what is the product?

x^2 -16 • x^3 - 2x^2 + x———— ——————–—
2x +8 x^2 +3x -4

I bet the ODE is supposed to read

[tex]x^2y''-14xy'+56y=0[/tex]

Then if [tex]y=x^r[/tex], we have [tex]y'=rx^{r-1}[/tex] and [tex]y''=r(r-1)x^{r-2}[/tex], and substituting these into the ODE gives

[tex]r(r-1)x^r-14rx^r+56x^r=0\implies r(r-1)-14r+56=r^2-15r+56=0[/tex]

Solving for r, we find

[tex]r^2-15r+56=(r-8)(r-7)=0\implies \boxed{r=8\text{ or }r=7}[/tex]

so that [tex]y_1=x^8[/tex] and [tex]y_2=x^7[/tex] are two fundamental solutions to the ODE. Thus the general solution is

[tex]\boxed{y(x)=C_1x^8+C_2x^7}[/tex]

Given that [tex]y(1)=4[/tex] and [tex]y'(1)=3[/tex], we get

[tex]\begin{cases}4=C_1+C_2\\3=8C_1+7C_2\end{cases}\implies C_1=-25\text{ and }C_2=29[/tex]

So the particular solution is

[tex]\boxed{y(x)=29x^7-25x^8}[/tex]

Answer:

11.5, 20, 28.5

Step-by-step explanation:

Given AP

5th term is 37, then common difference is;

Then the 2nd, 3rd and 4th terms:

Answer:

we get only one solution that is 23 + 17 = 40

Hope it helps

Answer:

b≠0 means b is not equal to zero.

Hope I helped!

Best regards!

Answer:

The special symbol ≠ It is used to show that one value is not equal to another. a ≠ b says that a is not equal to b. Example: 4 ≠ 9 shows that 4 is not equal to 9.

Step-by-step explanation:

Answer:

B) f(x) = x if x ≤ -2

            2 if x > -2

Step-by-step explanation:

B) f(x) = x if x ≤ -2 (The x and y coordinate have the same value)

            2 if x > -2

Answer: 98

Step-by-step explanation: 53+45 = 98 subtract that from 180 you get 82 which is the other corner. the other side of the line adds up to 180 with the 82

Answer:

Step-by-step explanation:

inside the triangle

a + 53 + 45 = 180

a + 98 = 180

a = 82

x + 82 = 180

x = 98

Answer:

Can u add more context pls then I'll answer

Step-by-step explanation:

Answer:

It would cost $90.66

Step-by-step explanation:

because 180 dived by 204 equals 1.13 then times that by 80 and there's your answer

Answer:

Hey there!

Left 2 units: (7,-2)

Down 1 unit: (7, -3)

Final answer: (7, -3)

Let me know if this helps :)

Answer:

A - 6

Step-by-step explanation:

The lines are parallel.

Theorem: If two parallel lines are cut by a transversal, then same side interior angles are supplementary.

The angles measuring 16x + 4 and 80 are supplementary, so thjeir measures add to 180.

16x + 4 + 80 = 180

16x + 84 = 180

16x = 96

x = 6

Step-by-step explanation:

92007(1)1

since one is on the tens value, always jump to the next number.

It is greater than 5 add one to the next no.

= 9201000, The rest become zeros

Answer:

- This study is an example of Experimental study

- The survival time is the dependent variable.

- The type of diet is the independent variable.

Step-by-step explanation:

I) This research study is an experimental study because it makes use of a scientific approach using 2 variables which in this case are organic diet and survival time.

II) Survival time is the dependent variable because it depends on the response of the patients to the organic diet.

III) Type of diet is the independent variable because it doesn't depend on any other factor or variable.

Answer:

[tex]\mathbf{E(X) = \dfrac{3}{4}}[/tex]

Step-by-step explanation:

From the given data, the cumulative distribution function of a random variable can be represented as:

[tex]F_X(t) =\left\{ \begin{array}{c}0........... t <-1 \\ \dfrac{1}{2} ... -1 \leq t < 1\\ \dfrac{1}{2} ....... 1 \leq t < 2 \\ 1 .............. t \geq 2\\\end{array}\right.[/tex]

The objective is to estimate E(X), to do that, let's first evaluate the probability density function by differentiating the cumulative distribution function from above.

[tex]f_X(x) =\left \{ {{\dfrac{1}{2} .......1 \leq x \leq 2 } \atop {0..... otherwise }} \right.[/tex]

∴

[tex]f_X(t) =\left\{ \begin{array}{c} \dfrac{d}{dx}(0)=0........... <-1 \\ \dfrac{d}{dx}(\dfrac{1}{2} ) =0... -1 \leq t < 1\\ \dfrac{d}{dx}(\dfrac{1}{2}x) = \dfrac{1}{2}....... 1 \leq x < 2 \\ \dfrac{d}{dx}(1) = 0 .............. x \geq 2\\\end{array}\right.[/tex]

The expected value of x i

.e E(X) can now be estimated by taking the integral:

[tex]E(X) = \int ^{\infty}_{\infty} x f(x) \ dx[/tex]

[tex]E(X) = \int ^{1}_{- \infty} x 0 dx + \int^2_1 \ x \dfrac{1}{2}\ dx + \int ^{\infty}_2 \ x0dx[/tex]

[tex]E(X) = \int ^{2}_{1} x \dfrac{1}{2} dx[/tex]

[tex]E(X) = \dfrac{1}{2}[\dfrac{x^2}{2}]^2_1[/tex]

[tex]E(X) = \dfrac{1}{2}[\dfrac{4}{2}-\dfrac{1}{2}][/tex]

[tex]E(X) = \dfrac{1}{2} \times [\dfrac{3}{2}][/tex]

[tex]\mathbf{E(X) = \dfrac{3}{4}}[/tex]

Answer:

(2,9)

Step-by-step explanation:

The only point that could be included is (2, 9), since any of the other three would preclude the relationship between x and y values from being a function. Notice that 3, 4, and 7 are already connected/associated with other values in the Range of the function.

Answer:

Null hypothesis:

[tex]\mathtt{H_o : \mu = 21.21}[/tex]

Alternative hypothesis

[tex]\mathtt{H_1 : \mu \geq 21.21}[/tex]

t = -0.080

Decision Rule: To  reject the null hypothesis if t > 1.340 at t

Since t = -0.080, this implies that t < 1.340 that means the t statistics value did not fall into the rejection region. Hence, we fail to reject the null hypothesis at the level of significance 0.10

Conclusion: We conclude that there is insufficient evidence to support the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.

Step-by-step explanation:

Given that:

the sample mean [tex]\overline x[/tex] = 21.15

the standard deviation [tex]\sigma[/tex] = 4.7512

sample size N = 40

The objective is to test the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.

At the level of significance of 0.1

The null hypothesis and the alternative hypothesis for this study can be computed as follows:

Null hypothesis:

[tex]\mathtt{H_o : \mu = 21.21}[/tex]

Alternative hypothesis

[tex]\mathtt{H_1 : \mu \geq 21.21}[/tex]

This test signifies a one-tailed test since the alternative is greater than or equal to 21.21

The t-test statistics can be computed by using the formula:

[tex]t= \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \dfrac{21.15- 21.21 }{\dfrac{4.7152}{\sqrt{40}}}[/tex]

[tex]t = \dfrac{-0.06 }{\dfrac{4.7152}{6.3246}}[/tex]

t = -0.080

degree of freedom = n - 1

degree of freedom =  40 - 1

degree of freedom = 39

From the t statistical tables,

at the level of significance ∝ = 0.1 and degree of freedom df = 39, the critical value of [tex]\mathtt{{T_{39,0.10} = 1.304}}[/tex]

Decision Rule: To  reject the null hypothesis if t > 1.340 at t

Since t = -0.080, this implies that t < 1.340 that means the t statistics value did not fall into the rejection region. Hence, we fail to reject the null hypothesis at the level of significance 0.10

Conclusion: We conclude that there is insufficient evidence to support the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.

ans : A

reason : gradient = 0 and the line does not touch Y axis

i hope this helps :))

The equation of line l if the line is shifted 4 units to the right is x = 4, so option A is correct.

A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.

Given:

The lines y and l are given in the graph,

The equation of the line y can be written as shown below,

y = x + c

x = c  (as the y coordinate of the y-axis is zero)

The equation of the line shifted 4 units to the right can be represented as

y = mx + c

Here, the slope is 1 and the intercept is -4 so,

x = 4

Thus, the line l is x = 4.

To know more about the line:

https://brainly.com/question/2696693

#SPJ2

Answer:

The member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

Step-by-step explanation:

By finding the y-intercept, you can conclude that the member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

Answer:

the answer is A.The member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

Step-by-step explanation:

on edg 2020 :)

Answer: Option ( C ) Average speed in the ocean

Step-by-step explanation: This is because continuous quantitative variable is a variable whose value is obtained by measuring. The average speed is measured.

The example of a continuous quantitative variable that might be reported about each cruise ship is the average speed in the ocean so option (C) will be correct.

The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.

In another word, reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.

The quantitative variable is a variable whose value is measurable for example weight of any object.

In the given question the average speed in the ocean is only a variable and can be measured for each ship.

Hence"The example of a continuous quantitative variable that might be reported about each cruise ship is the average speed in the ocean".

For more about reasoning,

https://brainly.com/question/2923977

#SPJ5

QR = QU - RU

QR = 24 -19 = 5

QR = RS = ST = 5

QR + RS + ST = 5 + 5 + 5 = 15

TU = 24-15 = 9

SU = 5 + 9 = 14

Answer:

coordinates for the centroid is at (-3, -4)

Step-by-step explanation:

The centroid of a triangle is simply defined as the center point which is equidistant from the three vertices.

Let's denote the centroid as O. Thus, the coordinates of O will be: (O_x, O_y).

Now, the formula to calculate the centroid of a triangle with coordinates (O_x, O_y) is given by;

For x - coordinate;

O_x = (A_x + B_x + C_x)/3

For y - coordinate;

O_y = (A_y + B_y + C_y)/3

From the question,

A_x = 1

B_x = -10

C_x = 0

A_y = 0

B_y = -6

C_y = -6

Thus;

O_x = (1 - 10 + 0)/3

O_x = -9/3

O_x = -3

Also,

O_y = (0 - 6 - 6)/3

O_y = - 12/3

O_y = - 4

Thus, coordinates for the centroid is at (-3, -4)

n less than 7, is represented as this:

n>7

Step-by-step explanation:

You just need to think about what the question is, if it's less than, you use the > symbol to prove one variable is smaller than the other.

i hope this helps!

Answer:

[tex]\Huge \boxed{-n+7}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

n is the variable.

n less than 7 as an expression would be:

[tex]\Longrightarrow \ \ 7-n[/tex]

Rearranging terms:

[tex]\Longrightarrow \ \ -n+7[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

16)   2

17)   -5

18)   doesn't exist

19)   doesn't exist

20)  doesn't exist

21)   3

22)   4

23)   6

Step-by-step explanation:

16) as you move towards -9, the function adopts the value 2

17) as one moves towards x = -6 , from both sides (right and left) the function goes to the value -5

18) As one moves towards x = -4 (from the right and from the left, the functions seems to diverge towards + ∞. So normally the convention for limits stipulates: Undefined or Doesn't exist

19) f(-4) doesn't exist (for same reasons as above (there is a singularity here)

20) As one moves towards 2 from the right, the function gets towards the value 3, while approaching from the left the function goes towards the value 5. So formally we say that the limit doesn't exist (from the left and from the right limits don't agree)

21) f(2) is the well defined value of 3

22)  approaching x= 4 from the right and from the left both lead towards the value 4.

23) f(4) is 6

Answer:

4 dozen

Step-by-step explanation:

4 cups flour = 12 cookies    [1 dozen=12]

1 cup of flour= 12/4 cookies

                    =3 cookies

now,

16 cups of flour= 3*16 cookies

                        =48 cookies

                         = 4 dozens          [48/12=4    dozen]

therefore, 4 dozen cookies can be made with 16 cups of flour

Answer: 144

Step-by-step explanation:

Answer and Step-by-step explanation:

Let f(x) = x4 + x3 + x2 +x + 1 Є Z2[x]. Prove that f(x) is irreducible over Z2[x] or not?

Proof:-  

Let f(x) = x4 + x3 + x2+ x+1 Є Z2[X].  

Then f (0) = 1 = f(1), so f(x) has no roots,  By Factor theorem, which states that polynomial f(x) has a factor(x-a) if and only if f(a)=0.                                                                                                                                      Hence, f(x) has no linear factor.                                                                                                                                                 If f(x) is reducible, it must have factors of degree 2 and degree 3. But f(x) has no degree 2 factors.

We know that only irreducible quadratic in Z2[X] is x2  + x +1. When we divide f(x) by x2  + x +1 we get a remainder of 1, so x2  + x +1 is not a factor of f(x) therefore f(x) is irreducible.

Answer:

You have 14.8 grams of fat in total.

Step-by-step explanation:

6.8 + 8 = 14.8

Answer:

Domain = [0, 50]

Range   = [0, 3250]

Step-by-step explanation:

A function shows the relationship between two variables (independent variable and dependent variable). The independent variable is a variable not dependent on any variable, it is the input of the function while the dependent variable is a variable dependent on other variable, it is the output of the function.

The domain of a function is the set of all input variables (independent variable) and the range of a function is the set of all output variables (dependent variables).

In the function C(p) = 65p, p is the independent variable and C(p) is the dependent variable.

Since the hall can hold a total of 50 people, the domain of the function = [0, 50]

C(0) = 65(0) = 0, C(50) = 65(50) = 3250

Hence, the range of the function = [0, 3250]

Answer:

30.6 ounces of water

Step-by-step explanation:

Since on bottle holds 5.1 ounces, in order to find the amount of water in 6, you must take 5.1 and multiply it by 6 which gives you your final answer of 30.6 ounces. Hope this helps!

Answer:

30  units ^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

The base is on the left  b = 10  

The height is perpendicular to the base = 6

A = 1/2 * 10 * 6

  = 30  units ^2