1.CONVERT TO SCIENTIFIC NOTATION2.CONVERT TO STANDARD NOTATION
a. 895,000,000,000a. 3.65 x 108

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:

the first blank is 9 and the second is 8. when you switch the numbers in the equation the answer will still be the same. hope this was helpful!

Answer:72 is 8 times as many as 9 and 9 times as many as 8

Step-by-step explanation:

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

Answer:

7(45)=7(40)+7(5)

Step-by-step explanation:

We need to represent 7(45) using the distributive property to simplify.

We can write 45 as 40+5

So it becomes,

7(45) = 7(40+5)

Distributive property is : a(b+c)=ab+ac

a=7, b = 40 and c = 5

7(40+5)=7(40)+7(5)

So, the correct option is (4).

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:

[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:

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)

Answer:

0.08 pounds per pint.

Step-by-step explanation:

Given: The density of a certain material is such that it weighs 10 ounces per gallon.

We are to express this density in pounds per pint.

1 gallon ⇒ 10 ounces

1 pound = 16 ounces

How many pounds? = 10 ounces.

Cross-multiplying gives;

[tex]\frac{10 * 1}{16} = 0.625[/tex] pounds

1 gallon = 8 pints

The density in pounds per pint is;

0.625 pounds ÷ 8 pints = 0.078125 pounds per pint = 0.08 pounds per pint (answer rounded up to the nearest hundredth).

Answer:

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

Hope it helps

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:

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

Answer:

[tex] d = 9.4 units [/tex] (nearest tenth)

Step-by-step explanation:

Given the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], distance between (-4, 5) and (4, 0) is calculated as follows:

Let [tex] (-4, 5) = (x_1, y_1) [/tex]

[tex] (4, 0) = (x_2, y_2) [/tex]

[tex] d = \sqrt{(4 - (-4))^2 + (0 - 5)^2} [/tex]

[tex] d = \sqrt{(8)^2 + (- 5)^2} [/tex]

[tex] d = \sqrt{64 + 25} [/tex]

[tex] d = \sqrt{89} [/tex]

[tex] d = 9.4 units [/tex] (nearest tenth)

Answer:

Step-by-step explanation:

12x - 20 = 2x  -16 - 6x

12x - 20 = -4x - 16

16x - 20 = -4x

20x = 20

x = 1

Answer:

First backpacker should receive $4 and the second one $2

Step-by-step explanation:

notice that the total amount of rice for the three is 600 g.

Then, the first one that gave 400 g contributed 400 out of 600, that is 400/600 = 2/3

The second one contributed 200 out of 600, that is 200/600 = 1/3

then the first one should receive 2/3 of the $6 = (2/3) x 6 = $4

and the second one should receive 1/3 of the %6 = (1/3) x 6 = $2

If 5 's multiplied many times then always unit digit will be 5.

If power of 2 is divide by 4 then , if remainder is zero then unit digit will be 6 and if remainder is 1 then unit digit will be 2 , if remainder is 2 then unit digit will be 4 and if remainder is 3 then unit digit will be 8.

First here we analyse when many of 2's is multiplied.

[tex]2^{1} =2\\2^{2} =4\\2^{3}=8\\2^{4} =16\\2^{5} =32\\2^{6}=64[/tex]

Here , we observed that after [tex]2^{4} =16[/tex] , unit digit will be repeat.

So, If power of 2 is divide by 4 then , if remainder is zero then unit digit will be 6 and if remainder is 1 then unit digit will be 2 , if remainder is 2 then unit digit will be 4 and if remainder is 3 then unit digit will be 8.

Now, analyse when many of 5's multiplied.

[tex]5^{1}=5 \\5^{2}=25\\5^{3}=125[/tex]

So, When  5 's multiplied many times then always unit digit will be 5.

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Answer: Associative Property of Addition

Step-by-step explanation: The problem (6 + 7) + 8 = 6 + (7 + 8)

demonstrates the associative property of addition.

Notice that the addends, or the number we're adding,

are the same on both sides of the equals sign, 6 + 7 + 8.

The associative property of addition tells us that when we're adding more

than two numbers, the grouping of addends does not change the sum.

For example here, (6 + 7) gives us 13, and 14 + 8 gives us 21.

On the right side, (7 + 8) gives us 15, and 6 + 15 gives us 21.

So the sum is the same, regardless of which way we group the addends.

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 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:

Can u add more context pls then I'll answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can  calculate the length of side a using the Cosine Rule:

a^2 = 32.6^2 + 41.4^2 - 2.32.6.42.4 cos pi/6

a^2 = 456.01

a = √456.01

a = 21.35

By the Sine Rule:

32.6 / sin B = 21.35 / sin pi/6

sin B =  (32.6 * sin pi/6) / 21.35

sin B = 0.76347

B = 0.869 radians.

C = pi - pi/6 - 0.869 = 1.749 radians.

Answer: All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. So its Rational.

:)

Answer:

17 is an irrational number.

Step-by-step explanation:

17 is a prime number with no factors other than itself and 1 therefore minus square root of 17 is an irrational number.

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".

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Answer:

  A- When they are inverse functions

  C- when they are equal for all values of x

Step-by-step explanation:

The order of function application in a composition can be reversed if ...

_____

In the first case, the composition gives an output equal to its input for the functions in either order.

In the second case, you cannot tell the functions apart, since they produce the same output for the same input. Hence, you can't tell if they are reordered or not.

Answer:

You have 14.8 grams of fat in total.

Step-by-step explanation:

6.8 + 8 = 14.8

Answer:

  y = 1/2x -4

Step-by-step explanation:

Subtract 1 from both sides of the equation and simplify.

  y = 1/2(x -6) -1

  y = 1/2x -3 -1

  y = 1/2x -4

Answer:

y=1/2x-4

Step-by-step explanation:

y+1=1/2(x-6)

y=1/2(x-6)-1

y=1/2x-6/2-1

y=1/2x-3-1

y=1/2x-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:c

Step-by-step explanation:

7x - 5 is the factor of 21x²+13x-2.Option B is correct.

An equation is a statement indicating the equality of two expressions that contain variables and/or numbers. In essence, equations are questions, and the pursuit of methodically resolving these questions has been the impetus for the development of mathematics.

It is given that, the expression is 21x²+13x-2.

We have to find the factor of the expression.

Algebraic expression factorization is the process of identifying two or more expressions whose product equals the given expression. Algebraic expression factorization is hence the multiplication procedure in reverse.

[tex]=21x^2+13x-20 \\\\ =\left(21x^2-15x\right)+\left(28x-20\right) \\\\ =3x\left(7x-5\right)+4\left(7x-5\right) \\\\ =\left(7x-5\right)\left(3x+4\right)[/tex]

The factors of the expression are (7x-5) and (3x-4).

Thu option B is correct.

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Answer:

• First attachment's graph is correct

• Second attachment, the area is approximately 8.6

Step-by-step explanation:

Remember that the area between two curves is defined as the following:

[tex]\mathrm{The\:area\:between\:curves\:is\:the\:area\:between\:curve\:f(x)\:and\:curve\:g(x)\:on\:interval\:[a,b]} :\\A=\int _a^b|f\left(x\right)-g\left(x\right)|dx[/tex]

We are given the curves y = 7cos(2x), and y = 7 - 7cos(2x) on interval [0, π/2]. Therefore, applying the area formula, we have the solve the following integral:

[tex]\int _0^{\frac{\pi }{2}}\left|7\cos \left(2x\right)-\left(7-7\cos \left(2x\right)\right)\right|dx[/tex]

From now on take a look at the attachment. It shows how to solve the integral, and it's exact value. The area is not 9.727 as you entered, it is approximately 8.6. Your graph however was accurate, but there can be no work shown for that as it's much easier to use a graphing calculator.

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