Help pls!!! And thank you
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The boundary value and initial value statement are,

T surrounding = 100°c

IVP = \(T_i = 20^oc, T_f = 75^oc\\\).

What is Initial Value Problem?

In multivariable calculus, an initial value problem is an ordinary differential equation that also includes an initial condition that identifies the value of the unknown function at a specific location in the domain. An initial value problem is frequently solved when modelling a system in physics or another scientific field.

Consider a cylindrical potato, sliced into thin slices with thickness L = 1 cm, much smaller than the diameter slices.

Initial temperature \(T_i = 20^o\)

Final temperature = \(T_f = 75^o\)

Now we have to solve the given cases.

Consider the heat equation,

q = k(∂T / ∂x)                   ..(1)

(a) Now we have to find the boundary value

Boundary Value:

\(T_i = 20^oc, T_f = 75^oc\\\)

⇒ ΔT = [75 - 20]

⇒ΔT = 55°c

T surrounding = 100°c

IVP = \(T_i = 20^oc, T_f = 75^oc\\\)

Hence, the boundary value and initial value statement are,

T surrounding = 100°c

IVP = \(T_i = 20^oc, T_f = 75^oc\\\).

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Complete question:

Complete question is attached below,

The triangle is an οbtuse triangle.

Tο determine if the triangle is acute, οbtuse, οr right, we need tο check if it satisfies the Pythagοrean theοrem. Accοrding tο the Pythagοrean theοrem, in a right triangle, the sum οf the squares οf the lengths οf the legs (the shοrter sides) is equal tο the square οf the length οf the hypοtenuse (the lοngest side). Sο, if the sum οf the squares οf the twο shοrter sides is equal tο the square οf the lοngest side, then the triangle is a right triangle.

Let's calculate the squares οf the three sides:

The square οf the first side (18 cm) is 324.

The square οf the secοnd side (80 cm) is 6400.

The square οf the third side (81 cm) is 6561.

Nοw, we need tο determine if the sum οf the squares οf the twο shοrter sides is greater than οr less than the square οf the lοngest side. Sο, we have:

324 + 6400 = 6724

Since 6724 is less than 6561, the triangle dοes nοt satisfy the Pythagοrean theοrem and it is nοt a right triangle. Therefοre, the triangle is either an acute οr οbtuse triangle.

Tο determine if the triangle is acute οr οbtuse, we need tο find the largest angle οf the triangle. We can use the Law οf Cοsines tο find the largest angle οf the triangle, which is οppοsite the lοngest side. The Law οf Cοsines states that in any triangle:

\(c^2 = a^2 + b^2\) - 2ab cοs(C)

where a, b, and c are the lengths οf the sides οf the triangle, and C is the angle οppοsite the side c.

In οur case, a = 18 cm, b = 80 cm, and c = 81 cm. Sο, we have:

\(81^2 = 18^2 + 80^2 - 2(18)(80) cos(C)\)

6561 = 324 + 6400 - 2880 cοs(C)

Nοw, we can sοlve fοr cοs(C):

cοs(C) = (6400 + 324 - 6561) / (2(18)(80))

cοs(C) = -0.2216

Since cοsine is negative, the angle C is οbtuse.

Therefοre, the triangle is an οbtuse triangle.

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You want to know the classification of a triangle with side lengths 18 cm, 80 cm, and 81 cm. A triangle can be classified by looking at the measure of its largest angle. The classification of the triangle is the same as the classification of that angle: obtuse if > 90°, right if = 90°, and acute if < 90°.

The largest angle is always opposite the longest side. In a triangle with angles A, B, C and their opposite sides a, b, c, we can call the largest angle C. Its measure can be computed using the Law of Cosines, which tells you ...

  C = arccos((a² +b² -c²) / (2ab))

  C = arccos((18² + 80² - 81²) / (2×18×80)) = arccos(163/2880) ≈ 86.8°

The largest angle is less than 90°, so the triangle is an acute triangle.

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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SOLUTIONS

Quartile is also called as Quarter

A quartile divides data into three points—a lower quartile, median, and upper quartile—to form four groups of the dataset. The lower quartile, or first quartile, is denoted as Q1 and is the middle number that falls between the smallest value of the dataset and the median. The second quartile, Q2, is also the median.

Quartiles are values that divide your data into quarters. However, quartiles aren't shaped like pizza slices; Instead they divide your data into four segments according to where the numbers fall on the number line. The four quarters that divide a data set into quartiles are: The lowest 25% of numbers.

Therefore Quartile is also called as Quarter

The equation for the temperature, d, in terms of t (the number of hours since midnight), is:  d = 16 × sin((π/12) × t) + 55

To find an equation for the temperature, we need to determine the amplitude, period, phase shift, and vertical shift of the sinusoidal function.

The amplitude is half the difference between the high and low temperatures, which is (71 - 39) / 2 = 16 degrees. The period is the number of hours in a day, which is 24 hours. Since the temperature is at its highest point at 12:00 PM (midday), there is no phase shift. The vertical shift is the average of the high and low temperatures, which is (71 + 39) / 2 = 55 degrees.

Putting these values together, the equation for the temperature, d, in terms of t can be written as:

d = 16 × sin((2π/24) × t) + 55

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Answer:

A dilation would make them similar.  Similar is the same shape, but not necessarily the same size.  A dilation is a transformation that can make figures shrink or expand.  The other forms of transformations are rigid. They do not change the size.

Step-by-step explanation:

21 + (36 + 0 + 19) Equals 76.

A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.

Equation to be used: 21 + (36 + 0 + 19)

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I understand that the you are looking for is :

Several properties are used to evaluate this expression. Identify the property used in each step.

21 + (36 + 0 + 19)

21 + (36 + 19):

21 + (19 + 36):

(21 + 19) + 36:

40 + 36

76

Answer:

Hey i believe this is the answer

Step-by-step explanation:

Take a look at the screenshot

Also Desmos graphing calculator is a big help :) It might make you a little more confident

Answer:

24

Step-by-step explanation:

12+4+8= 24

12+12=24

8+4=12

Your answer is 24

Answer:

x-1=y or y+1=x

Step-by-step explanation:

I think thats right,

Answer:

Domain: (-5, ∞)

Range: [-4, 1]

Step-by-step explanation:

Domain is the set of all permissible values of x for the function. The smallest value of x is at x = -5. However note that there is an unfilled circle at x = -5 where y = -1. This means the point(-5, -1) is excluded in the function

The function flattens out at x = 3 and the arrow on the end of the function plot indicates that the x-value of the function goes up to ∞

The domain in interval form is (-5, ∞).
Be careful with the brackets. The regular parentheses ( and ) indicate that the extremes of the interval -5 and ∞ are not included in the interval. ∞ is never included. Such an interval is called an open interval.

The range is the set of y-values for the domain
Looking at the graph we can see that the lowest y value is -4 at x = -2 and it is a valid value for the function so included in the interval

The highest value of y is 1 and it becomes 1 at x =3 but since the plot after x = 2 is horizontal, that means the y value will be 1 for any value x >= 3

Therefore the range of the function is
[-4, 1]

Here note that we are using square brackets to indicate that -4 and 1 are included in the interval. Such an interval is called a closed interval.

Answer:

5x-3(9)=-12

5x-27=-12

+27. +27

5x = 15

÷5. ÷5

x= 3

Answer:

Let's solve for x.

y=95x−3y

Step 1: Flip the equation.

95x−3y=y

Step 2: Add 3y to both sides.

95x−3y+3y=y+3y

95x=4y

Step 3: Divide both sides by 95.

95x

95

=

4y

95

x=

4

95

y

Step-by-step explanation:

I think that can help :) wanna chat add me as  friend

Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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Factoring a quadratic in two variables with a leading coefficient of 1 involves finding two binomial factors that, when multiplied, produce the quadratic expression. The factors can be determined by identifying the common factors of the quadratic terms and arranging them appropriately.

To factor a quadratic expression in two variables with a leading coefficient of 1, we need to look for common factors among the terms. The goal is to rewrite the quadratic expression as a product of two binomial factors. For example, if we have the quadratic expression x^2 + 5xy + 6y^2, we can factor it as (x + 2y)(x + 3y) by identifying the common factors and arranging them in the binomial factors.

The process of factoring a quadratic in two variables may involve trial and error, testing different combinations of factors to find the correct factorization. Additionally, factoring methods such as grouping or using the quadratic formula can also be applied depending on the specific quadratic expression.

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let's move like the crab, backwards, let's get hmmm EF first

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{10}\\ o=\stackrel{opposite}{EF} \end{cases} \\\\\\ EF=\sqrt{ 17^2 - 10^2}\implies EF=\sqrt{ 189 }\implies EF\approx 13.7 \\\\[-0.35em] ~\dotfill\)

\(\sin( F )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{17}} \implies \sin^{-1}(~~\sin( F )~~) =\sin^{-1}\left( \cfrac{10}{17} \right) \\\\\\ F =\sin^{-1}\left( \cfrac{10}{17} \right)\implies F \approx 36^o \\\\[-0.35em] ~\dotfill\\\\ \cos(D )=\cfrac{\stackrel{adjacent}{10}}{\underset{hypotenuse}{17}} \implies \cos^{-1}(~~\cos( D )~~) =\cos^{-1}\left( \cfrac{10}{17} \right) \\\\\\ D =\cos^{-1}\left( \cfrac{10}{17} \right)\implies D \approx 54^o\)

Make sure your calculator is in Degree mode.

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. The probability of an up movement is approximately 0.4704, which corresponds to answer choice A.

The probability of an up movement in a binomial tree is given by the formula:

\(p = (e^{r - q} * u - d) / (u - d)\)

where r is the interest rate, q is the dividend yield, u and d are the up and down factors, respectively.

In this case, r = 0.03/12 = 0.0025 (monthly interest rate),

q = 0.01/12 = 0.000833 (monthly dividend yield), \(u = e^{\sigma * \sqrt{1/12}} = e^{0.16 * \sqrt{1/12}}\) ≈ 1.0403, and

d = 1/u ≈ 0.9614.

Substituting these values into the formula, we get:

\(p = (e^{0.0025 - 0.000833} * 1.0403 - 0.9614) / (1.0403 - 0.9614)\) ≈ 0.4704

Hence, the correct option is A) 0.4704.

The complete question is:

A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement?

0.4704

0.5065

0.5592

0.5833

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The y-intercept of the equation  g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation  g(x) = 3^x - 5 is y = -5

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The y-intercept is a point on the graph where the value of x is 0

This is represented by x= 0 or (0, y)

This means that we substitute 0 for x in the above equation

So, we have:

g(0) = 3^0 - 5

Evaluate the exponent 3^0

g(0) = 1 - 5

Evaluate the difference of 1 and 5

g(0)  = -4

Rewrite this point as

(0, -4)

This means that the y-intercept of the equation  g(x) = 3^x - 5 is (0, -4)

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The asymptote is a point on the graph where that is parallel to the graph

In the above equation, we have:

g(x) = 3^x - 5

Express the radical as 0

y = 0 - 5

Evaluate the difference of 0 and 5

y  = -5

This means that the asymptote of the equation  g(x) = 3^x - 5 is y = -5

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Answer:

He would sell 14 cars.

Step-by-step explanation:

Hope this helps

The 5-number summary for the given data is 23, 28, 29, 45, and 48, which will be used to construct the box plot.

To construct a box plot, we first need to determine the 5-number summary, which consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values of the data.

For the given data {45, 28, 28, 33, 45, 23, 40, 24, 46, 29, 34, 24, 29, 29, 48}, we arrange the values in ascending order to get: 23, 24, 24, 28, 28, 29, 29, 29, 33, 34, 40, 45, 45, 46, 48. The 5-number summary is then determined as follows: minimum (23), Q1 (28), median (29), Q3 (45), and maximum (48).

These values are used to construct the box plot, where the box represents the interquartile range (Q3-Q1), with the median line inside it, and the whiskers extend from the minimum to Q1 and from Q3 to the maximum.

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Let's write and equation for both cases.

In plan 1, it is 500 plus 3% comission. 3% is equivalent to multiply the amount it sale in the week, "x", by 0.03.

So, the equation for plan 1 is:

For plan 2, there is no fixed value, only comission of 5%, which is equivalent of multiplying the weekly sales, "x", by 0.05, so the equation is:

For both plans to result in the same salary, we have:

So, for both plans to result in the same salary, she have to sale 25,000 in a week.

The sum of the given expression { (w - 2.4) + (1 - 0.5w)​ } is 0.5w - 1.4.

Given the expression in the question;

(w - 2.4) + (1 - 0.5w)​

Remove the parenthesis

w - 2.4 + 1 - 0.5w

Collect like terms and simplify

w - 2.4 + 1 - 0.5w

w  - 0.5w - 2.4 + 1

1w  - 0.5w - 2.4 + 1

0.5w - 1.4

Therefore, the sum of the given expression { (w - 2.4) + (1 - 0.5w)​ } is 0.5w - 1.4.

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$2.6 million in 2000 dollars is more than what it would have cost to restore the courthouse.

The price index is the average price for a certain class of products or services during a particular time period.

An asset's current cost is determined by multiplying the base year cost by the current year's price index.

It was 2000.

Hospital: $2,635,417 ($500,000 x 126.5 / 24)

Courthouse: 1,700,000 $ x 126.5/108 = 1,991,204

The hospital will cost $2.6 million.

2,635,417 minus 1,991,204, or $644,213, is the difference with the courthouse. The cost of the hospital is $644,21300 more than the Courthouse.

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The right form of the question is:

In 1949, Sycamore, Illinois built a hospital for about $500,000. In 1987, the county restored the courthouse for about $1.7 million. The price index for nonresidential construction was 24 in 1949, 108 in 1987, and 126.5 in 2000. According to these numbers, the hospital cost about

a. $2.6 million in 2000 dollars, which is less than the cost of the courthouse restoration in 2000 dollars.

b. $2.6 million in 2000 dollars, which is more than the cost of the courthouse restoration in 2000 dollars.

c. $2.1 million in 2000 dollars, which is more than the cost of the courthouse restoration in 2000 dollars.

d. $2.1 million in 2000 dollars, which is less than the cost of the courthouse restoration in 2000 dollars.

Answer:

Sorry for the late answer but hopefully it helps others. The answer is A

Step-by-step explanation:

y = -x^2

The graph of a quadratic function, y=x² reflected over the x-axis will be y = -x²

Images that are reflected over each other are mirror images of each other.

Given the coordinates (x, y) reflected over the x-axis, the resulting equation will be (x, -y)

This shows that reflecting the function y = x²over the x-axis will negate the output function.

Hence the graph of a quadratic function, y=x² reflected over the x-axis will be y = -x²

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Answer:

150 because 2.5 × 6 = 15 × 10 = 150

Answer:

2x - 5 + 2y + 14 is not in slope intercept form

Step-by-step explanation:

Slope intercept form is y = mx + b

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

Step-by-step explanation:

Given expression:

Multiply both sides by the conjugate of the denominator to get rid of the fraction:

\(\\ \tt\longmapsto \dfrac{1+i}{3+4i}\)

\(\\ \tt\longmapsto \dfrac{(1+i)(3-4i)}{(3+4i)(3-4i)}\)

\(\\ \tt\longmapsto \dfrac{3-4i+3i-4i^2}{9-16i^2}\)

\(\\ \tt\longmapsto \dfrac{3-i+4}{9+16}\)

\(\\ \tt\longmapsto \dfrac{7-i}{25}\)