Find k such that x(t)=3^t is a solution of the differential equation dx/dt = kx

The identity property of multiplication is that the result of the multiplication of any number and one results in the number one.

The multiplication operation have multiple properties, which are presented as follows:

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2x:3y=4:8 is correct because it states that for every 2 units of x, there are 3 units of y, so the ratio of x to y is 4:8.

A. 2x:4y=4:8

B. 4x:2y=2:4

C. 4x:2y=4:8

D. 2x:4y=2:4

E. 3x:2y=2:4

F. 2x:3y=4:8

B, C, F

B. 4x:2y=2:4 is correct because it states that for every 4 units of x, there are 2 units of y, so the ratio of x to y is 2:4.

C. 4x:2y=4:8 is correct because it states that for every 4 units of x, there are 2 units of y, so the ratio of x to y is 4:8.

F. 2x:3y=4:8 is correct because it states that for every 2 units of x, there are 3 units of y, so the ratio of x to y is 4:8.

the complete question is :

Kiesha and her classmates wrote proportions for the reduction of a triangle. Which proportions are set up correctly? select three options.

A. 1/2:2/3:3/4

B. 3/2:2/3:1/4

C. 1/2:2/4:3/6

D. 1/4:2/3:4/5

E. 2/3:3/4:4/5

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2x:4y=4:8

B. 4x:2y=2:4

C. 4x:2y=4:8

D. 2x:4y=2:4

E. 3x:2y=2:4

F. 2x:3y=4:8

B, C, F

B. The formula 4x:2y=2:4 is accurate because it says that there are 2 units of y for every 4 units of x, making the x:y ratio 2:4.

C. 4x:2y=4:8 is true because it says that there are 2 units of y for every 4 units of x, making the x:y ratio 4:8.

F. 2x:3y=4:8 is true because it says that there are 3 units of y for every 2 units of x, making the x to y ratio 4:8.

Answer:

[tex] \sf \: x = 8[/tex]

Step-by-step explanation:

Given equation,

→ x + 10 = 18

Now the value of x will be,

→ x + 10 = 18

→ x = 18 - 10

→ [ x = 8 ]

Hence, the value of x is 8.

Answer:

C

Step-by-step explanation:

43x=42Divided 42by 43

x=42/43

x=2/3

The value of x is 42/43.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

43x = 42

Divide both sides with 43.

x = 42/43

Thus,

x = 42/43.

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Answer: Third Option: The car was at -60 feet at one second after it passed the camera. When was the car 5 feet to the west of the camera?

Step-by-step explanation:

The negatives in the equation most match the the numbers in the third option and it also the one that makes the most sense.

Hope this helps!! :)

For the given functions, the slope of f will be -1/2 and g will be -3/2, the respective y - intercepts will be -2 and 2.

The slope is m and the y-intercept is b in the slope-intercept equation (y=mx+b). It is also possible to rewrite some equations so that they appear to be in slope-intercept form. For instance, y=x can be written as y=1x+0, giving rise to a slope of 1 and a y-intercept of 0.

You can use the slope intercept formula y = mx + b if you know the slope of the line being studied and the given point is also the y intercept (0, b). In the formula, the term b stands in for the y value of the y-intercept point. In standard form, a quadratic equation is written as y=ax2+bx+c, where x and y are variables and a, b, and c are well-known constants.

1. The given equation is f(x) = -1/2 x - 2

Slope of the equation = -1/2

y - intercept = -2

Let us consider 2 points from g function,

(-2,4) and (0,1)

The slope of the equation will be = y2 - y1 / x2 - x1

= 1 - 4 / 0 + 2

= -3/2

Equation of line will be = y - yo = m (x - xo)

= y - 4 = -3/2 (x + 2)

= 2y - 8 = -3x - 6

= 3x + 2y = 2

= y = 2 - 3/2x

y - intercept = 2

2. For the equation f(x) = 6x - 1

slope of the equation = 6

y intercept = -1

For the given graph,

let us consider 2 points, (-1, 3) and (-2, 6)

Slope of the graph = 6 - 3 / -2 + 1 = 3/-1 = -3

Equation of line will be -

y - 3 = -3 (x + 1)

y - 3 = -3x - 3

y = 3x

y intercept will be 0.

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The decimal approximation for the solution is

x = -9.8635

The exponential equation can be written as

e^x = 1/41219

Taking the natural logarithm of both sides, we have:

x = ln(1/41219)

Using a calculator to evaluate the natural logarithm, we get:

x = -9.8635

So the solution set expressed in terms of natural logarithms is

x = ln(1/41219) = -9.8635

And the decimal approximation for the solution is

x = -9.8635

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The length of the smaller of the two missing sides is; 24

The sides that make up a right angle triangle are;

Hypotenuse

Opposite

Adjacent

Now, the smallest side has a length of 10.

Let the hypotenuse be x + 2 while the other unknown side will be x since they are consecutive even integers.

Thus, using Pythagoras theorem we have;

(x + 2)² = 10² + x²

Expanding the bracket gives;

x² + 4x + 4 = 100 + x²

x² will cancel out to get;

4x + 4 = 100

4x = 96

x = 96/4

x = 24

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The slope of the tangent is 2π.

The slope of a line, often denoted by the letter "m," is a measure of how steep or inclined the line is. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

To find the slope of the line tangent to the polar curve at a specific point, we need to differentiate the polar equation with respect to θ and evaluate it at the given value of θ.

The polar equation given is r = 4θ². To differentiate this equation with respect to θ, we need to express r in terms of θ and then differentiate. Since r = 4θ², we can rewrite it as:

r = 4θ² = 4(θ²)

Now, we can differentiate both sides of the equation with respect to θ:

dr/dθ = d(4θ²)/dθ

Using the power rule for differentiation, the derivative of θ² with respect to θ is 2θ:

dr/dθ = 4(2θ)

Simplifying, we get:

dr/dθ = 8θ

Now, we can evaluate this derivative at the given value θ = π/4:

dr/dθ = 8(π/4) = 2π

Therefore, the slope of the line tangent to the polar curve r = 4θ² at the point where θ = π/4 is 2π.

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Height 6 2 in cm is 187.96 cm.

To convert from feet and inches to centimeters, use the following two conversion equations:

6 feet + 2 inches = 190 centimeters = 1.8796 meters

(6"2' = 187.96 cm = 1.8796 m)

Multiply the value in feet by 30.48 to get the result of the conversion of feet in cm:

6 x 30.48 = 183cm

Multiply the value in inches by 2.54 to get the result of the conversion from inches to cm:

2 x 2.54 = 5.08cm

Now, add the two partial results to obtain the final value in cm:

183 + 5.08 = 188cm.

Divide the value 1.88cm by 100 to get the result in meters.

188/100=1.88m

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No, it is not necessarily true that ∀xp(x) ∨ ∀xq(x) is true if it is true that ∀x(p(x) ∨ q(x)).

For example, if we let p(x) be "x is an even number" and q(x) be "x is an odd number", then it is true that ∀x(p(x) ∨ q(x)) because all numbers are either even or odd. However, it is not true that ∀xp(x) ∨ ∀xq(x) because not all numbers are even and not all numbers are odd. In formulaic terms, if p(x) and q(x) are predicates over some domain, then ∀x(p(x) ∨ q(x)) is true, which can be expressed as ∀x[p(x) ∨ q(x)], while ∀xp(x) ∨ ∀xq(x) is not true, which can be expressed as [∀xp(x)]∨[∀xq(x)].

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Solving the problem using basic algebra, the total number of hamburgers that were sold on Saturday can be obtained as 108 hamburgers.

The word problem that has been formulated in the question falls under the basic discipline of mathematics known as algebra.

Algebra is a branch of mathematics that deals with mathematical variables and the rules for manipulating these variables to solve diverse mathematical problems.

Let the total number of hamburgers sold be x.

In the question, it is given that the total number of cheeseburgers sold would be 3 times the number of hamburgers sold. Then the number of cheeseburgers sold would be 3x.

It is also given that the total number of hamburgers and cheeseburgers sold together is 432.

Using these data, the equation can be formulated as x + 3x = 432.

As x and 3x are variables of the same nature, which is x, they can be added to obtain the answer as 4x, hence the equation becomes

4x = 432. Solving for x, we get

x = 432 ÷ 4

x = 108.

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The mean () of the test is 150, while the standard deviation () is 25. In the case of a normal distribution, your z score would be: z = (x - ) / = (190 – 150) / 25 = 1.6.

A Z-score of 0 implies that the data point’s value is the same as the mean score. A Z-score of 1.0 indicates that the result is one standard deviation from the mean. The z-scores’ mean is always 0. The z-scores’ standard deviation is always 1. The z-score distribution graph always has the same form as the original sample value distribution graph. The total of the squared z-scores equals the number of z-score values.

z = (x – μ) / σ

z=[tex]\frac{(190-150}{25} = 1.6[/tex]

Take the raw data, remove the mean, then divide by the standard deviation to get the z-score. The data point of interest is represented by X. Mu and sigma reflect the population’s mean and standard deviation.

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We would have a graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100. Option A

We have to determine the nature of the graph that we have in the context of the question. In this case, we must recall that the function that we have would look something of the nature; y = 10x + 120 where y is the money raised and x is the number of students that attends the dance.

Here we can see that the nature of the equation just looks like the equation of the straight line graph that is given as; y = mx + c

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y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2), found by integrating the ODE y′ = 16x and using the initial condition y(e) = 53.

What is differential equation ?

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable.

mu(x) = e^(int 16 dx) = e^(16x^2/2)

multiply both sides of the differential equation by the integrating factor to obtain:

mu(x) * y′ = 16x * mu(x)

Integrating both sides with respect to x, we get:

mu(x) * y = 8x^2 + C

Dividing both sides by the integrating factor, we get:

y = 4x^2 + Ce^(-16x^2/2)

Using the initial condition y(e) = 53, we can find the value of the constant C:

53 = 4e^2 + Ce^(-16e^2/2)

Solving for C, we get:

C = 53 - 4e^2

So the general solution for the differential equation is:

y = 4x^2 + (53 - 4e^2)e^(-16x^2/2)

Finally, to find y(e2), we plug in x = e2 into the general solution:

y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2)

And that gives us the value of y at x = e2.

y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2), found by integrating the ODE y′ = 16x and using the initial condition y(e) = 53.

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Integer -17 represents Rudy's score for 2 weeks.

A negative integer with a minus sign, a zero, or a positive natural number are all examples of integers.

The additive inverses of their positive counterparts are the negative numbers.

In mathematical notation, the Z is widely used to represent the set of numbers.

Rudy's scores:

Then, add 15 and -32 as follows:

= 15 + (-32)

= 15 - 32

= - 17

Therefore, integer -17 represents Rudy's score for 2 weeks.

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The line that passes through the given point and is parallel to the graph

y = -4x - 23.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Equation: y=-4x+3

As, we know that the slope of parallel line are same.

Now, using slope- intercept form

y = mx+ b

y = -4x+ b

Now, the line passes through (-4, -7).

So, y= -4x + b

-7 = -4(-4) + b

-7 = 16 + b

b = -23

So, the equation of parallel line is

y = -4x - 23

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If an algorithm is O(n), where n is the input size, then the execution time will scale linearly with the input size.

If an algorithm is O(n), where n is the input size, then the execution time will scale linearly with the input size. Therefore, if the input size is doubled, the execution time will also double. Mathematically, this can be expressed as:

Execution Time (With Doubled Input Size) = 2*Execution Time (With Original Input Size).

For example, if the execution time for an algorithm with an input size of 8 is 10 seconds, then the execution time for an input size of 16 will be 20 seconds. This is due to the fact that the algorithm's complexity is linear, and thus its runtime increases linearly with the input size.

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The correct check digit for the UPC code 6-73419-23216- is "3".

The check digit is used to verify the accuracy of the UPC code when it's scanned. It's the last digit of a UPC code and is calculated using a formula based on the first 11 digits.

The formula involves adding up the digits in the odd-numbered positions and multiplying the sum by three, then adding up the digits in the even-numbered positions, and subtracting the second sum from the first sum.

The check digit is then calculated by taking the difference and finding the smallest number that, when added to the difference, is a multiple of 10. The result of this calculation is the check digit.

In this case, the correct check digit is "3".

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Answer:

9.2

Step-by-step explanation:

The maximum number of skateboards Julio can make is 7.

A division is a process of splitting a specific amount into equal parts.

Given that, Julio has 3 yards of wood he needs 2/5 of a yard to make a skateboard, we need to find how many skateboards can be made,

So, to find the number of skateboards we will divide total length of wood to the length of on skateboard,

Therefore,

The number of skateboards = 3 / 2÷5

= 3×5/2

= 15/2

= 7.5

Hence, the maximum number of skateboards Julio can make is 7.

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Students will learn how to construct simple equations corresponding to practical situations and thus finding the solution of the equations .

In the time-independent Schrödinger equation it is stated that

                               [tex]-h/2m.d²ψ(x)/dx²+V(x)ψ(x)=Eψ(x)[/tex]

And it is common to give V(x)

some standard "forms": the infinite well, the finite square well, etc.

The problem is that I'm finding it pretty difficult to get what V(x)

actually is. I've read in books that it is the potential energy, but...

As far as I know, the potential energy depends on the properties of the particle itself (its mass, its charge), but, for instance, the finite square well is defined as

                          [tex]V(x)={−V0 if -a < x < a[/tex]

                                 [tex]{0 if|x| > a[/tex]

where V0  is a positive constant. In this case,V0 seems to be fixed, but wouldn't it depend on the properties of the particle.

A concrete and intuitive example of this would be appreciated.  

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Answer:

  3(x-8)(x+5)

Step-by-step explanation:

You want to factor the quadratic 3x² -9x -120.

Each of the coefficients is divisible by 3, so that is the first thing we can factor out:

  = 3(x² -3x -40)

To factor the quadratic, we need factors of -40 that have a sum of -3.

  -40 = -40(1) = -20(2) = -10(4) = -8(5)

The last of these factor pairs have a sum of -3, so the factorization is ...

  = 3(x -8)(x +5)

__

Additional comment

The product of factors (x+a) and (x+b) is ...

  (x +a)(x +b) = x² +ax +bx +ab = x² +(a+b)x +ab

This is why we're looking for factors of -40 = ab, that have the sum (a+b) = -3.

There is sufficient data to conclude that contemporary males are taller than 18th century males​ ,The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.

X = 70.1 represent the sample mean

σ = 2.52 represent the population standard deviation  

n = 30 is  sample size  

μ = 65.2 represent the value that we want to test

∝, represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

pₙ represent the p value for the test (variable of interest)  

We need to conduct a hypothesis in order to check if the mean is higher than 65.2, the system of hypothesis would be:  

Null hypothesis: μ ≤ 65.2

Alternative hypothesis: μ > 65.2

If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t = X - μ / σ/√n = 10.65

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

And the best conclusion for this case would be:

The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.

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The radius r of the circle is  28 m

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

Arc length,

   S = rθ

=> 16 = r (4/7)

=> r=(16*7)/4 =  28 m

The radius r of the circle is  28 m

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If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

We have a coefficient matrix of linear equations in the problem. If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. In light of this theorem, we conclude that the system is consistent.

If and only if a linear system's coefficient matrix and augmented matrix have the same rank, the system is said to be consistent.

If a pivot, or 1, appears in each column of the reduced row echelon form of the coefficient matrix of a linear system of equations involving four distinct variables, then the reduced row echelon form of the coefficient matrix is, let's say, A is an identity matrix, here 3, because there are four variables.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Therefore,

If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

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If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

We have a coefficient matrix of linear equations in the problem. If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. In light of this theorem, we conclude that the system is consistent.

If and only if a linear system's coefficient matrix and augmented matrix have the same rank, the system is said to be consistent.

If a pivot, or 1, appears in each column of the reduced row echelon form of the coefficient matrix of a linear system of equations involving four distinct variables, then the reduced row echelon form of the coefficient matrix is, let's say, A is an identity matrix, here 3, because there are four variables.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Therefore,

If a pivot position exists in each row of the assumed coefficient matrix. As a result, it is accurate to say that the coefficient matrix's bottom row also has a pivot point. There won't be room for an in the enhanced column as a result. So, we can state that the system is consistent.

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If an angle measures 69° then measure of its complementary angle is

90° - 69° = 21°. thus option a is answer.

In geometry, two angles are considered complementary if their sum is equal to 90 degrees. If an angle has a measure of 69 degrees, its complementary angle would be the angle that produces 90 degrees when 69 degrees are added to it. We simply deduct the given angle's measure from 90 degrees to determine the measure of the complementary angle:

90° - 69° = 21°

This is because the sum of complementary angles is always equal to 90 degrees.

Therefore, a 69° angle's complementary angle is a 21° angle.

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The measure of the complementary angle of 69° is 21°.

The complementary angle of an angle is the angle that adds up to 90°. To find the measure of a complementary angle, you can subtract the given angle from 90°. In this case, the given angle is 69° so the complementary angle would be 90° - 69° = 21°. Therefore the measure of the complementary angle of 69° is 21°.

To calculate the measure of the complementary angle, you can use the following formula: Complementary Angle = 90° - Given Angle. The complementary angle of an angle is the angle that completes a right angle (90°). The complementary angle of an angle can be found by subtracting the given angle from 90°. If an angle measures 69°, then the measure of its complementary angle is 21°.

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The estimated area of the unshaded rectangle is 5625 square inches.

The formula for calculating the area of a rectangle. Rectangle surface area. A = l × b.

Once the length and breadth of a rectangle are determined, the area is computed.

The area of a rectangle may be calculated by multiplying its length and width.

The estimated value of the length of the shaded square is: 11 inches

The estimated value of the area of the unshaded rectangle is: 5625 square inches.

To find the estimated length of the shaded square,

We can use the square root of the area:

√(125) = 11

To find the estimated area of the unshaded rectangle,

We can multiply the length by the width:

75 * 11 = 825

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The value of 10⋅(10−4) is equal to 60. This is because 10 multiplied by the difference between 10 and 4 (which is 6) is equal to 60.

10⋅(10−4) is an expression that can be expanded by multiplying 10 by each term inside the parentheses. Since ⋅=2, 10 multiplied by 10 is equal to 10⋅10, which is equal to 100. 10 multiplied by 4 is equal to 10⋅4, which is equal to 40. Therefore, 10 multiplied by the difference between 10 and 4, which is 6, is equal to 10⋅6, which is equal to 60. Therefore, the answer to 10⋅(10−4) is equal to 60.

To solve this expression, it is important to understand the order of operations. First, anything inside of parentheses must be solved first. Then, multiplication must be solved before addition or subtraction. Because there is only one operation inside the parentheses, which is subtraction, it is easy to solve 10⋅(10−4) by multiplying 10 by each of the terms inside the parentheses. Since 10 multiplied by 10 is equal to 100 and 10 multiplied by 4 is equal to 40, 10 multiplied by the difference between 10 and 4 is equal to 10 multiplied by 6, which is equal to 60. Therefore, the answer to 10⋅(10−4) is equal to 60.

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