show your work please

The solution to the differential equation dz/dt = 7te²z that passes through the origin is z = e⁷/³e² t³.

To solve the differential equation dz/dt = 7te² z that passes through the origin, we will use separation of variables method.

First, we separate the variables and write the equation as:

1/z dz = 7te²  dt

Next, we integrate both sides with respect to their variables:

∫(1/z)dz = ∫7te² dt

ln|z| = ⁷/³e²  t³ + C

where C is the constant of integration.

Now, we apply the initial condition that the solution passes through the origin, which means that z(0) = 0. This condition implies that the constant of integration C is equal to 0. Therefore, we have:

ln|z| = ⁷/³e²  t³

Taking the exponential of both sides, we get:

|z| = e⁷/³e²  t³

Since we know that the solution passes through the origin, we can conclude that z = 0 when t = 0. Therefore, we take the positive value of the absolute value of z:

z = e⁷/³e²  t³

So, the solution to the differential equation dz/dt = 7te²  z that passes through the origin is z = e⁷/³e² t³.

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The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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In each row, the 15 number of the student is arranged. For the given condition, the equal number of the student is to be arranged.

A seating arrangement is an arrangement shows that how the peoples are arranged so that the complete utilization is done.

The given data in the problem is;

The total no of student is 345 students

If the same number of the students are to be arranged for the given row, the following calculation is done;

The numbers of the student in each row is found as;

\(\rm n= \frac{Total \ no \ of \ student\ }{Total\ no \of \ rows } \\\\\ n= \frac{345}{23} \\\\ n= 15 \ student\)

Hence, in each row, the 15 no of the student is arranged.

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Answer:

Step-by-step explanation:

If diameter is 5, then the radius is 2.5 cm.

Area of circle = πR²

Area = 3.14 * 2.5^2 = 3.14 * 6.25 = 19.625

Circumference = π * Diameter

Circumference = 3.14 * 5 = 15.7

Answer:

Step-by-step explanation:

Objective: find the circumference and area of a circle.

Given values; diameter: 5cm, pie: 3.14.

Step one:

Circumference: pie x diameter

= 3.14 x 5cm = 15.7 cm (circumference)

Step two:

Area: ( pie x radius to the power of 2)

= 3.14 x 6.25 cm

= 19.625 (area)

Note that Elvira sells a total of 364 bags to earn a profit of $200, which can be determined using the unitary methods.

The unitary approach is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value.

We know that:

Elvira makes money to buy decorations for the cafeteria by selling little bags of chips in the snack bar.

If each bag costs $0.35 and she can sell the bag for $0.90.

Total profit earn = $200

The following steps can be used to determine the total number of bags she sells to earn the profit of $200:

First find the total profit she earns to sell one bag.

= 0.90 - 0.35

= $0.55

Now, using the unitary method find the total number of bags she sells to earn a profit of $200 If she earns a profit of $0.55 to sell one bag.

= 363.63  364 bags

Thus, she sells 364 bags to earn a profit of $200.

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Answer:

Step-by-step explanation:

emma really smells bad do not answer this question

Answer:

210 + -1x

Step-by-step explanation:

Simplifying

X + (x + -30) = 180

Reorder the terms:

X + (-30 + x) = 180

Remove parenthesis around (-30 + x)

X + -30 + x = 180

Reorder the terms:

-30 + X + x = 180

Solving

-30 + X + x = 180

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '30' to each side of the equation.

-30 + X + 30 + x = 180 + 30

Reorder the terms:

-30 + 30 + X + x = 180 + 30

Combine like terms: -30 + 30 = 0

0 + X + x = 180 + 30

X + x = 180 + 30

Combine like terms: 180 + 30 = 210

X + x = 210

Add '-1x' to each side of the equation.

X + x + -1x = 210 + -1x

Combine like terms: x + -1x = 0

X + 0 = 210 + -1x

X = 210 + -1x

Simplifying

X = 210 + -1x

Answer:

20

Step-by-step explanation:

1,2,5 have the same ratio as 4,8,20 and add up to 32

Answer:

First problem: 2sqrt(5)

Second problem: 20 ft

Step-by-step explanation:

First problem:

The geometric mean, x, of a and b is

a/x = x/b

Here you have 4 and 5, so the geometric mean, x, of 4 and 5 is

4/x = x/5

Cross multiply.

x^2 = 4 * 5

x = sqrt(4 * 5)

x = 2sqrt(5)

Second problem:

Ratio of lengths of sides is

1 : 2 : 5

Add all numbers, 1 + 2 + 5 = 8

The ratio of the longest side to the perimeter is

5 : 8

Let the longest side have length x.

5/8 = x/32

8x = 5 * 32

8x = 160

x = 20

Answer: 20 ft

Answer:

The circumcenter of a triangle is a point that is equidistant from all three vertices.

Step-by-step explanation:

What is equidistant from the vertices of a triangle?

The circumcenter of a triangle is a point that is equidistant from all three vertices.

Step 1:

\(2 {x}^{2} - 5x - 12\)

Step 2:

\(2 {x}^{2} - 8x + 3x - 12\)

Step 3:

\(2x(x - 4) + 3(x - 4)\)

Step 4:

\(\blue{(x - 4)(2x + 3)}\)

Answer:

\(3(x - 2) = 12\)

\(x - 2 = 4\)

\(x = 4 + 2\)

\(x = 6\)

The answer is:

x = 6

Work/explanation:

For now, I will focus on the left side, and use the distributive property.

\(\begin{gathered}\sf{3(x-2)=12}\\\\\sf{3x-6=12}\\\\\bf{Add~6~on~each~side}\\\\\sf{3x=18}\\\\\sf{x=6}\end{gathered}\)

Hence, x = 6.

(a) the required monthly loan payment on the car is approximately $528.23, (b)your friend still owes approximately $17,833.86 on the car loan after the 24th monthly payment, (c)it will take your friend approximately 23 months (rounded up to the nearest month) to pay off the remaining loan she owes after the 24th payment, given the increased monthly payment of $100.

(a) The required monthly loan payment on the car can be calculated using the formula for the monthly payment on a loan. Given a car loan of $28,000, financed at an interest rate of 0.50% per month for 60 months, the monthly payment can be determined using the following formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Plugging in the values, we have:

Monthly Payment = (28000 * 0.005) / (1 - (1 + 0.005)^(-60))

Calculating this, the required monthly loan payment on the car is approximately $528.23.

(b) After making the 24th monthly payment, your friend still owes a remaining balance on the car loan. To calculate this, we need to determine the remaining balance based on the number of payments made and the original loan amount. We can use the formula:

Remaining Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Payments - (Monthly Payment * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate)

Plugging in the values, we have:

Remaining Balance = 28000 * (1 + 0.005)^24 - (528.23 * ((1 + 0.005)^24 - 1) / 0.005)

Calculating this, your friend still owes approximately $17,833.86 on the car loan after the 24th monthly payment.

(c) If your friend decides to pay $100 more each month after the 24th payment, we can calculate the number of months it will take her to pay off the remaining loan balance. Using the increased monthly payment, we can calculate the new remaining balance and divide it by the increased monthly payment to determine the number of months needed to pay off the loan.

New Remaining Balance = Remaining Balance - (Monthly Payment + Additional Monthly Payment) * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate

Number of Months = New Remaining Balance / (Monthly Payment + Additional Monthly Payment)

Plugging in the values, we have:

New Remaining Balance = 17,833.86 - (528.23 + 100) * ((1 + 0.005)^x - 1) / 0.005

Number of Months = New Remaining Balance / (528.23 + 100)

By solving the equation, it will take your friend approximately 23 months (rounded up to the nearest month) to pay off the remaining loan she owes after the 24th payment, given the increased monthly payment of $100.

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Answer:

3.2

Step-by-step explanation:

Simplify the expression.

Just divide the numbers.

Answer:

14.7

Step-by-step explanation:

Answer:

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Step-by-step explanation:

here's a link to the answers

A function that represents the piecewise function g include the following:

C. g(x) = {-2x - 2, -∞ < x ≤ 1.

             {1/4(x - 3)³ + 5,  1 < x < 5.

             {-3x + 16,          5 ≤ x < ∞.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce these three functions;

When the domain is -∞ < x ≤ 1, we have:

g(x) = -2x - 5 (negative slope function).

When the domain is 1 < x < 5, we have:

g(x) = 1/4(x - 3)³ + 5.

Therefore, the above absolute value function is defined for every value of x that is greater than 3.

When the domain is 5 ≤ x < ∞, we have:

g(x) = -3x + 16.

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Answer:

Approximately \(50\; \rm m \cdot s^{-2}\), assuming that air resistance is negligible and that the rock was released with zero initial velocity.

Step-by-step explanation:

Let \(g\) denote the gravitational acceleration on this planet.

Let \(x\) denote the displacement of this rock during this fall. Let \(t\) denote the duration of this fall. Assume that the rock was released with an initial velocity \(v_{0} = 0\; \rm m \cdot s^{-1}\).

Assume that the air resistance is negligible (such that gravity is the only force on this rock). The acceleration \(a\) of the rock during the fall would be constantly equal to the gravitational acceleration \(g\).  

Since the acceleration of the rock during the fall was constantly \(a = g\), the following SUVAT equation would apply:

\(\displaystyle x = \frac{1}{2}\, a \, t^{2} + v_{0}\, t\).

Rearrange this equation to find an expression for acceleration \(a\):

\(\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2}\end{aligned}\).

Convert the height and duration of this fall to standard units:

\(\begin{aligned}h &= 89\; \rm km \times \frac{10^{3}\; \rm m}{1\; \rm km} \\ &= 8.9\times 10^{4}\; \rm m\end{aligned}\).

\(\begin{aligned}t &= 0.99\; \rm min \times \frac{60\; \rm s}{1\; \rm min} \\ &= 59.4\; \rm s\end{aligned}\).

Substitute in the values to find the value of acceleration \(a\):

\(\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2} \\ &= \frac{89000\; \rm m}{(59.4\; \rm s)^{2} / 2} && (\text{Note that $v_{0} = 0\; \rm m\cdot s^{-1}$.}) \\ &\approx 50\; \rm m\cdot s^{-2} \end{aligned}\).

By the assumptions above, the acceleration of this rock during this fall would be equal to the gravitational acceleration on this planet. Thus, \(g \approx 50\; \rm m\cdot s^{-2}\) on this planet.

Answer:

2=750

Step-by-step explanation:

2500 divide by 10 and ans * 3

Answer:

2.750

Step-by-step explanation:

you times 2500 by 3 divide by 10

Answer:

12.125 or 890

Step-by-step explanation:  If you do 970/80 that will equal 12.125

or it's 890 because you can have 4,000 games and if you do 970-80= 890.

The length of a fish at the 90th percentile of the length distribution is approximately 23.84 inches.

To find the length of a fish that is at the 90th percentile of the length distribution, we use the normal distribution formula as shown here: $$z = \frac{x - \mu}{\sigma}$$ where: x = the length of the fish, μ = the mean length of the fish population, σ = the standard deviation of the length of the fish population, z = the z-score.

We can use the z-score table to find the z-score for the 90th percentile, which is 1.28. Therefore, we can plug in the values and solve for x: $$1.28 = \frac{x - 20}{3}$$.

Multiplying both sides by 3, we get: $$x - 20 = 3(1.28)$$$$x - 20 = 3.84$$$$x = 20 + 3.84$$$$x = 23.84$$. Therefore, the length of the fish that is at the 90th percentile of the length distribution is 23.84 inches.

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Answer:  x = -2 through 1

Step-by-step explanation:

The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!

When one dimension of a prism is doubled, the volume of the prism also doubles. When two dimensions are doubled, the volume increases by a factor of four. When all three dimensions are doubled, the volume increases by a factor of eight.

The volume of a prism is determined by multiplying its base area by its height. Let's consider a prism with dimensions length (L), width (W), and height (H). If one dimension is doubled, let's say the length (L), the new length becomes 2L. Since volume is proportional to the product of the dimensions, the new volume is calculated as (2L) * W * H, which simplifies to 2(L * W * H). Therefore, the volume doubles when one dimension is doubled.

Similarly, when two dimensions are doubled, let's say the length (L) and width (W), the new length becomes 2L and the new width becomes 2W. The new volume is calculated as (2L) * (2W) * H, which simplifies to 4(L * W * H). Hence, the volume increases by a factor of four when two dimensions are doubled.

When all three dimensions are doubled, each dimension becomes twice its original value. So, the new volume is calculated as (2L) * (2W) * (2H), which simplifies to 8(L * W * H). Consequently, the volume increases by a factor of eight when all three dimensions are doubled.

In summary, doubling one dimension doubles the volume, doubling two dimensions increases the volume by a factor of four, and doubling all three dimensions increases the volume by a factor of eight.

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The given series is divergent.

We can use the limit comparison test to determine the convergence or divergence of the given series:

First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)

Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):

lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)

= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)

= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)

= ∞

Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.

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Answer: To use the method of completing the square to solve the quadratic equation x^2 + x + 9 = 0, we can follow these steps:

Move the constant term to the right-hand side of the equation:

x^2 + x = -9

Add the square of half the coefficient of the x-term to both sides of the equation:

x^2 + x + (1/2)^2 = -9 + (1/2)^2

x^2 + x + 1/4 = -35/4

Rewrite the left-hand side as a square:

(x + 1/2)^2 = -35/4 + 1/4

(x + 1/2)^2 = -34/4

Take the square root of both sides:

x + 1/2 = ±sqrt(-34/4)

Solve for x:

x = -1/2 ± sqrt(-34)/2

So the number that needs to be added to "complete the square" is (1/2)^2 = 1/4.

Step-by-step explanation:

The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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Answer:

Step-by-step explanation:

P(first blue) =  444/ 1554

P(second blue) = 443/1553

P(first blue + second blue) = 444/ 1554 * 443/1553 = 0.08

Answer:

1) a = 60°

3) The perimeter of the rhombus is 16 inches.

5) The length of the longer diagonal is approximately 7 inches.

Step-by-step explanation:

From the attached diagram, we begin to compare the options

1)a = 60°

From the question, we are told that:

One interior angle is 30 degrees and another is a degrees

The sum of angles in a rhombus = 360°

There are 4 angles in a rhombus and each angle should normally be equal to 90° hence,

a = 90° - 30°

a = 60°

2) x = 3 in.

Looking at the attached diagram,

We solve for x using Pythagoras Theorem

a² + b² = c²

a = 2 inches

b = x = ??

c = 4 inches

Hence,

2² + b² = 4²

b² = 4² - 2²

b² = 16 - 4

b² = 12

b = √12

b = 3.4641016151 inches

Option 2 is incorrect

3) The perimeter of the rhombus is 16 inches.

A rhombus is a quadrilateral with 4 sides that are equal to each other.

The perimeter of a Rhombus = 4a

Where a = Length of the side of a rhombus

From the above question, we are told that, the length of each side = 4 inches

Hence, perimeter = 4 × 4

= 16 inches.

Option 3 is correct

4)The measure of the greater interior angle of the rhombus is 90°.

The measure of the greater interior angle = 2 × a°

a° has already been solved for in option 1 as 60°

Hence,

Measure of the greater interior angle = 2 × 60°

= 120°

Option 4 is not correct.

5)The length of the longer diagonal is approximately 7 inches.

Since the Rhombus forms 4 equal triangles, it means the diagonals are the same.

Hence, the length of the longer diagonal

= 2 × 3.4641016151

= 6.9282032303 inches

Approximately = 7 inches.

Option 5 is correct.

Hence, the correct options are

1) a = 60°

3) The perimeter of the rhombus is 16 inches. The measure of the greater interior angle of the rhombus is 90°.

5) The length of the longer diagonal is approximately 7 inches.

Answer:

a,c,e/1,3,5 to simplify it!

Step-by-step explanation:

just took the test on edge :)

The length of AC is approximately 4.64 units.

In this case, we know the measure of angle B is 50 degrees, and we know that angle C is a right angle (90 degrees). Therefore, angle A must have a measure of 40 degrees (since the sum of the angles in a triangle is always 180 degrees).

We also know the length of side AB is 6 units. To find the length of AC, we can use the sine function as follows:

sin(50 degrees) = length of side opposite angle B / length of hypotenuse

sin(50 degrees) = AC / hypotenuse

We can rearrange this equation to solve for AC:

AC = hypotenuse * sin(50 degrees)

To find the hypotenuse, we can use the Pythagorean theorem, which tells us that the sum of the squares of the lengths of the two legs of a right triangle equals the square of the length of the hypotenuse. In this case, we have:

AB^2 + AC^2 = hypotenuse^2

6^2 + AC^2 = hypotenuse^2

We can rearrange this equation to solve for the hypotenuse:

hypotenuse = sqrt(6^2 + AC^2)

Now we can substitute this expression for the hypotenuse into the earlier equation to solve for AC:

AC = sqrt(6^2 + AC^2) * sin(50 degrees)

This equation is a bit tricky to solve algebraically, but we can use numerical methods (such as iteration) to find a solution. Using a calculator or computer, we can find that the length of AC is approximately 4.64 units.

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--The complete question is, Solve the trigonometry problem, For a right angle triangle ABC, Angle C is 90 degrees. Angle B is 50. Length of AB is 6 units. Find the length of AC.--

Answer:

You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.

Step-by-step explanation:

Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.