Evaluate the expression: |5-6|

The given number written in scientific notation is 1.4398 × 10⁴

From the question, we are to write the given number in scientific notation.

The given number is 14,398.

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Thus,

To write the numbers in scientific notation, we will express the number as the multiplication of a number between 1 and 10 and a power of 10.

A number between 1 and 10 that can easily be formed from the number is 1.4398

Then, we can write that

14,398 = 1.4398 × 10⁴

Hence, the given number written in scientific notation is 1.4398 × 10⁴

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Answer:

32X^9

Step-by-step explanation:

The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:

The components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).

This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle

From the graph, the coordinates are:

component 1: (6, -6) to (3, -6)

component 2: (7, -6) to (6, -6)

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Answer: -42 7/8

Step-by-step explanation: Hope this help:D

Answer:

31.4 in^2 i think

Step-by-step explanation:

The solution of the equation 2x² + 4x=1 using quadratic formula  is x = 0.22, -2.22

A quadratic formula is a formula that provides the solution(s) to a quadratic equation.

Given a quadratic equation of the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we can put the coefficients in the quadratic formula:

x = (-b±√(b²-4ac))/(2a)

Given: 2x² + 4x=1, we can rewrite it as:

2x² + 4x - 1 = 0  

a = 2, b = 4 and c = -1 . Put these values in the quadratic formula:

x = (-b±√(b²-4ac))/(2a)

x =  (-4±√(4²-4×2×-1))/(2×2)

x = (-4±√(16+8))/(4)

x = (-4±√24)/(4)

x = (-4±√24)/(4)

x = (-4±4.899)/4

x = (-4+4.899)/4, (-4-4.899)/4

x = 0.22, -2.22

Therefore, the solution of 2x² + 4x=1 is x = 0.22, -2.22

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Answer:

15 students

Step-by-step explanation:

The fraction of students who will repeat the exam is:

\(1-\frac{6}{9}\)

=\(\frac{9}{9} -\frac{6}{9} =\frac{3}{9}\)

simplified is:

\(\frac{1}{3}\)

Extract this fraction of 45:

\(45(\frac{1}{3} )=\frac{45}{3} =15\)

Hope this helps

Answer:

No,because it does not go with pythagoras thorem

"From a table of integrals, we know that for \(\(a \neq 0\)\) and \(\(b \neq 0\):\)

\(\[\int \cos(at) \, dt = \frac{1}{a} \cdot \cos(at) + \frac{1}{b} \cdot \sin(bt) + C\]\)

and

\(\[\int e^a t \cos(bt) \, dt = \frac{e^{at}}{a} \cdot \cos(bt) + \frac{b}{a^2 + b^2} \cdot \sin(bt) + C\]\)

Use this antiderivative to compute the following improper integral:

\(\[\int_{-\infty}^{0} \cos(3t) \, dt = \lim_{{T \to \infty}} \int_{0}^{T} e^t \cos(3t) \, e^{-st} \, dt = \lim_{{T \to \infty}} \text{ if } s \neq 1, \, \text{ or } \lim_{{T \to \infty}} \text{ if } s = 1.\]\)

For which values of \(\(s\)\) do the limits above exist? In other words, what is the domain of the Laplace transform of \(\(\frac{1}{\cos(3)} \cdot e^t \cos(3t)\)\)?

Evaluate the existing limit to compute the Laplace transform of  on the domain you determined in the previous part:

\(\[L\{e^t \cos(3t)\\).

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Answer:

what question all of them if you want to answer all of them go to a new tab and look up calculator hope i help a little

Step-by-step explanation:

Answer:

sin J = \(\frac{15}{29}\)

cos J = \(\frac{21}{29}\)

tan J = \(\frac{5}{7}\)

x = 14.6

Step-by-step explanation:

1st pic:

1st, find the missing side lenght:

\(a^{2} = c^{2} - b^{2}\)

\(a^{2} = 58^{2} - 42^{2}\)

\(a^{2} = 3364 - 1764\)

\(\sqrt{a^{2}} = \sqrt{1600}\)

a = 40

sin = \(\frac{opposite}{hypothenuse}\) ⇒ \(sin J = \frac{30}{58} = \frac{15}{29}\)

cos = \(\frac{adjacent}{hypothenuse}\) ⇒ \(cosJ = \frac{42}{58} = \frac{21}{29}\)

tan = \(\frac{opposite}{adjacent}\) ⇒\(tanJ = \frac{30}{42} = \frac{5}{7}\)

2nd pic:

use sine:

sin = \(\frac{opposite}{hypothenuse}\)  

sine 59 = \(\frac{x}{17}\)

sine of 59 is 0.857:

0.857 = \(\frac{x}{17}\)

multiply 17 on both sides:

0.857 x 17 = \(\frac{x}{17}\) x 17

14.569 = x

round to the nearest tenth:

14.569 = 14.6

The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

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Answer:

888

Step-by-step explanation:

Im pretty sure this is the answer, if helpful please mark me as brainiest :>

The first step is to determine the side lengths of the small box.

Side length = ∛64 = 4 in

Side lengths of the medium boxes = 4 x 2 = 8 inches

Volume of the medium box = 8³ = 256 cubic inches

The ratio of the sides of the small box to the medium box = 4 : 8 = 1:2.

The ratio of the area of the small box to the medium box= (4 x 4) : (8 x 8) =  1:4.

The ratio of the volume of the small box to the medium box = 4³ : 8³ = 1 : 8.

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The quadratic equation that has (3·x + β) ans (3·x + a) as the roots can be presented as follows;

9·x² - 7.5·x - 3 = 0

A quadratic equation is an equation that can be expressed in the form; y = a·x² + b·x + c, where, a ≠ 0, and a, b, and c are numbers.

The quadratic equation -2·x² - 5·x + 6 = 0, divided by a factor of -1 indicates that we get;

2·x² + 5·x - 6 = 0

The quadratic formula indicates that we get;

x = (-5 ± √(5² - 4 × 2 × (-6))/(2 × 2) = (-5 ± √(73))/4

Let a = (-5 + √(73))/4 and let β =  (-5 - √(73))/4)

(3·x + ((-5 + √(73))/4)) × (3·x + (-5 - √(73))/4) = 9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4)

9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4) = 9·x² - 15·x/2 - 3 = 0

Therefore, the equation that has (3·x + β) ans (3·x + a) as roots is the equation

9·x² - 15·x/2 - 3 = 9·x² - 7.5·x - 3 = 0

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Answer:

In Jan - 13,759

In Feb - 9,854

In both - 23,613

Step-by-step explanation:

hope it helps

Answer:

what's the question at the bottom

\(\\ \rm\Rrightarrow tan16.5=\dfrac{H}{13.5}\)

\(\\ \rm\Rrightarrow H=13.5tan16.5\)

\(\\ \rm\Rrightarrow H=13.5(0.296)\)

\(\\ \rm\Rrightarrow H=3.996ft\)

The standard equation of a circle with center (3, 2) and passes through (1, 2) is (x - 3)² + (y - 2)² = 4.

The standard equation of a circle with center (3, 2) and passes through (1, 2) can be determined as follows:

Formula: The standard equation of a circle with center (a, b) and radius r is

(x - a)² + (y - b)² = r²

Where,

The given center is (3, 2) and the given point on the circle is (1, 2).

The radius of the circle can be calculated as the distance between the center and the given point on the circle.

D = distance between (3, 2) and (1, 2)

D = √[(1 - 3)² + (2 - 2)²]

D = √4D = 2

Therefore, the radius of the circle is 2.

Substitute the values in the formula for the standard equation of a circle with center (a, b) and radius r:

(x - a)² + (y - b)² = r²(x - 3)² + (y - 2)²

= 2²(x - 3)² + (y - 2)²

= 4

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Answer:

it's D because

6/2=3

So you then divide 15/3=5

Answer:

Step-by-step explanation:

To find the general solution to the given differential equation y^(4) + 2y" + y = 3 + cos(2t), we can follow these steps.Therefore, the correct option is:

o y = c_1cost + c_2sint + t(c_3cost + c_4sint) + 3 + (1/9)sin(2t)

1. Start by finding the complementary function by assuming y = e^(rt), where r is a constant:

  Substitute this assumption into the differential equation:

  r^4e^(rt) + 2r^2e^(rt) + e^(rt) = 0

  Simplify the equation:

  e^(rt)(r^4 + 2r^2 + 1) = 0

2. Solve the equation r^4 + 2r^2 + 1 = 0 to find the roots:

  Let's substitute u = r^2:

  u^2 + 2u + 1 = 0

  (u + 1)^2 = 0

  u + 1 = 0

  u = -1

  Substitute back u = r^2:

  r^2 = -1

  r = ±i

  Therefore, the roots of the equation are r = ±i.

3. Based on the roots, the complementary function is:

  y_c = c_1cos(t) + c_2sin(t) + c_3cos(t) + c_4sin(t)

       = (c_1 + c_3)cos(t) + (c_2 + c_4)sin(t)

4. To find a particular solution, guess a form that matches the non-homogeneous term:

  y_p = At^2 + B + Ccos(2t) + Dsin(2t)

5. Take derivatives of y_p and substitute them into the differential equation to solve for the coefficients A, B, C, and D.

6. Substituting the values of A, B, C, and D back into the particular solution y_p, we get:

  y_p = t^2 + 3 + (1/9)cos(2t) + (1/9)sin(2t)

7. The general solution is the sum of the complementary function and the particular solution:

  y = y_c + y_p

    = (c_1 + c_3)cos(t) + (c_2 + c_4)sin(t) + t^2 + 3 + (1/9)cos(2t) + (1/9)sin(2t)

Therefore, the correct option is:

o y = c_1cost + c_2sint + t(c_3cost + c_4sint) + 3 + (1/9)sin(2t)

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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Answer:

40 years old.

Step-by-step explanation:

\(x - \frac{2}{5} x = 24 \\ \frac{3}{5} x = 24 \\ x = 24 \div \frac{3}{5} = 40\)

Partial initialization allows us to initialize only some elements of an array, leaving the rest with default values.

The statement you provided, `int num]= (88, 92, 75, 95, 82)`, contains syntax errors and is not a valid example of partial initialization of an array in C or C++.

To understand partial initialization of an array, let's consider a correct example. Suppose we have an integer array named `num` with a size of 10. We want to initialize the first five elements of the array with specific values, and the remaining elements should be set to 0. Here's how partial initialization would look like:

int num[10] = {88, 92, 75, 95, 82};

In this example, we declare an integer array `num` with a size of 10. We provide an initializer list inside curly braces `{}` to initialize the elements of the array. The first five elements are explicitly initialized with values `88`, `92`, `75`, `95`, and `82`. The remaining elements are automatically set to 0 because we haven't provided explicit values for them.

Partial initialization allows us to initialize only some elements of an array, leaving the rest with default values. It's particularly useful when we want to set certain values while keeping others as defaults, such as zero in the case of integers.

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Answer:

(6 ± √72i) / 6

Hope this helps.

Answer:

Step-by-step explanation:

3\(x^{2}\)-6x+9=0

3\(x^{2}\) +3x-9x+9=0  (splitting  -6x as +3x & -9x)

3x(x+1)-9(x+1)=0

(x+1)(3x-9)=0

x=-1,3

The value of the function f(x) = g(x) is \(x^2 -8x + 15 = 0\)

Data;

Solving the function above by substitution method, we just need to substitute the values where required and solve.

\(f(x) = g(x)\)

Substituting the value,

\(x^2 - 7x + 13 = x - 2\\x^2 -7x - x + 13 + 2 = 0\\x^2 -8x + 15 = 0\)

The value of the function f(x) = g(x) is \(x^2 -8x + 15 = 0\)

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The probabilities of HH, TT, and HT or TH are 0.25, 0.25, and 0.50.

Probability means the occurrence of a random event. The value of probability can only be from 0 to 1.

The sample space will be

Sample = 4 {HH, HT, TH, TT}

The probability of getting Head on both coins will be

P(HH) = 0.25

The probability of getting Tail on both coins will be

P(TT) = 0.25

The probability of getting one Head and one Tail will be

P(HT, TH) = 0.5

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