I need help solving this

The coefficient of the second derivative (t2) is constant, so the equation is linear.

1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2  ->  2nd. order non-linear differential equation

2. t2(d2y/dt2)+t(dy/dt)+2y=sin t  ->  2nd. order linear differential equation

3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3  ->  3rd. order non-linear differential equation

4. y''-y+y2=0  ->  2nd. order non-linear differential equation

The order of a differential equation is the highest derivative involved in the equation. For example, in the equation 1 + y2(d2y/dt2) + t(dy/dt) + y = et2, the highest derivative is the second derivative (d2y/dt2), so this equation is of 2nd order. Linearity is determined by whether the coefficients of each derivative are constants, or whether they depend on the function y and its derivatives. In this equation, the coefficient of the second derivative (1+y2) is not constant, so the equation is non-linear. Similarly, in equation t2(d2y/dt2)+t(dy/dt)+2y=sin t, the coefficient of the second derivative (t2) is constant, so the equation is linear.

Learn more about derivative here:

https://brainly.com/question/25324584

#SPJ4

One kind of average is the mean. It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.

Given data :

a ) Mean =

              x = [tex]\frac{\left \{ {{i=10} \atop {i=1}} \right.}{n} Xi[/tex] = 101 / 10 =  10.1 hundreds of dollars

The median is the 50th percentile To determine the location index for the median (2nd

quartile (p =50) we do the following:

The index is

                               i  = [tex]\frac{p}{100}[/tex] (n) = [tex]\frac{50}{100}[/tex] (10) = 5 integer

Since the index, 5, is an integer, the 2nd quartile is determined by finding the average of

the 5th and 6th values from the lower or higher end of the sorted data. This is:

                Median = [tex]Q_{2}[/tex] = [tex]\frac{10 + 11}{2}[/tex] = 10.5 hundreds of dollar

Mode = most frequently occurring observation = 11 hundreds of dollars ( two times )

Here i attached graph

Learn more about mean refer to :

https://brainly.com/question/20118982

#SPJ4

"

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

[tex]Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7[/tex]

The potential energy of the spring-mass system is equal to  1/2kx². Thus, figure I is a correct representation.

where x is the mass's deviation from the average location, or O.

Consequently, the graph would be symmetric about a vertical line that passes through O and would exhibit a quadratic variation with respect to x.

Thus, figure I is a correct representation.

The graph illustrates how the potential and kinetic energy of a block coupled to a spring that follows Hooke's law changes over time.

Due to the potential and kinetic energy's x2 variation, both graphs are parabolas.

Know more about spring-mass system

https://brainly.com/question/13008311

#SPJ4

The vertex angle of the isosceles triangle is 22°.

What is isosceles triangle?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

We know that an isosceles triangle is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180degrees.

Base angle = 3vertex angle+13.

=> 2base angle + vertex angle = 180°

=> 2(3 vertex angle +13)+vertex angle = 180°

=> 6 vertex angle+26+vertex angle = 180

=> 7 vertex angle = 180-26

=> 7 vertex angle = 154

=> vertex angle = 154/7 = 22°.

Hence the vertex angle of the isosceles triangle is 22°.

To learn more about isosceles triangle refer the below link

https://brainly.com/question/29793403

#SPJ1

The required solution of the given algebraic expression is x = 6.

The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.

Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1  = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1

Combining like terms on each side of the equation, we get,
According to the question

x + 7 = 13
x = 6

Thus, the required solution of the given algebraic expression is x = 6.

Learn more about algebraic expression here:

https://brainly.com/question/953809

#SPJ1  

Answer:

x + 7 = 13

Step-by-step explanation:

(in case you also need it) x = 6

The density of the unknown metal exists 8.9 g/mL.

The mass of an object divided by its volume is how dense it is. The gram per cubic centimeter (g/cm³) unit of density is frequently used. How much mass is present in a given area is referred to as density. Try to picture a drawer full of socks. Its density is particular. Consider that when you remove a sock, the drawer's density changes. This is due to the socks' shifting mass while the drawer's remaining constant volume.

The definition of density is the mass of a substance per unit volume. The degree to which matter is packed together is fundamentally measured by density. It is a specific physical quality of a specific object. Greek scientist Archimedes is credited with discovering the density principle.

The density (D) is equal to mass (m) divided by volume (V): D = m/V

To find the mass of the object:

m = 156 g - 105.5 g = 50.5 g

To find the volume of the volume:

V = 30.7 mL - 25 mL = 5.7 mL

The density is:

D = m/V = 50.5 g  / 5.7 mL = 8.9 g/mL

Therefore, the density exists 8.9 g/mL.

The complete question is:

A graduated cylinder was filled with water to the 25.0 mL mark and weighed. Its mass was 105.5g. An object made of an unknown metal was placed in the cylinder and completely submerged in the water. The water level rose to 30.7 mL. When reweighed, the cylinder, water and metal object had a total mass of 156.0g. Based on these measurement, what is the density of the unknown metal?

To learn more about density refer to:

https://brainly.com/question/1354972

#SPJ4

The number of cycles per day and the production quantity per cycle.

Number of cycles per day = (Product Daily Quantity/Production Quantity per Cycle)

For Product A:

Number of cycles per day = (18/Production Quantity per Cycle)

For Product B:

Number of cycles per day = (16/Production Quantity per Cycle)

For Product C:

Number of cycles per day = (6/Production Quantity per Cycle)

For Product D:

Number of cycles per day = (14/Production Quantity per Cycle)

Using the data from the excel file, we can calculate the production quantity per cycle and the number of cycles per day.

For Product A:

Production Quantity per Cycle = 18/3.75 = 4.8

Number of cycles per day = 3.75

For Product B:

Production Quantity per Cycle = 16/2.5 = 6.4

Number of cycles per day = 2.5

For Product C:

Production Quantity per Cycle = 6/1.5 = 4

Number of cycles per day = 1.5

For Product D:

Production Quantity per Cycle = 14/2.25 = 6.2

Number of cycles per day = 2.25

Therefore, for this set of vehicles, the number of cycles per day and the production quantity per cycle are as follows:

Product A: 3.75 cycles per day, 4.8 units per cycle

Product B: 2.5 cycles per day, 6.4 units per cycle

Product C: 1.5 cycles per day, 4 units per cycle

Product D: 2.25 cycles per day, 6.2 units per cycle

Learn more about data here:

https://brainly.com/question/14893265

#SPJ4

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

given that

they have 10 bags full of coins

in each bag are infinite coins.

but one bag is full of forgeries, and you can't remember which bag.

you know that genuine coins weigh= 1 gram

forgeries weight = 1.1 gram

now, we need to find which bag has  forgeries  in minimum readings

then take 1 coin from the first bag, 2 coins from the second bag . . . 10 coins from the tenth bag

If there are no forgeries, then total weight will be

= (1+2+3+4+5+6+7+8+9+10) = 55 grams

Therefore total weight should be 55 grams if the total weight is more than 55 grams then it has forgeries coins

To know more about weight:

https://brainly.com/question/23312072

#SPJ4

Total weight=55gm ,then there is no forgeries coin bag

1 bag with forgeries = take 1 coin from first bag

from 2 bag = take 2 coin

and similarly with all 10 bags.....

from 10th bag = take 10 coin

if there is no forgeries ,then  total weight    = (1+2+3+4+5+6+7+8+9+10)

                                                                        =55gm

If bag weight 55.3 than we know that there are 3 forgeries.

So total weight=55 ,then there is no forgeries coin bag if weight is more than 55 than there is forgeries coin.

Learn more about coin here:-

https://brainly.com/question/29869268

#SPJ4

Answer:4999 combos

Step-by-step explanation:

max:75999

min:71000

*zip codes are 5 digits long

75999-71000=4999

The values of p and q are given as follows:

p = 3.5, q = 6.

Hence the factored expression is given as follows:

2(x - 1.5)(x - 2)(x + 2).

The function f(x) is divisible by 2x² - 7x + 6, which has the roots given as follows:

x = 1.5 and x = 2.

(using a quadratic equation calculator with coefficients a = 2, b = -7 and c = 6).

Hence the following relation holds true, considering the linear factors of the function:

2x³ + px² + 8x + q = 2(x - 1.5)(x - 2)(x - a).

In which a is the third root.

Hence:

2x³ + px² - 8x + q = 2(x² - 3.5x + 3)(x - a)

2x³ + px² - 8x + q = 2(x³ - x²(3.5 + a) + x(3.5a + 3) - 3a)

2x³ + px² - 8x + q = 2x³ - x²(7.5 + 2a) + x(7a + 6) - 3a.

Hence the system of equations is given as follows:

From the second equation, the value of a is given as follows:

7a = -14

a = -2

Then the value of q is given as follows:

q = -3a = 6.

The value of p is given as follows:

p = 7.5 - 4

p = 3.5

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

The amount invested at 8% is 64,500-32,000 = 32,500

Step-by-step explanation:

one investment: 3%, amount: x

the other: 8%, amount: 64,500-x because x is invested at 3%

0.03x+0.08(64,500-x) = 3,560

0.03x+5,160-0.08x = 3,560

-0.05x = -1,600 divide both sides by 0.05 and remember that -/- = +

x = 32,000 This is the amount invested at 3%

The amount invested at 8% is 64,500-32,000 = 32,500

Answer:

To find the remainder when f(x) is divided by (x-a) , we substitute x = a in the polynomial f(x) and we get the remainder.

remainder = f(a)

In this case, we have f(x)=5x^6-2x^2-5, and x+2 is the divisor and we substitute x=-2

so, remainder = f(-2) = 5*(-2)^6-2*(-2)^2-5 = -643

So, the remainder when f(x) is divided by x+2 is -643

The graph for the given mode function, y ≥ |x| - 4 is attached below.

In mathematics, the modulus function is a function for which any input value of x, output will be always positive

Given that,

The modulus function,

y  ≥  |x| - 4

We can write given function in a following two ways-

y  ≥  x - 4

y  ≥  -x - 4

So, for any value of x

y should be greater than modulus functions value

Plotting graph for  y  ≥  x - 4

So first draw line  x - 4

Now, here we have inequality sign

So left side region will be our desired space

Similarly, Plotting graph for  y  ≥  -x - 4

So first draw line  -x - 4

Now, here we have inequality sign

So right side region will be our desired space

Hence, Graph is drawn for the given function

To know more about Modulus function check:

https://brainly.com/question/13103168

#SPJ1

The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.

1904: 78 medals

1908: 82 medals

1912: 88 medals

1920: 94 medals

Mean = 86 medals

1. Add the total number of medals awarded to the US during the first four summer Olympic Games: 78 + 82 + 88 + 94 = 342

2. Divide the total number of medals by the number of Olympic Games (4): 342 / 4 = 85.5

3. Round the mean to the nearest whole number: 86 medals

The mean number of medals won by the United States during the first four summer Olympic Games is 86 medals.

Learn more about mean here

https://brainly.com/question/15323584

#SPJ4

Answer:

Why don't you use this app and take a picture and see if someone got the answer

A. The probability that a sample of taxpayers from this income group are:

n = 30: 0.8159

n = 50: 0.8796

n = 100: 0.9332

n = 400: 0.9984

B. Advantages of a larger sample size are:

it increases precision

reliability of estimate of the population mean

standard error of the mean decreases

Using the z-score below:

For a sample size of 30, the z-score is 1.28.

For a sample size of 50, the z-score is 1.64.

For a sample size of 100, the z-score is 2.33.

For a sample size of 400, the z-score is 3.29.

a. The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $157 of the population mean for each of the following sample sizes:

n = 30: 0.8159

n = 50: 0.8796

n = 100: 0.9332

n = 400: 0.9984

b. The advantage of a larger sample size when attempting to estimate the population mean is that it increases the precision and accuracy of the estimate. As the sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the standard error of the mean decreases.

In this case, as the sample size increases from 30 to 400, the probability of the sample mean being within 157 of the population mean increases from 0.8159 to 0.9984.

learn more about population mean: https://brainly.com/question/29441200

#SPJ1

Ten to fifty is the range of the scores. The most frequent result is a 10 with a right-skewing bias.

Probability histogram

The height of each bar must be equal to the probability, the width of each bar must be the same, and the bars must be centered on the amount of money gathered.

The distribution is skewed to the right because the highest bar in the histogram is to the left and there is a tail of lower bars to its right.

The most frequent score is 10 due to the fact that the top bar in the histogram is centered at 10.

The result is:

Ten to fifty is the range of the scores.

The most frequent result is a 10 with a right-skewing bias.

Ten to fifty is the range of the scores.

Know more about Probability histogram

https://brainly.com/question/1741571

#SPJ4

The value of the following venn expressions of sets is (A)=1 ,(B)=50,(C)=20 and (D)=130 respectively.

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.

Symmetric difference between two sets A and B defined by,

AΔB=(A\B) ∪ (B\A)

AΔB=(A∩B') ∪(A'∩B).

we have n(A)=20 n(B)=50, n(A∩B)=0, n(U)=200

SO,

(A) Find n(A∩B)

n(A∩B) =0 (GIVEN)

(B) Find n(A∩B')

n(A∩B') =n(B)-n(A∩B)

          = 50-0

           =50

(C) Find n(A∩B')

n(A'∩B) =n(A)-n(A∩B)

          =20-0

          =20

(D) n(A'∩B') =n(U)-n(A'∩B)-n(A∩B)-n(A∩B')

             =200-20-0-50

            = 130.

thus, the above is the value of expression.

learn more about Venn diagram.

https://brainly.com/question/29301560

#SPJ4

if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that Triangle ABC has sides that are 6 cm and 11 cm

The third is represented by the inequality 5 < ×.

We know that the sum of sides of a triangle must be greater than the third side.

5<6+11

5<17

Hence, if Triangle ABC has sides that are 6 cm and 11 cm. The third is represented by the inequality 5 < 17.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

About 80 necklaces have more than 28 beads. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.

P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)

P(x > 28) = P(x - 24 / 4 > 1)

P(x > 28) = 1 - ∅1

P(x > 28) = 1 - 0.8413

P(x > 28) = 0.1587

Multiply both sides by 500, then we have

500 P(x > 28) = 0.1587 × 500

500 P(x > 28) = 79.35

500 P(x > 28) ≈ 80

About 80 necklaces have more than 28 beads. Then the correct option is C.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ1

The missing options are given below.

A. About 24 devices have more than 28 beads.

B. About 48 necklaces have more than 28 beads.

C. About 80 necklaces have more than 28 beads.

D. About 96 necklaces have more than 28 beads.

The peak of the mountain has a height of 14805 feet.

In this problem we find the case of an exponential function for atmospheric pressure (p), in pounds per square inch, in terms of height (x), in miles, whose expression is introduced below:

[tex]p(x) = 14.7 \cdot e^{- 0.21\cdot x}[/tex], for x ≥ 0.

If we know that p(x) = 8.164 lb / in², then the height of the peak of a mountain is:

[tex]8.164 = 14.7\cdot e^{-0.21 \cdot x}[/tex]

[tex]0.555 = e^{-0.21\cdot x}[/tex]

Then, by relationship between exponential and logarithmic functions and logarithm properties:

㏑ 0.555 = - 0.21 · x · ㏑ 1

㏑ 0.555 = - 0.21 · x

x = - (1 / 0.21) · ㏑ 0.555

x ≈ 2.804

Finally, convert miles into feet:

x = 2.804 mi × (5,280 ft / 1 mi)

x = 14805.12 ft

To learn more on exponential functions: https://brainly.com/question/28596571

#SPJ1

The best name for quadrilateral QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0) include the following: C. Trapezoid.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral QRST on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral QRST on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a trapezoid.

Read more on quadrilateral here: brainly.com/question/6561516

#SPJ1

Answer:



Step-by-step explanation:

sin 300° = sin (300° - 360°) = sin (-60°) = -sin 60° = -(1/2)

cos 945° = cos (945° - 360°) = cos (585°) = cos (-295°) = -cos 295°

tan (-675°) = -tan (675° - 360°) = -tan 315°

so

sin 300° − cos 945° + tan(−675°) = -(1/2) - (-cos 295°) + (-tan 315°)

It is not a trivial task to simplify the above equations without using a calculator.



= -(1/2) + cos 295° + tan 315°

As we know that cos(x) = cos(360°-x) = -cos(x) and tan(x) = -tan(360°-x) = -tan(x)

= -(1/2) - cos 295° - tan 315°

As we know that cos(295°) = cos(360°-65°) = cos(65°) and tan(315°) = tan(360°-45°) = tan(45°)

= -(1/2) - cos(65°) - tan(45°)

= -(1/2) - 0.4226 - 1

= -0.5 - 0.4226 - 1

= -1.4226

.

The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.

f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above.

We can calculate g'(x) as follows:

g'(x) = 2f'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3

1. Start by taking the derivative of g(x) with respect to x. This is done using the chain rule, since g(x) is defined by another differentiable function f(x):

g'(x) = d/dx[21 + J' f(t) dt] = 2f'(x)

2. Now, substitute the function f(x) into the equation for g'(x):

g'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3

The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.

learn more about derivative here

https://brainly.com/question/25324584

#SPJ4

To earn back the amount Helen spent on certification, she would need to earn $90. Since her base salary is $55 per month, she would need to teach an additional $90 - $55 = $35 in classes. Since she earns $5 per class, she would need to teach $35 / $5 = 7 classes.

So, Helen will need to teach 7 classes to earn back the amount she spent on certification.

Her total earning for teaching 7 classes would be $55 (base salary) + $5 (per class) * 7 (classes) = $110

Therefore Helen's expenses and earning would be $90 (certification cost) and $110 (earning) respectively.

Answer:

the first expression i think is the line going downwards

and the second is the line going upwards

Step-by-step explanation:

i think sorry if it wrong

hope the annotating will help you! If this is not the thing you want let me know so that I can edit the way the question actually is...

Step-by-step explanation:

reading the question thoroughly, we find out that volume (V) and radius (r) of the cone is given, and we just have to find out the length (h) of the cone

V = πr²h/3

Putting the given values in place,

V = 75.36 cm³

V = 75.36 cm³r = 2 cm

V = 75.36 cm³r = 2 cmπ = 3.14

Now, since we calculating for h, we can interpret the formula in the terms of h, i.e.

h = 3V/(πr²)

h = 3×75.36/(3.14×2²)

h = 226.08/12.56

h = 18 cm

Thus, the height of the ice cream cone is 18cm

Hope this helped!

a. visits of the college students, b. herbal tea, d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

Despite the name, herbal tea is not actually "tea" as these beverages typically do not contain the leaves or leaf buds of tea plants. Herbal teas are made from tisanes, which are blends or infusions of dried fruits, flowers, spices or herbs in water.

The lurking variable in this experiment is - a. visits of the college students.

The explanatory variable in this experiment is - b. herbal tea

Which of the following may be correctly concluded from this study - d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

To learn more about Herbal Tea refers to;

brainly.com/question/21602288

#SPJ1

Option D is the correct answer that is The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.

The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches is represented in v(3)-v(1)/3-1.

The difference in volumes is

V(r+3) - V(r) = 4π [tex](r+3)^{3}[/tex] /3 - 4π [tex]r^3}[/tex]/3

= 4π/3( (r+3)[tex]^{3}[/tex] -  [tex]r^{3}[/tex])

= 4π/3( [tex]r^{3}[/tex]+ 9[tex]r^{2}[/tex]+ 27r + 27 -  r∧3 )

= 4π/3(9 [tex]3^{3}[/tex] + 27r + 27 )

= 12π( [tex]r^{2}[/tex]+ 3r + 3 ) in cube

A balloon is a sphere shape. A sphere is a solid figure where each endpoint is equidistant from the center. It is like a 3-Dimensional version of a circle shape. The volume of a sphere is 4/3πr∧3 and its surface area is  4πr∧2. Here r is the radius of the sphere.

To know more about sphere visit:

https://brainly.com/question/20394302

#SPJ4