(Chapter 10) If x = f(t) and y = g(t) are twice differentiable, then (d^2y)/(dx^2) =(d^2y/dt^2)/ (d^2x/dt^2)

Answer:

f(4) = 0

Step-by-step explanation:

If the value of x is between 0 and 5, then the f(x) will equal 0.

x = 4 is greater than 0 and less than 5, so f(4) = 0

Explanation: Just like any of your two-step equations,

in this inequality,  start by isolating the x term which in this

case is -3x by subtracting 5 from both sides.

That leaves you with -3x < -24.

To get x by itself, divide both sides by -3 but watch out.

When you multiply or divide both sides of an inequality by a

negative number, you must switch the direction of the inequality sign.

So we have x < 8 and put your final answer in

set notation and it look like this → {x: x < 8}.

The sentence "A slice of pizza is a sector of a circle" is true.

A sector is a portion of a circle that is bounded by two radii and an arc. In the case of a pizza slice, the crust represents the two radii, and the arc represents the curved edge of the slice.

Just like a sector, a pizza slice has an angle at the center of the circle.

Therefore, a slice of pizza can be considered as a sector of a circle. The shape and properties of a pizza slice align with the definition of a sector.

It's important to note that while a slice of pizza is a sector of a circle, not all sectors are shaped like pizza slices.

Sectors can have various sizes and angles depending on the size of the central angle and the radius of the circle.

To summarize, a slice of pizza is indeed a sector of a circle because it meets the criteria of having two radii and an arc.

Learn more about sector from the given link

https://brainly.com/question/22972014

#SPJ11

the amount of paint required is dependent on the size of the area that needs to be painted.

In an equation or algebraic expression, an uncertain amount is denoted by a symbol in algebra, which is often a letter. A variable is, in the simplest terms, a quantity that can change and is not fixed. The two primary categories of variables are categorical and numerical. Then, for both categorical and numerical variables, discrete or continuous subcategories are created for each category. In this section, a summary of several categories is provided. a measure that can take many different forms. Something that can alter; the sign of a variable; a variable in a scientific experiment.

Because it is the variable which the homeowner may alter or control, the area of the house that needs to be painted in this scenario is the independent variable. Because it depends on the portion of the home that needs to be painted, the overall quantity of paints that need to be obtained is a variable that is dependent. To put it a different way, the amount of paint required depends on the size of the area that needs to be painted.

To know more about variables visit :-

https://brainly.com/question/2466865

#SPJ1

Answer: The first is when we have what is called infinite solutions. This happens when all numbers are solutions. The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions. ...

Answer:

A.

(1,3)

(2,7)

(3,11)

(4,15)

Step-by-step explanation:

I plotted the points into a graphing calculator

The unsubsidized loan has the lowest overall cost. Compared to the subsidized loan, you would save $4,261, and compared to the private loan, you would save $7,305.

The federal unsubsidized loan with 5.7% interest for 10 years would result in the lowest overall cost. You would save money compared to the other two options.

To compare the loan options, you need to calculate the total interest paid over the term of each loan. The subsidized loan, with an interest rate of 6.9%, would accrue interest while you're in school, but the government would cover that interest. After graduation, you would start paying the interest and principal for 10 years. For the unsubsidized loan, with a 5.7% interest rate, the interest would accrue during school and be capitalized into the loan balance at graduation. You would then pay interest and principal for 10 years. The private loan, with a 5.0% interest rate and a 17-year term, would also accrue interest during school and capitalize it at graduation, after which you'd pay interest and principal for 17 years.

Using an online loan calculator, the total interest paid for each option is as follows:
- Subsidized loan: $23,529
- Unsubsidized loan: $19,268
- Private loan: $26,573

To know more about the unsubsidized loan, click here;

https://brainly.com/question/30280583

#SPJ11

The slope of the tangent line to the curve at P(0.25, 20).

The point P(1/4,20) lies on the curve y = 5/x.

If Q is the point (x,5/x) and we have to find the slope of the secant line PQ for various values of x.

We have the following values of x:If x = 0.35, the slope of PQ is:

(5/0.35 - 20) / (0.35 - 0.25)

= (14.29 - 20) / 0.1= -57.1

If x = 0.26, the slope of PQ is: (5/0.26 - 20) / (0.26 - 0.25)= (19.23 - 20) / 0.01= -77.7

If x = 0.15, the slope of PQ is: (5/0.15 - 20) / (0.15 - 0.25)= (33.33 - 20) / -0.1= -133.3

If x = 0.24, the slope of PQ is: (5/0.24 - 20) / (0.24 - 0.25)= (20.83 - 20) / -0.01= -83.3

Based on the above results, guess the slope of the tangent line to the curve at P(0.25, 20).

We can observe that as we take x closer to 0.25, the slope of the secant line PQ is decreasing, and from the above calculations, we can guess that the slope of the tangent line to the curve at P(0.25, 20) is approximately -80.
To know more about  tangent line visit:

https://brainly.com/question/31617205

#SPJ11

The equation that represents the graph of function g is: g(x) = 3f(x).

A linear function is often expressed as y = mx + b (slope-intercept form), where the slope of the function is the value of "m", while the y-intercept, which is the point where the line cuts the y-axis is the value of "b".

To find the linear function equation for the graph of g, find the slope (m) and determine the point on the y-axis where the line intercepts it, b.

Slope of function g (m) = rise/run = 3/1

Slope of function g (m) = rise/run = 3

The graph of the function of g intersects the y-axis at 0. b = 0

The slope of function .f = 1. This means the slope of function g is three times the slope of the function of .f.

Therefore, the best representation for the graph of function g is: g(x) = 3f(x).

Learn more about function graph on:

https://brainly.com/question/4025726

#SPJ1

Answer:

10.35

Step-by-step explanation:

Add 10.25+14.35+15.45+9.60= 49.60

60-49.65=10.35

Answer:

56 cents

Step-by-step explanation:

cost/amount=price

4/2.24=0.56

5.6/10=0.56

6.72/12=0.56

The unit tangent vector to the curve r(t) = (cos(t), sin(t), t) at t = 1 is T(1) = (-sin(1), cos(1), 1)/√(sin^2(1) + cos^2(1) + 1). The unit normal vector to the curve r(t) = (cos(t), sin(t), t) at t = 1 is N(1) = (-cos(1), -sin(1), 0)/√(cos^2(1) + sin^2(1)).The length of the curve C from t = 0 to t = 2π is given by the integral of the magnitude of the derivative of r(t) with respect to t over the interval [0, 2π].

Step 1: Find the derivative of r(t): r'(t) = (-sin(t), cos(t), 1).

Step 2: Calculate the magnitude of the derivative: ||r'(t)|| = √(sin^2(t) + cos^2(t) + 1) = √2.

Step 3: Integrate the magnitude of the derivative over the interval [0, 2π]:

Length of C = ∫[0, 2π] ||r'(t)|| dt = ∫[0, 2π] √2 dt = 2π√2.

Therefore, the unit tangent vector to the curve at t = 1 is T(1) = (-sin(1), cos(1), 1)/√(sin^2(1) + cos^2(1) + 1), the unit normal vector is N(1) = (-cos(1), -sin(1), 0)/√(cos^2(1) + sin^2(1)), and the length of the curve C from t = 0 to t = 2π is 2π√2.

Learn more about vector :  brainly.com/question/24256726

#SPJ11

Answer:

\(9a^{2}\)+6\(ab\)+\(b^{2}\)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

The negative solution to the question is -6

A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.

The question can be interpreted as;

x^2 - 54 = 3x

x^2 - 54 - 3x = 0

x^2 - 3x - 54 = 0

Finding the common factors

x^2 - 9x + 6x -54 = 0

Factoring out the common factors

x(x-9) +6(x-9) = 0

(x+6)(x-9) = 0

Hence,

x + 6 = 0

x = -6

Hence, -6 is the negative solution to the question

Learn more word problems at:https://brainly.com/question/21405634

Answer:

\(36 {x}^{2} + 4 {y}^{2} \)

Step-by-step explanation:

1.) expand the bracket by raising everything inside the bracket by 2

\( {6}^{2} {x}^{2} + {2}^{2} {y}^{2} \)

2.)simplify the equation

\( = 36 {x }^{2} + 4 {y}^{2} \)

i think that's the answer..

Answer:

1200

Step-by-step explanation:

i=prt

=80,000*0.02*9/12

=1200

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

To learn more about the similar triangles visit:

https://brainly.com/question/25882965.

#SPJ1

The store that sells strawberries at a cheaper unit price is Fine Foods.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/1 = 6/3 = 10/5 = 14/7

Constant of proportionality (k) = 2.

Therefore, an equation for the price of strawberries at Fine Foods is y = 2x and as such, it sells strawberries at a cheaper unit price.

Read more on proportional relationship here: brainly.com/question/20167968

#SPJ1

Answer:

B sorry if you im wrong

Step-by-step explanation:

Your welcome :)

Answer:

The answer is B :)

Step-by-step explanation:

A. The value of the parameter is 0.1002 km⁻¹

B. The probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value is 0.651.

a. We are given that the density function of the double exponential distribution is:

f(x) = λ/2 * exp(-λ|x|)

where λ is the parameter to be determined.

We know that the standard deviation of this distribution is 40.9 km. The standard deviation of a double exponential distribution is given by:

σ =√(2)/λ

Substituting σ = 40.9 km, we get:

40.9 = √(2)/λ

λ = √2)/40.9

λ ≈ 0.1002 km⁻¹

b. To find the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value, we need to find the probability that the random variable X lies between µ - σ and µ + σ, where µ is the mean value of the distribution.

The mean value of a double exponential distribution is given by:

µ = 0

So, we need to find the probability that |X| < σ, which can be written as:

P(-σ < X < σ) = P(X < σ) - P(X < -σ)

Using the cumulative distribution function (CDF) of the double exponential distribution, we get:

P(X < σ) = (1/2) * [1 - exp(-λσ)]

P(X < -σ) = (1/2) * [1 - exp(λσ)]

Substituting λ ≈ 0.1002 km^-1 and σ = 40.9 km, we get:

P(-σ < X < σ) = P(X < σ) - P(X < -σ) ≈ 0.651

Therefore, the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value is approximately 0.651.

To know more about standard deviation visit:

brainly.com/question/23907081

#SPJ11

Answer: 56

Step-by-step explanation:

Given that :

Marbles in bag are only red and blue ;

Probability of randomly choosing a red = 2/7

Number of red marbles in bag = 16

The total Number of marbles =?

P(choosing a red marble) = required outcome / Total possible outcomes

Required outcome = number of red marbles

Total possible outcomes = total number of blue and red marbles

Total number of blue and red marbles = x

P(choosing a red marble) = required outcome / Total possible outcomes

2/7 = 16 / x

Cross multiply

2x = 16 * 7

2x = 112

x = 112 / 2

x = 56 marbles

Total number of marbles = 56

Answer:

-61b - 30

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

3(-8b - 9b - 10) - 10b

Step 2: Simplify

Answer:

25151/100000

Step-by-step explanation:

Answer:

points

Step-by-step explanation:

Answer:Takeyour time

Step-by-step explanation:

Answer:

\(30x^3-15x^5+35x^4-43\)

Step-by-step explanation:

\(30x^3-15x^5+35x^4-43\)

Use the distributive rule and distribute 5x into the brackets. Then use the order of operation rule to do what is after the brackets.