The answer is option B: $8,014,195.

We can use the formula for the future value of an annuity to solve this problem:

FV = PMT x [(1 + r)^n - 1] / r

Where:

PMT = $12,000 (annual payment)

r = 11.5% (annual interest rate)

n = 40 (number of years)

Plugging in the values, we get:

FV = $12,000 x [(1 + 0.115)^40 - 1] / 0.115

FV ≈ $8,014,195

Therefore, the answer is option B: $8,014,195.

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Answer:

27

36 ft

45 ft

$189

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

original dimension = (8 x 9) / 2 = 36

(10 x 9) / 2 = 45

(6 x 9) / 2 = 27

cost of deck = sum of sides x cost per square feet

sum of sides = 36 + 27 + 45 = 108

108 x 1.75 = 189

Answer:

-7 < k < 7

Step-by-step explanation:

The absolute value of the variable k will be less than 7.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result. The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

A number k is less than 3 units from 10. Then the equation is given as

k + 3 < 10

Simplify the equation, then the value of the variable k will be

k + 3 < 10

k < 10 - 3

k < 7

The absolute value of the variable k will be less than 7.

Your question was incomplete, your question was probably be...

A number k is less than 3 units from 10.

What's the absolute value inequality?

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Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

The answer is -285

Step-by-step explanation:

Answer:

the correct answer is option c. y= 192/x