Answers
Answer:
Option 1.
f(x)= 5^x
Step-by-step explanation:
1) I identified the equation as an exponential equation
2) I plugged the equations into a graphing calculator, and then did 2nd+GRAPH. The only equation with 5 in the Y column was 1.
Related Questions
if an axial load p of 250 n is applied to it, determine the change in its length. ep=2.70gpa , νp=0.4 .
Answers
Let's determine the change in length of the material.
Given:
Axial load (P) = 250 N
Young's modulus (E) = 2.70 GPa = 2.70 x 10^9 Pa (converting GPa to Pa)
Poisson's ratio (ν) = 0.4
To find the change in length, we can use the formula for deformation under axial load:
ΔL = (P * L) / (A * E)
In this formula, ΔL represents the change in length, L is the original length, and A is the cross-sectional area of the material. However, we do not have information on the original length (L) or the cross-sectional area (A) of the material in your question.
Without the values for the original length and cross-sectional area, we cannot calculate the change in length of the material using the given data. If you can provide these missing values, I would be happy to help you find the change in length of the material under the axial load.
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1) [20 Points] Consider the DE 2x - x²y" - xy' - 15y = 2x 4 x
x5 A) Verify that y₁ = x and y₂ = x² the DE: x2y" - xy' – 15y = 0. - satisfy
B) Solve the given nonhomogeneous DE by using variation of parameters.
Answers
We will verify that the functions y₁ = x and y₂ = x² satisfy the homogeneous differential equation x²y" - xy' – 15y = 0.
The we will solve the nonhomogeneous differential equation 2x - x²y" - xy' - 15y = 2x + 4x² + x⁵ using the variation of parameters method.
To verify if y₁ = x and y₂ = x² satisfy the homogeneous equation x²y" - xy' – 15y = 0, we need to substitute these functions into the equation and check if it holds true. Let's start by finding the first and second derivatives of y₁ and y₂. The first derivative of y₁ is y₁' = 1, and the second derivative is y₁" = 0. Substituting these into the equation, we have x²(0) - x(1) - 15x = -x - 15x = -16x ≠ 0. Therefore, y₁ = x does not satisfy the homogeneous equation.
For y₂ = x², the first derivative is y₂' = 2x, and the second derivative is y₂" = 2. Substituting these into the equation, we have x²(2) - x(2x) - 15(x²) = 2x² - 2x² - 15x² = -15x² = 0. Therefore, y₂ = x² satisfies the homogeneous equation x²y" - xy' – 15y = 0.
Moving on to solving the nonhomogeneous differential equation 2x - x²y" - xy' - 15y = 2x + 4x² + x⁵ using variation of parameters, we assume the particular solution to be of the form yₚ = u₁(x)y₁ + u₂(x)y₂, where u₁(x) and u₂(x) are unknown functions to be determined.
We calculate the Wronskian W(y₁, y₂) = x(2x) - (x²)(1) = x². Then, we find the functions u₁(x) and u₂(x) by integrating the following equations:
u₁'(x) = -y₂(x)f(x) / W(y₁, y₂) = -(x²)(2x + 4x² + x⁵) / x² = -(2x³ + 4x⁴ + x⁷),
u₂'(x) = y₁(x)f(x) / W(y₁, y₂) = (x)(2x + 4x² + x⁵) / x² = 2 + 4x + x⁴.
Integrating u₁'(x) and u₂'(x) yields u₁(x) = -(1/8)x⁴ - (4/15)x⁵ - (1/8)x⁸ + C₁ and u₂(x) = 2x + 2x² + (1/5)x⁵ + C₂, where C₁ and C₂ are constants of integration.
Finally, the general solution to the nonhomogeneous equation is given by y(x) = y_h(x) + yₚ(x), where y_h(x) is the general solution to the homogeneous equation (which we found to be y_h(x) = A(x)x + B(x)x², where A(x) and B(x) are arbitrary functions) and yₚ(x) = u₁(x)y₁ + u₂(x)y₂.
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Slope is equal to rise divided by one. If you know the horizontal distance (run) in the slope, how can you find the vertical distance (rise)?
Answers
Answer:
By multiplying the run by the slope, we get the rise value
Step-by-step explanation:
Mathematically. we have
slope = rise/run
Now, given that we know the run and we have the value of the slope, how can we get the rise
To get the rise, we simply have to multiply the run by the value of the slope
Hence, multiplying the run by the value of the slope will give the value of the vertical distance which is the rise
Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant speed. Help Frank determine how long the remainder of the trip will take. Include a table or diagram to support your answer
Answers
Answer:
10.6 hours
Step-by-step explanation:
what is the instantaneous rate of change calculator?
Answers
The instantaneous rate of change calculator is the tool that displays the rate of change
The change in the rate at a certain point is referred to as the instantaneous rate of change in mathematics. It is equivalent to the rate of change in a function's derivative value at a particular location. The obtained graph is identical to the slope of the tangent line if a graph for the instantaneous rate of change at a particular point is drawn.
A free online tool known as the Instantaneous Rate of change calculator shows the rate of change, the first-order differential equation for the specified function. This tool speeds up the calculation and shows the rate of change at a particular position in a split second. With time, the tool is now widely accepted and is often used is variety of calculations.
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ASAP. Will give you the brainliest answer!!! Please show working out.
Answers
Answer:
1250 pigs------------------------------
Find the area using formula:
\(A=(b_1+b_2)h/2\)Substitute values into formula to get:
\(A=(12*5^3+8*5^3)(2*5^3)/2=(20*5^3)(2*5^3)/2= (10*5^3)(2*5^3)\)Since each pig gets 2*5³ m² of land, by dividing the area by this number, Daniel can put:
10*5³ = 10*125 = 1250 pigs in the fieldFind the equation of a line passing through the point (0,1) and parallel to the line 2x – 3y = 6.
Answers
The given equation of the line is
\(\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=\frac{2}{3}x-2 \end{gathered}\)Hence slope of the line is
\(\frac{2}{3}\)Since the line passing through (0,1) parallel to the given line then slope is same for both of them
Since (0,1) is a point so the intercept is c=1
So the equation is
\(\begin{gathered} y=mx+c \\ y=\frac{2}{3}x+1 \end{gathered}\)What is something that you multiply and get -48 but when you add you get 13
Answers
Answer:
16 and -3
16 times -3 equals 48
16 + (-3) is equal to 16 - 3 which is 13
I need help to understand this problem cause I forgot how to do it.
Answers
Answer:
f (-4) = -5
Step-by-step explanation:
Look at the graph and see the y coordinates when x = -4.
Here, when x = -4, y = -5.
By what degree might a variable without a clear operational definition affect statistics performed on it?
Results could be totally different.
grades are an example of a sample.
Samples are chosen at random from the population.
Answers
A variable without a clear operational definition can greatly impact the accuracy and reliability of statistics performed on it. To ensure accurate and meaningful results, it is important to have clear, well-defined variables in any research study.
The lack of a clear definition can lead to inconsistencies in data collection, making it difficult to accurately interpret and analyze the results.
Step 1: When a variable has no clear operational definition, researchers may measure or interpret it in different ways, leading to inconsistencies in data collection.
Step 2: These inconsistencies can affect the reliability and validity of the collected data, which in turn impacts the accuracy of the statistical analysis performed.
Step 3: As a result, the findings from such analyses may not accurately represent the true relationships or patterns within the sample or the population, leading to incorrect conclusions.
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What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is positive Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive Negative, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is negative Negative, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is negative
Answers
Answer:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Step-by-step explanation:
There are an even number of negative factors, so the product is positive:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
algebra 2 please help me
Answers
Answer:
D. 2 and 5
(Just so you know, I'm not 100% sure this is right but I'm pretty sure I've answered this exact problem before)
Step-by-step explanation:
You have to look at the intersection points between the two lines. The x values are going to be the solution, and in this case line g(x) intersects f(x) at (2,-1) and (5,-4) so you take the x values and have your solutions.
Square root of 32 x square root of 1 over 18
Answers
\( \sqrt{32} \times \sqrt{ \frac{1}{18} } \\ = \sqrt{32} \times \frac{ \sqrt{1} }{ \sqrt{18} } \\ = \sqrt{32} \times \frac{1}{ \sqrt{18} } \\ = \frac{\sqrt{2 \times 2 \times 2 \times 2 \times 2}}{ \sqrt{2 \times 3 \times 3} } \\ = \frac{ \sqrt{ {2}^{2} \times {2}^{2} \times 2} }{ \sqrt{2 \times {3}^{2} } } \\ = \frac{2 \times 2 \times \sqrt{2} }{3 \times \sqrt{2} } \\ = \frac{4 \times \sqrt{2} }{3 \times \sqrt{2} } \\ = \frac{4}{3} \)
Answer:\( \frac{4}{3} \)
Hope it helps...ray4918 here to help
Help me please, I'm stuck
Answers
Answer:
Gradient: 5
y-intercept: (0, 15)
Step-by-step explanation:
The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.
what is the absolute value to |x|=8
Answers
Answer:
x = 8 or x = -8
Step-by-step explanation:
Answer:
absolute value will always be positive
the answer is x=8
find the indefinite integral. (use c for the constant of integration.) sin4 5 d
Answers
The indefinite integral of \(sin^4(5)\) with respect to the variable is given by:
∫\(sin^4(5) dx = (1/8)(x - (1/5)sin(5x)cos(5x) + (2/25)sin^3(5x)) + C,\)
where C represents the constant of integration.
To find the indefinite integral of \(sin^4(5)\) , we can use integration techniques and trigonometric identities. We can rewrite \(sin^4(5)\) as \((sin^2(5))^2\) and then apply the power rule of integration.
By using the power rule, we integrate each term individually. The integral of \((sin^2(5))^2\)simplifies to \((1/8)(x - (1/5)sin(5x)cos(5x) + (2/25)sin^3(5x))\).
The constant of integration, denoted by C, is added to account for all possible antiderivatives of the function.
Therefore, the indefinite integral of sin^4(5) with respect to x is given by \((1/8)(x - (1/5)sin(5x)cos(5x) + (2/25)sin^3(5x))\)., where C represents the constant of integration.
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Lucy brought 4 of her scarves to a secondhand store to sell. She was paid the same amount
of cash for each scarf. Before she left, Lucy spent $10.50 of her earnings on a used sweater,
She had $7.50 remaining. What was the value of each scarf?
Answers
Answer: $4.50
Step-by-step explanation:
If she spent 10.50, and had 7.50 left, her total was 18.
$18/4=$4.50
Use the Pythagorean Theorem to find the missing side.
a- 8
b- 16
c- 26.83
d- 14.42
Answers
Step-by-step explanation:
b²=20²-12²
b=√16²
b=16
missing length=24-16=8
missing side ²=12²+8²
side²=144+64
side²=208
side = 14.42.
option D is correct answer.
hope this helps you.
What is the sum?
3
2.
Answers
Se tiene la urna del problema anterior con todas las pelotas dentro. Calcula la probabilidad de que, al sacar dos pelotas de forma consecutiva, una tras otra, la primera sea blanca y la segunda sea amarilla.
Answers
Answer:
i dont understand i dont understand
Write the slope intercept form of the equation of the line through the given points.
through: (0, 2) and (-4, -1)
Answers
Answer:
You use the formula (y to the second power minus y to the first power minus the same formula with the two different points
Step-by-step explanation:
Determined three ways have a total cost of six dollars each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.
Answers
The cost of the apples is 2.9 dollars.
The cost of the bananas is 5.7 dollars.
How to find the number of fruits bought?The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.
Therefore,
let
x = number of apples
y = 2x
where
y = number of bananasTherefore, using equations,
1.5(x) + y(0.30) = 6
Hence,
where
y = 2x
1.5(x) + 2x(0.30) = 6
1.5x + 0.6x = 6
2.1x = 6
divide both sides by 2.1
x = 6 / 2.1
x = 2.9 dollars
y = 2(2.9) = 5.7 dollars
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Write an algebraic expression for the word phrase below. Which factor of yourexpression is a sum of two terms?the product of 5.8 and the sum of 9 and a number n
Answers
the algebraic expression is
\(5.8(9+n)_{}\)the factor of the expression that is a sum is
\(9+n\)The outcome is random if we know the possible values it can have, but not which particular value it takes
Answers
The outcome is random if we know the possible values it can have, but not which particular value it takes.
Is the outcome random if we know the possible values it can have?Randomness refers to the property of a process or system where the outcome is uncertain, unpredictable, and not predetermined. In a random process, we know the set of possible outcomes.
But we cannot determine which particular outcome will occur until it actually happens. For example, when flipping a fair coin, the possible outcomes are heads or tails.
But we do not know which one will come up until the coin is flipped. Randomness is a fundamental concept in probability theory and is used to model and analyze a wide range of phenomena.
Including games of chance, genetics, and quantum mechanics.
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help i need help with this question
Answers
A right cylinder has a radius of 12 units and a height of 15 units. What is the total surface area, in units squared?
Answers
Answer:
2034.72 units²
Step-by-step explanation:
Formula for surface area of a cylinder is:
2πrh + 2πr²
The radius is 12 and the height is 15, so we plug it in:
2π(12·15) + 2π(12)²
2π(12·15) + 2π(12)²=2034.72.
a spinner has eight equally sized regions labeled from 1 to 8. we spin the spinner twice. what is the probability that the first spin is no more than 6 and the second spin is no less than 7? write your answer as a simplified fraction.
Answers
Probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
probability that first spin is grey = 6/8probability that second spin is blue = 2/8probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16learn more about probability click here:
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please answer i need to go through this easy
Answers
Answer:
A
Step-by-step explanation:
Henry's balloon started at 10 miles but tasha started at 15 and Henry's travelled at 7 mph but tashas travels at 6mph
the half life of an element in the periodic table measured over a period of time, t, is modeled by the function f(t)=16(1/2)^t. what is the initial amount of the element
Answers
The initial amount of the element is 16
How to determine the initial amount?The function is given as:
f(t) = 16(1/2)^t
Set t = 0, to determine the initial amount
f(0) = 16(1/2)^0
This gives
f(0) = 16 * 1
Evaluate
f(0) = 16
Hence, the initial amount of the element is 16
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question 19in this list of numbers, what is the median? 97, 96, 95, 93, 93, 90, 87, 86, 84, 78, 75, 74, 70, 68, 65.9383.48680
Answers
The median of the given list of numbers is 87.
To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.
If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
First, let's arrange the numbers in ascending order:
65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680
There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.
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