Use the vertical line test to determine whether the function. If not, identify two points a vertical line would pass through.

The value for f'(x) is a) f'(0) = -3/2,  b)  \(f'(0) = \frac{-15}{2} * cos(2^{(\frac{3}{2})})\).

To find the derivative f'(x) of the given functions, apply the chain rule and the power rule of differentiation. Calculate f'(x) for each function and evaluate f'(0).

a. f(x) = arctan(e⁽⁻³ˣ⁾)

To find f'(x), use the chain rule:

f'(x) = d/dx [arctan(e⁽⁻³ˣ⁾)]

= (1 / (1 + (e⁽⁻³ˣ⁾)²)) × d/dx[e^⁽⁻³ˣ⁾]

= (1 / (1 + e⁽⁻⁶ˣ⁾)) × (-3e⁽⁻³ˣ⁾)

To evaluate f'(0), substitute x = 0:

f'(0) = (1 / (1 + e⁰)) × (-3e⁰)

= (1 / 2) × (-3)

= -3/2

Therefore, f'(0) = -3/2.

b. \(f(x) = sin((x^3 - 5x + 2)^{(\frac{3}{2})})\)

To find f'(x), use the chain rule and the power rule:

\(f'(x) = \frac{d}{dx} sin((x^3 - 5x + 2)^{(\frac{3}{2})})\)

\(= cos((x^3 - 5x + 2)^{(\frac{3}{2})}) * \frac{d}{dx} [(x^3 - 5x + 2)^{(\frac{3}{2})}]\)

\(= cos((x^3 - 5x + 2)^{(\frac{3}{2})}) * \frac{3}{2} (2x^2 - 5)\)

To evaluate f'(0), substitute x = 0:

\(f'(0) = cos((0^3 - 5(0) + 2)^{(\frac{3}{2})}) * (\frac{3}{2}) * (2(0)^2 - 5)\)

\(= cos(2^{(\frac{3}{2})}) * (3/2) * (-5)\)

= \(\frac{-15}{2} * cos(2^{(\frac{3}{2})})\)

Therefore, \(f'(0) = \frac{-15}{2} * cos(2^{(\frac{3}{2})})\).

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The z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

The mean of the set of data is equal to the sum of all the quantities in the data, and divide by the no of quantities.

Given:

The standard deviation, d = 182.56,

The mean, m = 265.95,

The observation value, X = 235.90

Calculate the z score by the following formula given below,

Z = (X - m) / d,

Here, Z is the Z score,

Z = 235.90 -  265.95 / 182.56

Z =  -0.165

Therefore, the z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.

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Answer:

120 - 14 = 106

Step-by-step explanation:

7 x 2 = 14

10 x 12 = 120 therefore you,

120 - 14 = 106

The area of the shaded region is 106 m².

We have,

The area of the rectangle:

= length x width

From  the figure,

Bigger rectangle dimensions:

Length = 12 m

Width = 10 m

Smaller rectangle dimensions:

Length = 7 m

Width = 2 m

Now,

The shaded region.

= Area of the bigger rectangle - Area of the smaller rectangle

= 12 x 10 - 7 x 2

= 120 - 14

= 106

Thus,

The area of the shaded region is 106 m².

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Answer: False

=============================================================

Explanation:

The radical is one step away from being fully isolated. We would apply the rule that \(\frac{\sqrt{A}}{\sqrt{B}} = \sqrt{\frac{A}{B}}\)

In this case,

\(\frac{\sqrt{x+3}}{\sqrt{x-1}} = \sqrt{\frac{x+3}{x-1}}\)

Meaning that the equation

\(\frac{\sqrt{x+3}}{\sqrt{x-1}} =3\)

is the same as

\(\sqrt{\frac{x+3}{x-1}} = 3\)

From here, we square both sides and use algebra to isolate x.

It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

Answer: p=8

Step-by-step explanation:(−23)(p)−6p=−112

−8p+−6p=−112

(−8p+−6p)=−112(Combine Like Terms)

−14p=−112

−14p=−112

−14p/−14 = −112/−14

p=8

Answer:

Hi! I'll do my best to explain for you.

-6(2x-3)+2x =0     First, set the equation equal to zero.

-12x+18+2x=0      Then, distribute the -6 by multiplying it with the -2 and -3.

-10x+18=0            Combine the like terms, which are -12x and 2x, to get -10x.

-10x=-18               You want to get the x on 1 side. Subtract 18 from both sides.

x=-18/-10              Divide by -10 on both sides.

x=1.8                    Simplify the fraction. The answer is x=1.8.

I hope this helped!

The decimal calculation for Arturo's is 18.97, Bonnie's is 20.51, Courtney's is 31.42, Dawson's is 35.00.

Measurement is the process of assigning a numerical value to a physical quantity, such as length, weight, temperature, or time. Measurements are used to quantify and compare different aspects of the world around us, and they play a crucial role in many areas of science, engineering, and everyday life.

Measurements can be made using a variety of tools and techniques, ranging from simple rulers and scales to sophisticated scientific instruments. The accuracy and precision of a measurement depend on many factors, including the quality of the measuring instrument, the skill of the person making the measurement, and the conditions under which the measurement is taken.

In order for measurements to be meaningful and useful, they must be expressed in units that are well-defined and universally accepted. The International System of Units (SI) is the most widely used system of units in the world, and it is based on seven fundamental units of measurement, including the meter for length, the kilogram for mass, the second for time, and the kelvin for temperature.

Student           Measurement (yards)    Decimal Calculation

Arturo           6√28                            18.97

Bonnie           8√17                            20.51

Courtney   10π                            31.42

Dawson           3.5√100                    35.00

To calculate the decimals, we can use a calculator to evaluate the square roots and π, and then multiply by the given constant factor, and round the result to the nearest hundredth yard.

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The complete question is:

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

256

Step-by-step explanation:

4⁴

= 4 × 4 × 4 × 4

= 16 × 16

= 256

Answer: about 87.96459430051421

Step-by-step explanation: 28 x 3.14 = the answer

According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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Answer:

A parallel line has the same slope, but is translated away from the line it is parallel to. Let's create an equation using what we have:

−

1

=

−

3

(

−

2

)

+

b

−

1

=

6

+

b

−

7

=

b

y

=

−

3

x

−

7

Hope this helped!!

Answer:

47

Step-by-step explanation:

First, we convert 20¾ pounds into ounces.

1 lb = 16 oz

20¾ pounds * 16 oz/lb = 332 oz

Now we divide 332 oz by 7 oz.

332/7 = 47 3/7

You can make 47 full bags, and you'll have 3/7 of an ounce left.

Answer:

hopefully this is the right answer 1/

4

< 10/

4

< 20/

4

Step-by-step explanation:

The correct statements that apply to the given limits are:

Option A: Multiply by (√(x + 2) + 3)/(√(x + 2) + 3)

Option D: "Divide out a common factor of x - 7."

Option E: The limit of the given expression is 1/6.

Option: We generally multiply by the conjugate of the expression to eliminate square roots in simplification. Thus, option A applies.

Option B: Get x - 1 in the numerator:

This statement is not correct. The expression does not involve x - 1 in the numerator.

Option C: Get (x - 7)(√(x + 2) - 3) in the denominator:

This statement is not correct due to the fact that we want to simplify the expression, and not introduce a more complex denominator.

Option D: Divide out a common factor of x - 7:

This statement is correct because by factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.

Option E: Calculate the limit as 1/6:

After canceling out the common factor of x - 7, the simplified expression becomes:

lim x -> 7 (√(x + 2) - 3)/(x - 7)

= lim x -> 7 1/(√(x + 2) + 3)

To find the limit, we substitute the value x = 7 into the simplified expression:

lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6

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Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

Answer:

10^4

Step-by-step explanation:

4 0's so 10^4

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

Gareth should expect to pay $850.00 to the IRS.

Step-by-step explanation:

Gross vs. net income.

70,000 should be your answer, since 5-10 will maker the coefficient plus 1. since the number in front of 6 is 5, 6 will be 7. so 70,000

Answer:

The Answer is 70000

Step-by-step explanation:

Answer:

981.11

981.11+4005-00000.98- 400+1=4586.13

Step-by-step explanation:

Just order of operations

Hope this helps!

Answer:

981.11

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

-5=-3x+1

-1         -1

-6=-3x

divide both sides by -3

x=2

The value of x when f(x) = - 5, In the function f(x) = - 3x + 1 is 2.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = - 3x + 1.

Now, when f(x) = - 5 the equation would be,

- 5 = - 3x + 1.

- 5 - 1 = - 3x.

- 6 = - 3x.

3x = 6.

x = 2.

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The shaded area is 4.28 square centimeters

The image that completes the question is added as an attachment.

Start by calculating the area of the triangle using:

Area = 0.5bh

Where:

b = h = r = 2

So, we have:

Area = 0.5 * 2 * 2

Evaluate

Area = 2

Next, calculate the area of the semicircle using:

Area = 0.5πr²

So, we have:

Area = 0.5 *  3.14 * 2²

Evaluate

Area = 6.28

Subtract the area of the triangle from the semicircle

Shaded = 6.28 - 2

Evaluate

Shaded = 4.28

Hence, the shaded area is 4.28 square centimeters

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Scenario a: 4x+7=64

Scenario b: 4(7+x)=64

x represents how much the bags of rice weigh in each scenario.

Answer:

5 4

Step-by-step explanation:

its fristly 5

ok then bb

Answer:

5x5x5x5=625

Step-by-step explanation:

Answer:

10:

7/4π = 5.5(1decimql place)

11:

50π = 157.1(1 decimal place)

Step-by-step explanation:

the equation is (angle/360) X πr^2

Answer:
B) 46 degrees