Find the solution of the differential equation that satisfies the given initial condition. dy 5xe, y(0) = 0 dx -In + = -5x² 2 X

The value of Tessa's investment after 44 years would be $96,814.13, rounded to the nearest cent.

To calculate the value of Tessa's investment after 44 years, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.

Plugging in the values we have:

P = $9600

r = 0.046 (4.6% annual interest rate)

n = 12 (compounded monthly)

t = 44 years

A = $9600(1 + 0.046/12)^(12*44) = $96,814.13

Therefore, the value of Tessa's investment after 44 years would be $96,814.13, rounded to the nearest cent.

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The equation of the  circle , with diameter  DEis (x - 5)² + (y - 7)² = 80

An equation is an expression that appears as the relationship between two or more variables and numbers. since the  standard equation  for a circle  is (x - h)² + (y - k)² = r², where    (h, k)  is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7) and the  Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.

the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80

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Answer:

(x - 5)² + (y - 7)² = 80

Step-by-step explanation:

Answer: 16.2

Step-by-step explanation:

Answer:

16 1/5

Step-by-step explanation:

write the mixed number as a sum of the whole number and the fractional part

2 + 1/5 + 14

add the numbers

16 + 1/5

write the sum of the whole number and the fraction as a mixed number

16 1/5

or 81/5 or 16.2

Answer:

b=14

Step-by-step explanation:

b^2=196

Square root both sides

b=14

Hopes this helps please mark brainliest

Answer:

14

Step-by-step explanation:

You're just looking for the square root of 196, and \(\sqrt{196} = 14\)

Answer:

Around 3000 BC

Answer:

It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.

The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.

As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.

In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.

Step-by-step explanation:

SELF EXPLANATORY

It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.

This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

  about 3.08 L

Step-by-step explanation:

You want the number of litres in the volume of a cylindrical can 14 cm in diameter and 20 cm high.

A litre is a cubic decimeter, 1000 cubic centimeters. As such, it is convenient to perform the volume calculation using the dimensions in decimeters:

The volume of the cylinder is given by the formula ...

  V = (π/4)d²h . . . . . . . where d is the diameter and h is the height

  V = (π/4)(1.4 dm)²(2.0 dm) ≈ 3.079 dm³ ≈ 3.08 L

The cylindrical can will hold about 3.08 litres.

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Answer: The correct answer is A,D, and F

Step-by-step explanation:

The remote interior angles of ∠1 are ∠3 and ∠2

The remote interior angles of a triangles are the two angles that are not adjacent to the exterior angle. The remote interior angles do not share the vertex of the exterior angle.

The angles inside the triangle that are opposite the exterior angle are referred to as remote interior angles. Remote interior angles, then, are those that do not share a triangle's vertex or corner with the outer angle.

Given data ,

Let the triangle be represented as ΔABC

Now , the measures of angles of ABC are

The measure of ∠A = ∠3

The measure of ∠B = ∠2

The measure of ∠C = ∠4

And , the exterior angle of the triangle is ∠1

So , angles inside the triangle that are opposite the exterior angle are referred to as remote interior angles.

The remote angles are ∠3 and ∠2

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10-1 = 9 feet left

9 x 12 = 108 inches

108 / 8 inches per bow = 13.5 bows

she can make 13 bows

Answer:

Veronique: A = 1,000 (1 + 0.05) superscript 7, Lily: A = 1,800 (1 + 0.09) Superscript 7

Step-by-step explanation:

the equation used to calculate future value of an investment (or bank deposit) using compound interest is:

future value = present value x (1 + interest rate)ⁿ

Answer:

the answer would be A

Step-by-step explanation:

what the person above said.

Step-by-step explanation:

x + 3y = 1

x = 1 - 3y-(i)

7x + 8y = 11

x= 11-8y/7-(ii)

substituting eqn (i) in eqn (ii)

11-8y/7= 1-3y

11-8y=7-21y

13y=-4

y=-4/13

putting the value of y in eqn (i)

x=1-(-12/13)

x=25/13

7 fishes οf the new released initially in the given expοnential pοpulatiοn grοwth. (οptiοn c)

Expοnential pοpulatiοn grοwth means that whatever the pοpulatiοn size is, it keeps increasing because the pοpulatiοn per individual remains the same, accelerating pοpulatiοn grοwth that is limited by limited resοurces. Hence, this increase in pοpulatiοn size is knοwn as expοnential pοpulatiοn grοwth.

The grοwth οf their pοpulatiοn is mοdeled by the expοnential functiοn

P(t)=\(7b^{t}\) ,where t is the time in weeks after the release and b is a pοsitive unknοwn base.

Initially that is t=0

sο fοr t=0,

p(0)=7×1 [since sοmething tο the pοwer zerο is equal tο 1]

Hence, P(0)=7

sο there were 7 fishes initially.

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The required monthly payment for 6.4% of interest is $16846.6.

Interest is the cost of borrowing money or the fee you charge to lend it. Most frequently, interest is shown as an annual percentage of the loan amount. The interest rate for the loan is denoted by this proportion. ​

We have,

Purchasing price = $200,000

Down payment = 5% of $200,000

= $10000

Remaining Amount = $190000

Interest of one year = 6.4%

Amount of interest =  6.4% of $190000

Amount of interest = $12160

Total amount = f $190000 + $12160

Total amount = $202160

Monthly payment = $16846.6

Thus, required monthly payment is  $16846.6.

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Answer:

30 cm

Step-by-step explanation:

This question asks for the total distance travelled by both ants combined. Regardless of the direction they travelled, the ants' distance travelled together(13 + 17) is 30 centimeters total.

Hope this helps!

Answer:

I think it would be A

Step-by-step explanation:

because it took the students longer on problem one than it did for problem 2.

Answer: 9 times as large

Step-by-step explanation:

the original area: 15×15=225

the new area: (15×3)(15×3)=2025

2025/225=9

Hope this helps!! :)

Please let me know if you have any question

Answer:

x=22, y=45

Step-by-step explanation:

y=45 by definition (180-90)/2

180 = 46 + 2x

x = 22

Answer:  16

Step-by-step explanation: when ur doing subtacting  ur gonna notice a pattern like 11.25 10.75 10.25 9.75 9.25 because if u start with 19 and minus 0.50 the u get ur answers 16 the 11.25 dosnt count because that for the gift after u spend 7.24 on the gift ur gonna have 11.25 and keep couniting down but also keep tract on how many it takes to get to 2.75

a. To find the slope of the graph take 2 ordered pairs and replace its values in the following equation:

For example, choose (0,150) and (5,225):

The slope of the graph is 15.

b. The units of the slope (since it is a rate of change) are dollars per feet.

c. We already have the slope of the graph and its y intercept which is (0,150). Use this information to find the slope intercept form equation for the situation:

The weight of the fat, sinew, and trimming to be taken out from the whole tenderloin is given to be 1.65 pounds.  Therefore, the total edible tenderloin in pounds is 3.86155 pounds.

The total weight of the whole tenderloin is given to be 2.5 kg.The weight of the fat, sinew, and trimming to be taken out from the whole tenderloin is given to be 1.65 pounds.

To calculate the total edible tenderloin in pounds, we need to convert the weight of whole tenderloin from kg to pounds.

1 kilogram (kg) = 2.20462 pounds (lbs)

Therefore,2.5 kg = 2.5 x 2.20462 = 5.51155 lbs We are given that 1.65 pounds of fat, sinew, and trimming need to be taken out from the whole tenderloin.

So, the total edible tenderloin in pounds = 5.51155 - 1.65= 3.86155 pounds

Therefore, the total edible tenderloin in pounds is 3.86155 pounds.

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In an experimental study, random error due to individual differences can be reduced if a(n) control group is implemented.

One effective way to reduce random error due to individual differences in an experimental study is to include a control group. A control group serves as a baseline comparison group that does not receive the experimental treatment. By having a control group, researchers can isolate and measure the effects of the independent variable more accurately.

The control group provides a point of reference to assess the impact of individual differences on the study's outcome. Since both the experimental group and control group are subject to the same conditions, any observed differences can be attributed to the experimental treatment rather than individual variations.

This helps to minimize the influence of confounding variables and random error associated with individual differences.

By comparing the outcomes of the experimental group and control group, researchers can gain insights into the specific effects of the treatment while controlling for individual differences. This improves the internal validity of the study by reducing the potential bias introduced by individual variability.

In summary, including a control group in an experimental study helps to reduce random error due to individual differences by providing a comparison group that is not exposed to the experimental treatment. This allows researchers to isolate and measure the effects of the independent variable more accurately.

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Answer:

DH, CG, BF

Explanation:

Since the question is asking which lines are parallel to AE and AE is a vertical line, you need to look at the other vertical lines that are making up the sides of the box. These vertical lines are 1. DH 2. CG 3.BF.

Hope this helps.

If the resulting F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances are significantly different.

The F-test is a statistical test used to compare the variances of two groups.

In this problem, we will use it to compare the variance of the value added by the manufacturer and the variance of the cost of materials in manufacturing. The F-test is performed by dividing the larger variance by the smaller variance. The resulting F-statistic is then compared to the critical value of an F-distribution with degrees of freedom equal to the sample size minus one for each group.

Before we can perform the F-test, we need to determine which variable will be group 1. Typically, the variable with the smaller mean is designated as group 1. This is because we want to minimize the chance of making a type II error, which is failing to reject the null hypothesis when it is false. If we designated the variable with the larger mean as group 1, we might not detect a significant difference between the groups, even if one exists.

Once we have designated which variable will be group 1, we can perform the F-test. If the resulting F-statistic is greater than the critical value of the F-distribution, we reject the null hypothesis and conclude that the variances are significantly different.

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A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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Answer:

Your question cannot be correct

Step-by-step explanation:

A line passing through points (6,6) and (6,1) cannot have a slope of 5.

This line passing through these two points would be a vertical line.  The slope of a vertical line is considered UNDEFINED.

Answer:

-y+6

Step-by-step explanation:

-3 (y+2) +2y

-3y -6 +2y

-y+6

Answer:

-y-6

Step-by-step explanation: