What is the answer to each problem? Please hurry :)

I will give Brainlest to whoever answers correctly, thank you.

The absolute value function is defined as

\(|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}\)

If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.

If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.

But if x = 0, the derivative doesn't exist!

In order for the derivative of a function f(x) to exist at x = c, the limit

\(\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}\)

must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.

If x approaches 0 from below (so x < 0), we have

\(\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1\)

whereas if x approaches 0 from above (so x > 0), we have

\(\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1\)

But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.

Putting everything together, you can define the derivative of |x| as

\(\dfrac{d|x|}{dx} = \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1 & \text{for }x < 0 \end{cases}\)

The area and circumference to the nearest tenth include the following:

Area = 490.6 square meters.

Circumference = 78.5 meters.

In Mathematics, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 25/2 = 12.5 meters.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = 3.14 × 12.5²

Area of circle = 490.6 square meters.

In Mathematics, the circumference of a circle can be calculated by using the following mathematical expression:

Circumference of a circle, C = 2πr

Circumference of a circle, C = 2(3.14) × 12.5

Circumference of a circle, C = 78.5 m.

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The SRED Credit remainder after applying the maximum SRED Credit for this year is $0.

The Scientific Research and Experimental Development (SRED) program provides tax incentives for companies conducting eligible research and development activities. The SRED credit is calculated based on qualified SRED expenses and can be used to reduce the tax liability of a company.

In this case, the qualified SRED expenses for the current year are $10,000. However, the SRED credit remainder is determined after applying the maximum SRED credit for the year. Since the maximum SRED credit has already been applied, the remaining SRED credit is $0.

The taxable loss from the previous year ($50,000) and the part I tax before SRED ($1,500) are not directly relevant to determining the SRED credit remainder. The maximum SRED credit has already been utilized, resulting in a remaining credit of $0.

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Answer:

2. twice a number n subtracted from fifteen and four-tenths

Step-by-step explanation:

The rate of decrease in volume of the snowball when its diameter is 12 cm is approximately 1.36 cm³/min.

When a spherical snowball is melting, it's diameter decreases at a rate of 0.3 cm/min. The rate of change of volume of a sphere is given by:dV/dt= (4π/3)r²(dr/dt)Since the diameter is given as 12 cm, the radius of the snowball is 6 cm.So the diameter is decreasing at a rate of 0.3 cm/min.

We are to find the rate of decrease in volume of the snowball when the diameter is 12 cm.The radius of the snowball is given by r = 6 cm, and the rate of change of its diameter is d = -0.3 cm/min.At this point, we need to calculate the rate of decrease in volume of the snowball when the diameter is 12 cm.

The rate of decrease in volume of the snowball is given bydV/dt = (4π/3)r²(dr/dt)dV/dt = (4π/3)(6 cm)²(-0.3 cm/min)≈ -1.36 cm³/minTherefore, the rate of decrease in volume of the snowball when the diameter is 12 cm is approximately -1.36 cm³/min.

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The appropriate test statistic for the hypothesis being tested and to compare the test statistic to a critical value from a distribution table.

An index that is calculated from sample data and whose value determines whether to accept or reject a null hypothesis is a test statistic.

A test statistic is used to determine the probability of obtaining the observed data under the null hypothesis.

If the test statistic falls within a specified range, the null hypothesis is accepted.

If the test statistic falls outside of the specified range, the null hypothesis is rejected.

The test statistic is calculated from the sample data and is based on the distribution of the sample data.

There are many different types of test statistics, each of which is used to test a different hypothesis.

Some common test statistics include the t-statistic, the F-statistic, and the chi-square statistic.
The t-statistic is used to test the difference between the means of two populations.

The F-statistic is used to test the equality of variances between two populations.

The chi-square statistic is used to test the independence of two categorical variables.
In order to calculate a test statistic, one must first formulate a null hypothesis and an alternative hypothesis.

The null hypothesis is the hypothesis that is assumed to be true, and the alternative hypothesis is the hypothesis that is being tested. The test statistic is then calculated from the sample data, and its value is compared to a critical value from a distribution table.

If the test statistic is greater than or equal to the critical value, the null hypothesis is rejected. If the test statistic is less than the critical value, the null hypothesis is accepted.
In conclusion, a test statistic is an index that is calculated from sample data and is used to determine whether to accept or reject a null hypothesis.

It is important to use the appropriate test statistic for the hypothesis being tested and to compare the test statistic to a critical value from a distribution table.

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the correct answer is(d)

Answer: Heres the answer for you

Step-by-step explanation:

And also how you work the promblem out also.

Answer: 3w - 9/2

When combining like terms and simplifying the equation, the answer is 3w - 9/2

Hope this helps =)

Answer:

y=-3x+4

Step-by-step explanation:

im assuming that you need the equation of the table

to find slope, y2-y1/x2-x1    10-4/-2-0

6/-2=-3   slope=-3  

y=mx+b   just sub in the numbers from a point in the table

10=-3(-2)+b

10=6+b

b=4

y=-3x+b

The equation of the line is y = 1/2x + 2

First, we need to know that the formula that is used to represent the equation of a line is expressed as;

y = mx + c

Such that the parameters are enumerated as;

Using the formula for slope of a line, we have that;

Slope, m = 4 - 2/0 - 4

Subtract the values

Slope, m = 2/-4

Divide the values

Slope, m = -1/2

But intercept, c = 2

Then, we have that;

y = 1/2x + 2

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Answer:

1/50 or 20/1000(same thing but simplified)

Step-by-step explanation:

Answer:

\(m=\frac{-8}{5}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-1, 4)

Point (4, -4)

Step 2: Find slope m

Answer:

11/6 or 1.833

Step-by-step explanation:

⅔+ 7/6

12+21. 33

---------. =. ----

18. 18

dividing with side by 3

11/6 or 1.83

Answer:

7x+39>=53 and 16x+ 15>31 x>=2 (no solutions exist)

Step-by-step explanation:

Answer:

V = 512

Step-by-step explanation:

V = a³

V = 8³

V = 512

Answer: complaints of the wrongs done to the colonists.

the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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The terms of sequences are u₁ = 4, u₂ = 19 and u₃ = 364.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

A sequence is defined by the term-to-term rule

uₙ₊₁ = u₁² + 3

And  u₀ = 1,

a). The second term

u₁ = u₀² + 3

u₁ = (1)² + 3

u₁ = 4

b). The third term

u₂ = u₁² + 3

u₂= (4)² + 3

u₂ = 19

c). The fourth term

u₃ = u₂² + 3

u₃ = (19)² + 3

u₃ = 364

Therefore, The values, u₁ = 4, u₂ = 19 and u₃ = 364.

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Answer:

4,234 dekaliters converted to milliliters is 42340000.

Step-by-step explanation:

Answer: Your answer is going to be 42340000 millimeters.

Step-by-step explanation:

Find out how much one dekaliter is worth; multiply by that amount.

Answer:

(280+7) ÷ (7+7)

Step-by-step explanation:

hopefully this helps ya

The equation that is equal to 287 ÷ 7 is (280 + 7) ÷ (7 + 7). The correct option is C.

An equation is a statement in mathematics that shows that two expressions are equal. It has two sides that are separated by an equal sign.

To find the value of 287 ÷ 7, we can use the following methods:

We can simplify 287 ÷ 7 as follows:

287 ÷ 7 = 280 ÷ 7 + 7 ÷ 7

Note that 7 ÷ 7 simplifies to 1, so we have:

287 ÷ 7 = 280 ÷ 7 + 1

Therefore, the answer is C. (280 + 7) ÷ (7 + 7) = 287 ÷ 14 = 20.5.

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Answer:

yes

Step-by-step explanation:

use the vertical line test

ANSWER

y = 3.5x + 56

EXPLANATION

The slope of a line passing through points (x1, y1) and (x2, y2) is,

And the slope-intercept form of the equation of a line is,

Where m is the slope and b is the y-intercept.

In this problem, we have to use points (5, 73) and (7, 80) to find the equation of the line. First, we can find the slope,

For now, the equation is,

We have to find the y-intercept, by replacing x and y for the coordinates of one of the given points,

And solve for b,

The equation is,

The slope as a decimal is 3.5 and the y-intercept, rounded to the nearest whole number is 56, so the equation is y = 3.5x + 56

The value of variable x for the given equation, 5x - 16xy +16y² +7x + 17y² is −33 y²/ 4(3 − 4y).

An algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression said to be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor. An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.).

5x - 16xy +16y² +7x + 17y²

= 12x - 16xy + 33y²

Using the Quadratic Formula, we have:

x = −33 y²/ 4(3 − 4y)

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Answer:

  11.4

Step-by-step explanation:

You want the distance between C(-5, 5) and D(4, -2).

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is computed to be ...

  d = √((4 -(-5))² +(-2 -5)²) = √(81 +49) = √130

  d ≈ 11.4

The length of CD is about 11.4 units.

__

Additional comment

The distance formula is an application of the Pythagorean theorem. It computes the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

if d increases c will decrease AND  if c increases d will decrease.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalizes two ratios. For illustration, the ratio may be expressed as follows: 1: 3 (If there are 1 boy and 3 girls, then there are 3 girls for every 1 boy.)

since c and d are inversely proportional

a) if d increases c will decrease

because it is the property of the ratio and proportion

and same will be applied in b

b) if c increases d will decrease

that is obvious....

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Answer:

The answer is 1

To solve the initial value problem dx/dt - 6(x² - 1) = 0, with the initial condition x(0) = 5, we can separate variables and use partial fractions. The exact solution to the problem is ln|x² - 1| = (1/2) ln|((x - 1) / (x + 1))| + ln(24) - (1/2) ln(2/3).

To solve the initial value problem dx/dt - 6(x² - 1) = 0, we can separate variables and use partial fractions. Rearranging the equation, we have dx = 6(x² - 1) dt. Separating variables, we get 1 / (x² - 1) dx = 6 dt.

Using partial fractions, we decompose 1 / (x² - 1) into its partial fraction form: 1 / (x² - 1) = 1/2 * (1 / (x - 1)) - 1/2 * (1 / (x + 1)).

Integrating both sides, we have ∫(1 / (x² - 1)) dx = (1/2) ∫(1 / (x - 1)) dx - (1/2) ∫(1 / (x + 1)) dx.

The integral on the left side can be evaluated using the natural logarithm: ln|x² - 1| = (1/2) ln|((x - 1) / (x + 1))| + C, where C is the constant of integration.

To determine C, we substitute the initial condition x(0) = 5 into the equation and solve for C.

The exact solution to the initial value problem is then ln|x² - 1| = (1/2) ln|((x - 1) / (x + 1))| + ln(24) - (1/2) ln(2/3).

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Answer:

third option

(-3,3)

Step-by-step explanation:

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