what do you mean by arithmetic series?​

Answer:

d(0) = -3

Step-by-step explanation:

d(x) = -x + -3                           d(0)

d(0) = 0 - 3

d(0) = -3

So, the answer is d(0) = -3

The probability of all will fail is the lowest.

The given problem states that a missile guidance system has seven fail-safe components, and the probability of each failing is 0.2. The given variable is binomial. We need to find the following probabilities:

(a) Exactly two will fail.

(b) More than two will fail.

(c) All will fail.

(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.

(a) Exactly two will fail.

The probability of exactly two will fail is given by;

P(exactly two will fail) = (7C2) × (0.2)2 × (0.8)5
= 21 × 0.04 × 0.32768
= 0.2713

Therefore, the probability of exactly two will fail is 0.2713.

(b) More than two will fail.

The probability of more than two will fail is given by;

P(more than two will fail) = P(X > 2)
= 1 - P(X ≤ 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - [(7C0) × (0.2)0 × (0.8)7 + (7C1) × (0.2)1 × (0.8)6 + (7C2) × (0.2)2 × (0.8)5]
= 1 - (0.8)7 × [1 + 7 × 0.2 + 21 × (0.2)2]
= 1 - 0.2097152 × 3.848
= 0.1967

Therefore, the probability of more than two will fail is 0.1967.

(c) All will fail.

The probability of all will fail is given by;

P(all will fail) = P(X = 7) = (7C7) × (0.2)7 × (0.8)0
= 0.00002

Therefore, the probability of all will fail is 0.00002.

(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.

The probability of exactly two will fail is the highest probability, followed by the probability of more than two will fail. And, the probability of all will fail is the lowest probability. These results are reasonable since the more the number of components that fail, the less likely it is to happen. Therefore, it is reasonable that the probability of exactly two will fail is higher than the probability of more than two will fail, and the probability of all will fail is the lowest.

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Hence, 28 toy soldiers are the correct answer.

A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.

Let's refer to the quantity of toy soldiers as "x".

We are aware that x is within the range of 27 and 54 thanks to the problem.

x can be divided by 4 without any remainders.

The residual is 6 when x is divided by 7.

The leftover after dividing x by five is three.

These criteria allow us to construct an equation system and find x.

Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:

x = 4k, where k is some integer.

Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:

x ≡ 6 (mod 7)

This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:

4k ≡ 6 (mod 7)

We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:

4(1) ≡ 6 (mod 7)

4 ≡ 6 (mod 7)

It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.

k = 2:

4(2) ≡ 6 (mod 7)

1 ≡ 6 (mod 7)

k = 3:

4(3) ≡ 6 (mod 7)

5 ≡ 6 (mod 7)

k = 4:

4(4) ≡ 6 (mod 7)

2 ≡ 6 (mod 7)

k = 5:

4(5) ≡ 6 (mod 7)

6 ≡ 6 (mod 7)

k = 6:

4(6) ≡ 6 (mod 7)

3 ≡ 6 (mod 7)

k = 7:

4(7) ≡ 6 (mod 7)

0 ≡ 6 (mod 7)

We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:

x = 4(7) = 28

This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.

28 toy soldiers are the correct response.

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The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.

To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.

So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.

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Answer:

To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:

distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]

Using this formula, we can calculate the following distances:

a. Distance between M and P = 13 units

b. Distance between A and B = 5 units

c. Distance between C and D = 10 units

Answer:

I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.

for the first equation y=-x+6, y intercept is (0,6)

for equation two 2x-y=-9, y intercept is (0,9)

In both of the equations the x value is 1.

Solving for y without graphing. Y=9+2x

and x=-1

Step-by-step explanation:substitute i

HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5

It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.

The Riemann sum is:Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.

We can create a Riemann sum to estimate the value of the double integral ∬R (3-xy²) dA over the rectangular region R=[0, 4]×[-1, 2] by subdividing [0, 4] into m=2 intervals and [-1, 2] into n=3 intervals. Then we can evaluate the function at the upper left corner of each subrectangle, multiply by the area of the rectangle, and sum all the results.

The width of each subinterval in the x-direction is Δx=(4-0)/2=2, and the width of each subinterval in the y-direction is Δy=(2-(-1))/3=1. The area of each subrectangle is ΔA=ΔxΔy=2*1=2.

Therefore, the Riemann sum is:

Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.

Evaluating the function at the upper left corner of each subrectangle, we get:

(3-0*(-1)²)2 + (3-20²)2 + (3-21²)2 + (3-41²)*2 = 2 + 6 + 2 + (-22) = -12.

Thus, the estimate for the double integral is -12.

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Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

Answer:

30,000 grams

Step-by-step explanation:

multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g

Answer:

hi I'm really sorry I can't help

Answer:

2x - 13

Step-by-step explanation:

If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:

x + (x - 13) = 2x - 13

The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex]  tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.

Accοrding tο the given infοrmatiοn:

The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.

Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].

Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].

In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

Plugging in the values οf a, b, and c, we get:

[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]

Simplifying this expressiοn, we get:

[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

[tex]t = 2 \± 0.632[/tex]

Therefοre, the twο pοssible values οf t are:

t = 2 + 0.632 = 2.632 secοnds

t = 2 - 0.632 = 1.368 secοnds

Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

t = 2 ± 0.632

Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

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The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.

Given the equation in the question (3√x) - √(9x-17) = 1.

To solve for x in the given equation:

(3√x) - √(9x-17) = 1

We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:

(3√x) = √(9x - 17) + 1

Squaring both sides of the equation, we get:

(3√x)² = (√(9x - 17) + 1)²

9x = -16 + 2√(9x - 17) + 9x

Solve for 2√(9x - 17)

2√(9x - 17) = 16

36x - 68 = 256

Add 68 to both sides

36x - 68 + 68 = 256 + 68

36x = 324

x = 324/36

x = 9

Therefore, the solution is x = 9.

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Answer:

To solve the system of equations:

n + d = 21 ---(1)

0.05n + 0.10d = 1.70 ---(2)

We can use the substitution method by solving for one variable in terms of the other from equation (1) and substituting it into equation (2).

Solving equation (1) for n:

n = 21 - d

Substituting this expression for n into equation (2):

0.05(21 - d) + 0.10d = 1.70

Distributing the 0.05:

1.05 - 0.05d + 0.10d = 1.70

Combining like terms:

0.05d = 0.65

Dividing both sides by 0.05:

d = 13

Substituting this value of d into equation (1):

n + 13 = 21

Solving for n:

n = 8

Therefore, the solution to the system of equations is n = 8 and d = 13.

A student attempts a 10-question multiple-choice test where each question presents four options, and the student makes random guesses for each answer. So the probability of (a) P(5)= 0.058 and (b) P(More than 3)= 0.093.

Part 1: Calculation of probability of getting 5 questions correct

(a) P(5)The formula used to find the probability of getting a certain number of questions correct is:

P(k) = (nCk)pk(q(n−k))

Where, n = total number of questions

(10)k = number of questions that are answered correctly

p = probability of getting any question right = 1/4

q = probability of getting any question wrong = 3/4

P(5) = P(k = 5) = (10C5)(1/4)5(3/4)5= 252 × 0.0009765625 × 0.2373046875≈ 0.058

Part 2: Calculation of probability of getting more than 3 questions correct

(b) P(More than 3) = P(k > 3) = P(k = 4) + P(k = 5) + P(k = 6) + P(k = 7) + P(k = 8) + P(k = 9) + P(k = 10)

P(k = 4) = [tex]10\choose4[/tex](1/4)4(3/4)6 = 210 × 0.00390625 × 0.31640625 ≈ 0.02

P(k = 5) = [tex]10\choose5[/tex](1/4)5(3/4)5 = 252 × 0.0009765625 × 0.2373046875 ≈ 0.058

P(k = 6) = [tex]10\choose6[/tex](1/4)6(3/4)4 = 210 × 0.0002441406 × 0.31640625 ≈ 0.012

P(k = 7) = [tex]10\choose7[/tex](1/4)7(3/4)3 = 120 × 0.00006103516 × 0.421875 ≈ 0.002

P(k = 8) = [tex]10\choose8[/tex](1/4)8(3/4)2 = 45 × 0.00001525878 × 0.5625 ≈ 0.001

P(k = 9) = [tex]10\choose9[/tex](1/4)9(3/4)1 = 10 × 0.000003814697 × 0.75 ≈ 0.000

P(k = 10) = [tex]10\choose10[/tex](1/4)10(3/4)0 = 1 × 0.0000009536743 × 1 ≈ 0

P(More than 3) = 0.020 + 0.058 + 0.012 + 0.002 + 0.001 + 0.000 + 0≈ 0.093

Therefore, the probabilities of the given situations are: P(5) ≈ 0.058, P(More than 3) ≈ 0.093.

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The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.

Answer:

Step-by-step explanation:

It is set up

7x+5x+2y=20

7x+5x=12x

12x+2y=20

x=0

y=10

12(0)+2(10)=20

Ok so maybe this was not the same type of equation i thought it was it is not that easy!

The coordinates of your position If we start at the origin, we are moving only along the x-axis  of  a distance of 7 units in positive direction and then only in the negative y-axis direction and  z-coordinate is zero are (7,-6,0).

The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.

The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).

The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).

Therefore, the coordinates of our position are (7, -6, 0)

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The value of the additional data point is  [tex]$19.17$[/tex].

Let us first find the mean of the given data:

[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]

Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is

[tex]$(39+45+43+42+44+x)$[/tex].

Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:

[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]

Multiplying both sides of the equation by 6 we get:

[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]

We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].

Therefore, substituting all the values, we get:

[tex]193.83 + x = 213[/tex]

On subtracting [tex]$193.83$[/tex] from both sides, we get the value of

[tex]x. x = 213 - 193.83 = 19.17[/tex]

Therefore, the value of the additional data point is [tex]$19.17$[/tex]

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The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.

The margin of error for the 90% confidence interval is 25.4 days.

The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.

If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.

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We can be 99% confident that the average number of miles an automobile is driven annually in Alabama is between 21,342.6 and 24,637.4 miles

To answer this question, we need to use the following formula for a confidence interval for the mean: CI = (μ - z*(σ/√n), μ + z*(σ/√n)), Where μ is the population mean, z is the z-score for the given confidence level, σ is the population standard deviation, and n is the sample size. Using the given information, we can calculate the confidence interval for the mean:CI = (23500 - 2.575*(3900/√100), 23500 + 2.575*(3900/√100)), CI = (21342.6, 24637.4)

To summarize, we used the formula for a confidence interval for the mean and the given information to calculate the confidence interval for the average number of miles an automobile is driven annually in Alabama. This confidence interval is (21342.6, 24637.4), which means we can be 99% confident that the average number of miles an automobile is driven annually in Alabama is between 21,342.6 and 24,637.4 miles.

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Answer: The two angles are 117 degrees and 63 degrees.

Step-by-step explanation:

Supplementary angles are two angles whose sum is 180 degrees. Let the two angles be 13x and 7x, where x is a constant of proportionality.

We know that the sum of the angles is 180 degrees, so:

13x + 7x = 180

Combining like terms, we get:

20x = 180

Dividing both sides by 20, we get:

x = 9

So the measures of the angles are:

13x = 13(9) = 117 degrees

7x = 7(9) = 63 degrees

Therefore, the two angles are 117 degrees and 63 degrees.

Answer: 0.04

Step-by-step explanation:

In order to get 4% as a decimal, you must divide 4 by 100.

4/100 = 0.04

Thus, the answer to your question is 0.04

The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.

To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

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

In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:

A = $4,000.00(1 + 0.045/365)^(365*4)

A = $4,000.00(1.0001234)^1460

A = $4,889.68

The final amount is $4,889.68, which means that the interest earned is:

Interest = $4,889.68 - $4,000.00 = $889.68

We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:

$1.197204 / $1.00 = 1.197204

Interest earned = $889.68 x 1.197204 = $1,064.08

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Answer:

2 9/14

Step-by-step explanation:

a. Hence proved that the sum of fractions  [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

b. The value will be 7 for the expression

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.

Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.

Here,

a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

Using (a + b)(a - b) = a² - b²

⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]

⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]

⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]

⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]

⇒ [tex]$ -1+2}$[/tex]

⇒ 1

a. Hence proved that the sum of fractions  [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]

B. This will be done with the same process,

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]

There, will be same roots of every number until - 8

So,

⇒ [tex]$ -1+8}$[/tex]

= 7

b. The value will be 7 for the expression

⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]

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Answer:

y = 12x - 125

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 12x + 3 ← is in slope- intercept form

with slope m = 12

• Parallel lines have equal slopes , then

y = 12x + c ← is the partial equation

to fond c substitute (10, - 5 ) into the partial equation

- 5 = 12(10) + c = 120 + c ( subtract 120 from both sides )

- 125 = c

y = 12x - 125 ← equation of parallel line

Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.

Step-by-step explanation:

216 cm2 is the size of the rectangle border.

the translation of the question is

A painting including its frame is 25 cm long and 10 cm wide, what is the area of ​​the frame if it is 4 cm wide?

What is a rectangle's area?

When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:

A = lw.

The total area is therefore given by:

A = 25 x 10 = 250 cm².

The white region's size is shown by:

A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.

Hence, the border's area is as follows:

216 cm2 = 250 cm2 - 34 cm2.

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Answer:

x = -2 ,  y = 2

Step-by-step explanation:

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