Consider the following differential equation to be solved by variation of paramters.
y"+ y = csc(x)
Find the complementary function of the differential equation.
y_c (x) = ____
Find the general solution of the differential equation.
y(x) = _____

Answer:

21

Step-by-step explanation:

1/5 x 21 = 21/5

True.surface area refers to what is on the outside, while volume refers to what fits inside.

In their simplest consideration, surface area refers to the total area of the outer surface of an object or shape, while volume refers to the amount of space that an object or shape occupies or can hold on the inside. Surface area is typically measured in square units (such as square meters or square inches), while volume is measured in cubic units (such as cubic meters or cubic inches).

Surface area represents the sum of all the individual areas of the object's faces or surfaces, including its top, bottom, and sides. It is related to the object's exposure to the outside environment and often determines its interactions with the surroundings.

Volume, on the other hand, measures the capacity or extent of space that the object occupies or can contain. It provides information about the amount of material or substance present within the object and is essential for determining quantities, such as the amount of liquid a container can hold or the capacity of a room.

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Answer:

cant see the picture

Step-by-step explanation:

Answer:

The answer is C) 109.1 yards.

Step-by-step explanation:

Similarly to the last one, use the Pythagorean Theorem to find the answer:

\(50^{2} +b^2=120^2\)

This simplifies to:

\(2500 + b^2 = 14,400\).

Then, subtract 2500 from both sides, then square root both sides.

\(b =\sqrt{11900}\).

The answer is 109.08, which rounds to 109.1 yards.

Hope this helps! :)

Answer: 0.129 kg

Step-by-step explanation:

A gram to a kilogram can be found by dividing the value of grams by 1000, or multiplying the value by 0.001

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

31.9 cm² (3 s.f.)

Step-by-step explanation:

\(\boxed{area \: of \: sector = \frac{θ}{360º} \times \pi {r}^{2} }\)

∠AOD

= 360° -60° - 120° -45° (∠s at a pt.)

= 135°

Area of shape

\( = \frac{60°}{360°} (\pi)({2}^{2}) + \frac{120°}{360°} (\pi)(3^{2} )+ \frac{45°}{360°}(\pi)( 5 {}^{2}) + \frac{135°}{360°} (\pi)(3 {}^{2} )\)

\( = \frac{1}{6} (4\pi) + \frac{1}{3} (9\pi) + \frac{1}{8} (25\pi) + \frac{3}{8} (9\pi)\)

\( = \frac{4}{6} \pi + \frac{9}{3} \pi + \frac{25}{8} \pi + \frac{27}{8} \pi\)

\( = \frac{61}{6} \pi\)

= 31.9 cm² (3 s.f.)

D) The term "imaginary roots" describes the roots of the equation 3x2 - 4x + 5 = 0 the best.

The formula is the quadratic equation ax2 + bx + c = 0 in standard form.

x = [-b ± √(b2 - 4ac)]

/ 2a

It follows that

3x2 - 4x + 5 = 0

Here, an equals 3, b equals -4, and c equals 5.

Using these numbers as replacements in the formula

x = [-(-4) ± √((-4)2 - 4 × 3 × 5)]

/ (2 × 3)

By even more simplifying

x = [4 ± √(16 - 60)]

/6

x = [4 ± √-44]/ 6

As a result,

x = [4 ± 2√-11]/ 6

x = [2 ± I √11]/ 3

Additionally, b2 - 4ac = -44 0 is the discriminant. So, we have invented roots.

Therefore, the term "imaginary roots" is the best description of the roots of the equation 3x2 - 4x + 5 = 0.

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Full Question = Choose the best description of the roots of the equation 3x2 - 4x + 5 = 0.

Double root

Real and rational roots

Real and irrational roots

Imaginary roots

Answer:

80.4

Step-by-step explanation:

The radius is 12.8m so to find circumference we have to multiply it by 2, 12.8x2 equals 25.6. Since we find our diameter we multiply 25.6 by pie or 3.14 and we 80.384 and round to the tenths place. Which is 80.4

The probability that a fair coin will land heads up both times when coin flipped twice can be calculated by multiplying the probability of getting heads on the first flip by the probability of getting heads on the second flip. Since the coin is fair, the probability of getting heads on each flip is 1/2.

Step 1: Calculate the probability of getting heads on the first flip.
The probability of getting heads on the first flip is 1/2.

Step 2: Calculate the probability of getting heads on the second flip.
The probability of getting heads on the second flip is also 1/2.

Step 3: Multiply the probabilities of the individual flips.
1/2 * 1/2 = 1/4

Therefore, the probability that the coin will land heads up both times is 1/4.

Looking at the answer options provided:
a. 0
b. 0.20
c. 0.25
d. 0.50
e. 1

The correct answer is option c. 0.25.

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Answer:

$0.22 per foot

Step-by-step explanation:

So for context, 1 yard is 3 feet. So 2 yards is 6 feet. With this, by dividing $1.32 by 6, you can get the price per foot:

1.32 / 6 ---> $0.22 per foot.

59.99*2=119.98 initial fee

1319.90-119.98=1199.93

1199.93/12=99.993333333333

99.993333333333/2=49.99666666666666

$50

Given:

Chandra get a bonus if average quarterly sales for an year exceeds $70000.

From the bar diagram, we can find the sales for each quarter.

The height of each bar gives the sales for each quarter.

Since the data in the vertical column is given in thousands of dollars, multiply the height of the bar by 1000 to get the correct sales value.

The sales for the first quarter is $40000.

The sales for the second quarter is $100000.

The sales for the third quarter is $80000.

Let x be the sales for the fourth quarter.

Now, the average of the quarterly sales is,

Put A=70000 and solve the equation for x to obtain the sales for the fourth quarter so that Chandra gets bonus.

So, the sales of the fourth quarter must be $60000 in order for Chandra to earn the bonus.

Hence, option D is correct.

Answer:

Step-by-step explanation:

Find the length of BD:

Use the ΔBCD and the law of sines to find the angle x:

Answer:

Physics: 40℅

Chemistry: 20℅

Other: 90℅.

Hope you like my answer.

The radius of a cylinder is 4 inches and the height is 5 inches. The surface area is equal to the sum of the areas of all the faces of a solid.

A cylinder has two circular bases, and each circular base has an area of πr² square units, where r is the radius of the base. The lateral area of a cylinder is the area of the cylinder's curved surface, which is the height of the cylinder multiplied by the cylinder's base perimeter. It is given by the formula: 2πrh. The surface area of the cylinder is obtained by summing the lateral area and two times the area of the base. Hence, we have:

Surface area = 2πrh + 2πr²

Let us calculate the area of the two bases by plugging the given values into the formula.

Area of one base = πr²= π (4)²= 16π square inches

Therefore, the area of the two bases is 2 × 16π = 32π square inches. Thus, statement 2 is correct

Lateral area of a cylinderLateral area = 2πrh= 2 × π × 4 × 5= 40π square inches.

Thus, statement 3 is correct.

The total surface area of the cylinderTotal surface area = Lateral area + 2 × Area of base= 2πrh + 2 × πr²= 2πr(h + r)= 2π × 4(5 + 4)= 72π square inches.

Therefore, statement 5 is correct.

Therefore, the following statements are correct:Statement 2: The area of the two bases is 32π square inches.Statement 3: The lateral area is 40π square inches.Statement 5: The total surface area is 72π square inches are true.Therefore, the correct statements are 2, 3, and 5.

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Answer:

y = -3/4

Step-by-step explanation:

1. Simplify all terms - 8y + 6 = ?

2. Set to two sides - 8y = -6

3. Solve - y = -6/8 = -3/4

Hope this helps:)

The best prediction for the number of times that Leo will get an odd number is 200.

The probability of getting an odd number (1 or 3) is 2/4 = 1/2.

Using the expected value formula, we can predict the number of times that Leo will get an odd number:

Expected number of odd numbers = (probability of getting an odd number) x (total number of trials)

Expected number of odd numbers = (1/2) x (400) = 200

Therefore, the best prediction for the number of times that Leo will get an odd number is 200.

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If password begin with capital letter followed by lower case letter, and end with symbol , then the number of unique passwords which can be created using letters and symbols are 47525504.

The password must have 6 characters and the first character must be a capital letter, so, we have 26 choices for the first character.

For the second character, we have 26 choices for a lower-case letter.

For the third, fourth, and fifth characters, we can choose from any of the 26 letters (upper or lower case).

For the last character, we have 4 choices for the symbol

So, total number of unique passwords that can be created is:

⇒ 26 × 26 × 26 × 26 × 26 × 4 = 26⁵ × 4 = 47525504.

Therefore, there are 47525504 unique passwords that can be created using these letters and symbols.

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Answer:

x = 1+sqrt(69)/8 about 2.0383

or

x = 1-sqrt(69)/8 about -0.0383

Step-by-step explanation:

Use the quadratic formula:

(Move 17 to the left side first though)

(-b±√(b²-4ac))/2a

(1±sqrt(1-4*1*-17))/2(4)

x = 1±sqrt(69)/8

The most efficient method is the quadratic equation because the equation is not easily factorable and a!=1.

1.644 gml⁻¹ is is the new volume of the water .

What is density, ?

density = mass/volume

     ρ  = 12.5/7.6

      ρ = 1.644 gml⁻¹

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Answer:

The radius is  4 m.

Step-by-step explanation:

The area of a circle with radius r  is

A = π ⋅ r 2 ⇒ r = √ A π

Where  A = 50.24

Hence

r = √ 50.24 π = √ 16 = 4 m

The total amount that would be found in the account after 4 years, would be $ 641. 69

The total amount after 4 years in Arik's account can be found by the formula :

= A = Amount invested x ( 1 + r /n )ⁿ

The variables are:

Amount invested = $ 500

r = 6.25% = 0. 0625

n = 12

t = 4 years

The total amount is then :

A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾

A = $ 641. 69

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Answer:

huhh

Step-by-step explanation:

The type of sample that is selected to reflect the demographic characteristics of the population of interest is representative samples. Option b is correct.

Representative samples are selected to reflect the demographic characteristics of the population of interest. This sampling method aims to ensure that the sample closely resembles the larger population in terms of its demographic composition.

By including individuals from various demographic groups in the sample, representative samples allow for more accurate generalizations and conclusions to be drawn about the population as a whole. This sampling approach is commonly used in research studies and surveys to gather data that is representative of the larger population's characteristics and attitudes.

Therefore, b is correct.

Which type of sample is selected to reflect the demographic characteristics of the population of interest?

A. Convenience samples

B. Representative samples

C. Random samples

D. Cumulative samples

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Answer:

no clue

Step-by-step explanation: not sure

Answer

The armadillo and Glyptodon descended from a common ancestor.

Step-by-step explanation:

Answer:

5400 students

Step-by-step explanation:

30000×0.6(60%)=18000

18000×0.3(30%)=5400

The required answers ar(a)P = $2,000,r = 4.5%,n = 2 (b)$ 2985.17, (c) 4.45%

(A) Using the given information, we can identify the following values:

P = $2,000 (the present value or initial deposit)

r = 4.5% (the annual percentage rate)

n = 2 (the number of times per year that interest is compounded, since it is compounded semi-annually)

(B) To find the future value of the account balance after 9 years, we can use the formula:

\(S(t) = P(1 + r/n)^{nt}\)

where t is the time in years. Substituting the given values:

\(S(9) = $2,000(1 + 0.045/2)^{2*9}= $2,000(1.0225)^{18}\)

= $2,000(1.505016)

= $2985.17

Therefore, Monique will have $$2985.17 in the account in 9 years.

(C) The annual percentage yield (APY) takes into account the effect of compounding on the effective interest rate. It is calculated as:

\(APY = (1 + \frac{r}{n})^n - 1\)

Substituting the given values:

\(APY = (1 + 0.045/2)^2 - 1\)

= 0.0445 or 4.45%

Therefore, the annual percentage yield for the savings account is 4.45% rounded to 3 decimal places.

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We have;70° < DAB = 3.6x²70/3.6 < x²19.4 < x²√19.4 < x Hence, the value of x is approximately equal to 4.4 (rounded to one decimal place).

The given equation is m < DAB = 3.6x². We are to find the value of x. Given that m < DAB, the value of angle m is less than the value of angle DAB.Since, the sum of the angles in a triangle is equal to 180°.

Therefore, we have; m + A + B = 180°Substituting the given angle measures in the above equation, we get;m + 65° + 45° = 180°m + 110° = 180°m = 180° - 110° = 70°Now, m < DAB.

Therefore, we have;70° < DABFor any triangle, the length of the side opposite to an angle is equal to the product of the other two sides and the sine of the angle opposite to it.i.e.,

Opposite side of angle m = AB sinC = AB sin 65°

Opposite side of angle B = ACsinA = Ac sin45°Opposite side of angle DAB = BC sin70°We have the relationship between the sides of a right angled triangle as,

AB² + BC² = AC²Substituting the values of the opposite sides of the angles in the above equation,

we get;

AB² + AC²sin²45°

= BC²sin²70° + AC²sin²65° ⇒ AB² + AC²/2

= BC²/2 + AC²×(1-sin²70°)/2 + AC²×(1-sin²65°)/2⇒ 2AB² + AC²

= BC² + AC²×(cos²70° + cos²65°)Now,

we are given that;m < DAB = 3.6x²

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