Find The General Solution To Y' + 3 Cos 3x/Sin 3 X Y=1 y(t) = Suppose that Y(π/2)= 0 , What Is Y(π/4)

The width of the playground is 4/3 miles.

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here, the length = 2/4 miles and Area = 8/12 miles

Thus width = 8/12 / 2/4

                   = 4/3 miles

Hence, the width of the playground is  4/3 miles.

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

both question 5 and question 6 are answered...

Answer:

The mean absolute deviation (MAD) of the given data set is 2.75.

Step-by-step explanation:

Mean Absolute Deviation (MAD) is a way to measure how spread out a set of numbers is from their mean. A smaller MAD means the numbers are closer to the mean, while a larger MAD means they are more spread out.

To find the mean absolute deviation (MAD) of a set of data, first calculate the mean of the data set.

To find the mean, divide the sum of the data by the number of data points:

\(\textsf{Mean}=\dfrac{4+2+2+10}{4}=\dfrac{18}{4}=4.5\)

Therefore, the mean is 4.5.

Now calculate the absolute difference between each data point and the mean:

\(|4 - 4.5| = |-0.5| = 0.5\)

\(|2 - 4.5| = |-2.5|=2.5\)

\(|2 - 4.5| = |-2.5|=2.5\)

\(|10 - 4.5| = |5.5|=5.5\)

Finally, calculate the mean of the absolute differences by dividing the sum of the absolute differences by the number of data points:

\(\textsf{M.A.D.}=\dfrac{0.5+2.5+2.5+5.5}{4}=\dfrac{11}{4}=2.75\)

Therefore, the mean absolute deviation (MAD) of the given data set is 2.75.

Answer:

\(\frac{2}{3}\)

Step-by-step explanation:

\(\frac{y_{2} - y_{1}}{x_{2}- x_{1} } = \frac{2-0}{3-0} = \frac{2}{3}\)

Answer:2/3

Step-by-step explanation:

khan

Answer:

Yes, distance is never negative.

Answer:

No, distance is a postive if it was a negative number then yes

Step-by-step explanation:

Hope this help and Have good rest of your day or night

Answer:

153.94 cm

Step-by-step explanation:

d=2r (need radius (r) to solve for the area)

14=2r

r=7

A=πr²

A=π(7)²

A=π49

A=153.94

The value of x is less than or equal to 2 and 1 half. The correct option is B.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that inequality is 3¹/₂≥1.4x. The inequality will be solved as below,

3¹/₂ ≥ 1.4x

(14)/(10)x ≤ (5/2)

(5/10)x ≤  5/2

x ≤ (5/10) ÷ ( 5/2 )

x ≤ 2.5

x ≤ 2¹/₂

Therefore, the value of x is less than or equal to 2 and 1 half. The correct option is B.

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Answer: x <= 2 1/2

Step-by-step explanation: Got correct on test

Answer:

false

Step-by-step explanation:

11 ≠ 4

11=11

4=4

Answer:

\(\sqrt{2}\)

Step-by-step explanation:

A rational number has the form

\(\frac{a}{b}\) , where a and b are integers

Given

- \(\sqrt{2}\) ( multiplying by \(\sqrt{2}\) gives )

- \(\sqrt{2}\) × \(\sqrt{2}\)

= - 2

= \(\frac{-2}{1}\) ← a rational number

On the base of given lengths of the mast, cable, and base distance, the mast is not vertical. The discrepancy in the Pythagorean equation suggests an inconsistency in the dimensions of the system.

To determine if the mast is vertical, we need to consider the geometry of the situation and the lengths of the mast and the cable.

Given that the height of the mast is 5 m and the cable is 6.25 m long, we can visualize the scenario as a right triangle.

The mast represents the vertical side (opposite side) of the triangle, the cable represents the hypotenuse, and the distance from the base of the mast to the point where the cable is anchored represents the base (adjacent side) of the triangle.

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, as per the Pythagorean theorem.

Applying the theorem to this situation, we have:

(base)^2 + (height)^2 = (cable)^2.

Substituting the given values:

(3.75)^2 + (5)^2 = (6.25)^2.

Simplifying:

14.0625 + 25 = 39.0625.

39.0625 ≠ 39.0625.

The equation does not hold true, indicating that the mast is not vertical. The discrepancy suggests that the length of the cable is not appropriate for the given height and base distance.

To have a vertical mast, the length of the cable should be equal to the distance between the base and the point where the cable is anchored. In this case, the cable should be 3.75 m long, which is equal to the distance between the base and the anchor point. However, the given cable length is 6.25 m, which does not correspond to a vertical configuration.

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the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.

94.68 cm

The formula for circumference of a circle is C = 2πr, where r is the radius of the circle. Therefore, to find the circumference of the circle, we need to first calculate the radius.

The area of the circle is given as A = πr2.

Therefore, we can rearrange this equation to solve for the radius, which is

r = √(A/π)

Plugging in the given area, A = 3.14, we get

r = √(3.14/π) = √(3.14/3.14) = 1

Now, we can use the circumference formula to calculate the circumference, which is

C = 2πr = 2π(1) = 2π × 3.14 = 6.28 × 3.14 = 19.4568

Therefore, the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.

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The length and width of the room should be 50 feet, and the height should be 16 feet, in order to maximize the volume.

We have,

Volume = Length x Width x Height

Since we want to maximize the volume, we need to make the length, width, and height of the room as equal as possible.

So,

Length = Width

Now we can substitute the given values into the formula and solve for the dimensions of the room:

Volume = Length x Width x Height

Volume = (Length)² x Height

Volume = (Length)² x 16 (since the height of the room is 16 feet)

Volume = 16 (Length)²

The length of the house is 100 feet, and we have set the length and width of the room to be equal, so:

Length + Width = 100

Length + Length = 100

2 Length = 100

Length = 50

Therefore,

The length and width of the room should be 50 feet, and the height should be 16 feet, in order to maximize the volume.

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The sequence for the cost of bracelet in dollars = $0, $3, $6, $9 and $12.

Also the sequence for the cost of necklace is = $0, $6, $12, $18, $24.

The column given concerning the products contains the following amounts of products such as 0, 1, 2, 3, and 4 pieces.

Therefore to calculate the amount to be used to buy each product of bracelet and necklace in each column multiplication is carried out.

That is, 0×3, 1 ×3, 2×3, 3×3, and 4×3

which is = $0, $3, $6, $9 and $12 respectively for the bracelet.

0×6, 1 ×6, 2×6, 3×6, and 4×6

Which is = $0, $6, $12, $18, $24. respectively for the necklace.

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tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

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Answer: 15/11

Step-by-step explanation:

Answer:

15 ÷ 11 as a fraction is 15/11. As a mixed number it is 1 4/11.

Step-by-step explanation:

Answer: it's around 40

Step-by-step explanation:

With no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

A type of plant is introduced into an ecosystem and quickly begins to take over.

A scientist counts the number of plants after m months and develops the equation to model the situation, which is given as,

\(p(m)=19.3(1089)^m\)

Most recently, the scientist counted 138 plants.

\(138=19.3(1089)^m\\(1089)^m=7.15\)

Taking log both sides of the equation,

\(\log(1.089)^m=\log7.15\\m\log(1.089)=\log(7.15)\\m=\dfrac{\log7.15}{\log(1.089)}\\m\approx23.1\)

Thus, with no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

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Answer:

With no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

Step-by-step explanation:

Answer:

it is -21

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The sequence given by the terms 125,25,5 is a geometric sequence with common ratio 1/5.

In a geometric sequence, each term following the first is found by multiplying the preceding one by a constant, non-zero quantity known as the common ratio.

The nth term of a geometric series with first term a and common ratio r is given by \(a_n=ar^{n-1}\) .

In the given sequence, the first term denoted by a is 125. The second term is 25 and the third term is 5.

Ratio of the second term to first term = 25/125 = 1/5

And the ratio of third term to second term is = 5/25 =1/5

Hence since the ratios are equal therefore the sequence is geometric, and the common ratio is 1/5 .

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Answer:

Multiplication

The solution of given equation x = -20

Step-by-step explanation:

step (i) :-

given equation = -(x/4) = 5

multiply '1' on both sides we get

\( = - (( - \frac{x}{4} )) = - 5\)

\( = \frac{x}{4} = - 5\)

step (ii) :-

multiply '4' on both sides we get

\( = \: \: \: \: \: \frac{x}{4} \: \: \times \: 4 \: \: = - 5 \times 4\)

Cancellation '4' on left side we get

x = -20

conclusion:-

The solution of given equation x = -20

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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Answer:

Just QT and UX

Step-by-step explanation:

QT and TX intersect and are not parallel.

QU and ST are not parallel or intersecting.

QT and WX are not parallel or intersecting.

QT and UX are parallel.

Answer:

-13.64

Step-by-step explanation:

Answer:14.52 is the variation in water level

Step-by-step explanation:

Answer:

Jorge needs 1/2 apple to make the snack.

Our expression is

The measure of angle 10 is 30 degrees.

What is an angle?

we can see that angle 10 and angle 11 form a straight line, and angle 9 and angle 10 form a triangle with angle 11.

Since angle 11 is a right angle with a measure of 90 degrees, the sum of angles 9 and 10 in the triangle must be 90 degrees.

We know that the measure of angle 9 is 60 degrees, so we can solve for the measure of angle 10 as follows:

angle 9 + angle 10 = 90 degrees

60 degrees + angle 10 = 90 degrees

angle 10 = 90 degrees - 60 degrees

angle 10 = 30 degrees

Therefore, the measure of angle 10 is 30 degrees.

What is triangle ?

A triangle is a closed geometric shape that consists of three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.

Triangles are two-dimensional objects that lie flat in a plane, and they have a variety of properties and characteristics that make them important in mathematics and other fields. The angles and sides of a triangle can be measured and related to one another through various geometric formulas and theorems, and triangles are used in a wide range of applications, from basic geometry and trigonometry to engineering, physics, and computer graphics.

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Complete question is: If the measure of angle 11 is 90 degrees, and the measure of angle 9 is 60 degrees, the measure of angle 10 is 30 degrees.

Answer:

The answer is n=36 Hope this helps^_^

Step-by-step explanation:

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Answer:

Step-by-step explanation:

i took the test hope this helps

Answer: 3 I think !

Step-by-step explanation: