Enter the exact value in terms of
π
.

Using the definition of the derivative, the derivative of the function is f'(t) = 5t + 6. The domain of the function and its derivative are both the set of all real numbers.

The derivative is a concept in calculus that represents the rate of change or the slope of a function at a specific point. It is defined as the limit of the difference quotient of the function as the interval between the two points approaches zero. Mathematically, the derivative of a function f(x) at a point x is represented as f'(x) and can be expressed as:

f'(x) = lim h -> 0 [f(x + h) - f(x)]/h

where h is the interval between the two points.

The derivative is a fundamental tool for analyzing and understanding the behavior of functions, including their local maxima, minima, and inflection points, as well as for solving problems in physics and engineering.

The derivative of the function f(t) = 2.5t² + 6t can be found using the definition of the derivative:

f'(t) = limit as h -> 0 of [f(t + h) - f(t)]/h

= limit as h -> 0 of [2.5(t + h)² + 6(t + h) - (2.5t² + 6t)]/h

= limit as h -> 0 of [2.5t² + 5ht + 2.5h² + 6t + 6h - 2.5t² - 6t]/h

= limit as h -> 0 of [5ht + 2.5h² + 6h]/h

= limit as h -> 0 of [5t + 2.5h + 6]

= 5t + 6

The domain of the function f(t) = 2.5t^2 + 6t is all real numbers. The domain of its derivative f'(t) = 5t + 6 is also all real numbers.

Learn more about derivatives here: https://brainly.com/question/23819325

#SPJ4

Answer:  9

Step-by-step explanation:

Y=x2=9

Answer:

C

Step-by-step explanation:

How do we get from 4 to 20? Multiply 4 * 5 = 20.

How do we get from 20 to 100? Multiply 20 * 100.

Thus the answer is C where you multiply 5 by the previous function output.

I saw this pattern from experience, however you could also solve another way:

Simply plug in to the given functions in each answer choice.

For example, A:

f(1) = 4

f(n) = 16 * f(n - 1), for n >= 2

Now test values of n and check if they match the table.

f(1) = 4. This matches the table

f(2) = 16 * f(2 - 1) = 16 * f(1) = 16 * 4 = 64. This does not match the table.

You continue this process with the rest of the answer choices until you find a function, f(n), that gives the correct output of the table.

The point C is equidistant to (b) CL = CM = CN

From the question, we have the following parameters that can be used in our computation:

The triangle

From the triangle, we can see that the point C is the centroid of the triangle

As a general rule:

The centroid is the geometric centre of a triangle. It is equidistant from all the points present on the triangle.

This means that point C is equidistant from L, M and N

Read more about centroid at

https://brainly.com/question/7644338

#SPJ1

Answer:

Step-by-step explanation: 2 00

22

The height of the rectangular prism is 2x^3

The volume of a rectangular prism is given by the product of its length, width, and height.

We know that the volume is 48x^8, so we can write an equation:

48x^8 = (4x^2)(6x^3)(h)

We can simplify the left side:

48x^8 = 24x^5 * h

And divide both sides by 24x^5 to find the height:

h = 48x^8 / 24x^5 = 2x^3

So the height of the rectangular prism is 2x^3

Read more about volume at

https://brainly.com/question/463363

#SPJ1

A good way to save money in an interest-bearing account is using a savings account with intereste

The future of management relies on flexibility, adaptation and pragmatism.

The following ideas can help you make a plan to save and maximize your interest earnings.

1. High-Yield Savings Account. .

2. High-Yield Checking Account. .

3. CDs and CD Ladders.

4. Money Market Account.

5.. Treasury Bills.

Research suggests that thinking about the future,a process known as prospection,can help us lead more generous and fulfilled lives. Mindfulness is all the rage these days, and for good reason. Focusing on the moment can improve our well-being, foster compassion, and help our relationships.

For a better well-being we have to think about the future.

learn more about future planning from

https://brainly.com/question/27152368

#SPJ1

The total amount that he will be charged for the shipping is given as follows:

$34.88.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Jerry is charged $2.25 per pound for shipping, hence the constant is given as follows:

k = 2.25.

Meaning that the equation for the total cost for a weight of x pounds is given as follows:

y = 2.25x.

The total weight is given as follows:

3.2 + 3.8 + 4 + 4.5 = 15.5 pounds.

Hence the total cost is given as follows:

y = 2.25 x 15.5

y = $34.88.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer:

Greg borrowed $20,000.

Step-by-step explanation:

To calculate the principal (the amount borrowed), we can use the formula for simple interest:

I = Prt

where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.

Given that:

I = 1400

r = 7% (expressed as 0.07)

t = 4

P = I / (r * t) = 1400 / (0.07 * 4) = $20,000

Therefore, Greg borrowed $20,000.

Sarah consumes 12000 calories per day.

A calorie is a unit of energy.

Given is that Ben eats approximately 2,400 calories a day.

We can write the amount of calories eaten by Sarah as -

y = 5 x 2400

y = 12000

Therefore, Sarah consumes 12000 calories per day.

To solve more questions on energy, visit the link below -

https://brainly.com/question/22374134

#SPJ1

{Question in english -

Ben eats approximately 2,400 calories a day. His wife Sarah eats 5 as much. How many calories does Sarah eat a day?}

The fraction for the value of tan Z is 39/80

Trigonometric Identities are simply described as equalities that involves several trigonometry functions and also one that holds true for all the values of variables given in the equation.

The types of trigonometric functions as;

From the information given, we have that;

Hypotenuse = 89

Opposite side = 39

Adjacent = 80

tan Z = opposite/adjacent

substitute the values

tan Z = 39/80

Hence, the equation is 39/80

Learn about trigonometric identities on:

https://brainly.com/question/7331447

#SPJ1

The distance between the two points is 13 units.

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)

point 1 (1, 4): x1 = 1 , y1 = 4

point 2 (6, 16): x2 = 6 , y2 = 16

Using the formula with the given values:

d=√((x2 – x1)² + (y2 – y1)²

d=√((6 – 1)² + (16 – 4)²)

d=√(5² + 12²)

d = √169

d = 13 units

Therefore, the distance is 13 units.

Learn more about the distance between two points on:

brainly.com/question/17704491

#SPJ1

Answer:

[tex]r=14\mathring{}[/tex]

Step-by-step explanation:

[tex](5r-5)\mathring{}+(8r+3)\mathring{}=180\mathring{}\\5r-5+8r+3=180\mathring{}\\13r-2=180\mathring{}\\13r=180\mathring{}+2\\13r=182\mathring{}\\r=\frac{182}{13} \\\\r=14\mathring{}[/tex]

Given the problem:

Explain what are the figure below functions or not

The left graph is not a function, the right table is a function. To see if a graph is a function, use the vertical line test. Simply draw vertical lines down the graph, or you don't have to if you can imagine it. None of the vertical lines can pass through any points twice. So in this case, look at (6, 4) and (6, 6). Draw a vertical line down at x=6. It fails the vertical line test because the vertical line passes through the two points.

Next, the table on the right. It is a function. To determine whether a table is a function or not, look at the x values. No x value can duplicate. In this case, all x values are different.

Hope this helped.

Answer:

Step-by-step explanation:

To convert into a percent, multiply by 100

1)

a)0.543; = 0.543*100= 54.3%

b) 0.0098; = 0.0098*100=0.98%

c) 1.67; = 1.67*100=167%

To convert percentages into decimals, divide by 100

2)

a) 10%= 10÷100= 0.1

b) 0.010%= 0.010÷100= 0.0001

To convert mixed numbers into decimals, convert mixed numbers into improper fractions and divide

3)

a)2 1/3= 7/3= 2.333 =233.3%

b)5 3/5= 28/5= 5.6 =560%

To convert a fraction into a mixed number, divide the numerator by the denominator

4)

a) 11/4= 2+3/4= 2 3/4

b) 16/7= 2+2/7= 2 2/7

1. Convert decimals to percentages:

a) 0.543 can be converted to percentage by multiplying it by 100. So, 0.543 x 100 = 54.3%

b) 0.0098 can be converted to percentage by multiplying it by 100. So, 0.0098 x 100 = 0.98%

c) 1.67 can be converted to percentage by multiplying it by 100. So, 1.67 x 100 = 167%

2. Convert percentages to decimals:

a) 10% can be converted to a decimal by moving the decimal two places to the left. So, 10% = 0.10

b) 0.010% can be converted to a decimal by moving the decimal four places to the left. So, 0.010% = 0.0001

3. Convert mixed numbers to fractions and decimals:

a) 2 1/3 can be converted to a fraction by finding a common denominator of 3 and writing the whole number as a fraction. So, 2 1/3 = (2 x 3 + 1) / 3 = 7/3

It can also be converted to a decimal by dividing the numerator by the denominator. So, 7/3 = 2.333...

c) 5 3/5 can be converted to a fraction by finding a common denominator of 5 and writing the whole number as a fraction. So, 5 3/5 = (5 x 5 + 3) / 5 = 28/5

It can also be converted to a decimal by dividing the numerator by the denominator. So, 28/5 = 5.6

4. Convert fractions to mixed numbers:

a) 11/4 can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction. So, 11/4 = 2 3/4

b) 16/7 can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction. So, 16/7 = 2 2/7

Answer:

-5

Step-by-step explanation:

Let x be the number we are trying to find.

According to the problem statement, we know that:

3(x + 3) = x - 1

Expanding and solving for x, we get:

3x + 9 = x - 1

2x = -10

x = -5

So the number we were trying to find is -5.

Answer:

[tex]x = 1[/tex]

Step-by-step explanation:

In the rectangle, WU = 2NU, where WU = 13x - 1 and NU = 6

Replacing for the values in the equation: WU = 2NU, it becomes: 13x - 1 = 2 × 6

Going further:

[tex]13x - 1 = 12[/tex]

[tex]13x = 12 + 1 \\ 13x = 13[/tex]

[tex]x = \frac{13}{13} = 1[/tex]

Therefore, x = 1

Answer:

(i) To calculate the present value of 6 months of rent for the first apartment, we can use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value (6 months of rent, or $900 x 6 = $5400), r is the interest rate (8% converted to a monthly rate, or 0.08/12 = 0.0067), and n is the number of periods (6 months). So, PV = $5400 / (1 + 0.0067)^6 = $4911.46

(ii) To find the range of rent for the new apartment such that Lee would switch, we need to find the monthly rent that would result in a present value equal to or greater than $4911.46. Using the same formula, we can solve for the monthly rent (R) by setting PV equal to $4911.46 and n equal to 6. So, $4911.46 = R*(1+0.0067)^6. Solving for R, we get that the monthly rent must be between $732.32 and $766.58 in order to be more favorable than the first apartment.

Let's start by converting this word problem into math equations... This will make it much easier to choose an approach to the problem!

Write equations for both Dave and Angie. We will use the variables P for slices of pizza, and W for bottles of water bought.  

(1) Dave: [tex]3P+2B=12.75[/tex]

(2) Angie: [tex]1P+3B=7.75[/tex]

Now that we have these equations, it's much easier to tell that this is a system of two equations (two equations, two unknowns). To solve this system, we can use a variety of different methods. For this problem, let's use the Elimination method (removing one variable from the equation.

Start by multiplying (scaling) Angie's equation by a factor of -3, so that we will be able to remove Pizza slices from the equation:

(3) [tex]-3(1P+3B=7.75) \equiv -3P-9B=-23.25[/tex]

Now, let's add Angie's new equation to Dave's original:

[tex]-7B=-10.5[/tex]

Notice that we now only have one variable in this simple equation. This is very easy to solve!

Simplify:

[tex]B=1.5[/tex]

Now that we have the price for a bottle of water, we can substitute this value into either (1) Dave's or (2) Angie's original equation to find the price for a slice of Pizza (P). I will substitute into (1) Dave's equation:

Substitute:

[tex]3P+2(1.5)=12.75[/tex]

Simplify:

[tex]3P=9.75[/tex]

Divide:

[tex]P=3.25[/tex]

Finally, we have reached our conclusion... A slice of Pizza costs $3.25 and a bottle of water costs $1.5 at the concession stand! Let me know if you have any questions or want to learn other ways of solving this problem!

Answer:

The area of the first lawn is 64 = 24 square meters.

The area of the second lawn is 6 times bigger, so it is 246 = 144 square meters.

As the second lawn has the same width as the first one, 4 meters, we can calculate the length of the second lawn by dividing the area of the second lawn by its width.

So, the length of the second lawn is 144/4 = 36 meters.

Answer:

To find out how many of the first 76 slices sold during lunch tomorrow should be pepperoni pizza, we can use the information provided about the proportion of pepperoni pizza slices sold today. We can use the following formula to calculate the expected proportion:

(number of pepperoni slices / total number of slices) * 100

Plugging in the numbers we have:

(44 / (44 + 15 + 29)) * 100 = 44 / 88 * 100 = 50%.

So we can expect 50% of the first 76 slices sold during lunch tomorrow to be pepperoni pizza slices, which is equivalent to:

76 slices * 50% = 38 slices

Therefore, we expect 38 of the first 76 slices sold during lunch tomorrow should be slices of pepperoni pizza.

Step-by-step explanation:

There are (e) 125 positive integers that satisfy the n condition

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

(130n)^50 > n^100 > 2^200

[tex]\sqrt[50]{}[/tex][(130n)^50] > [tex]\sqrt[50]{}[/tex](n^100) > [tex]\sqrt[50]{}[/tex](2^200)

130n > n^2 > 2^4

130n > n^2 > 16

Solving each part, we get:

n^2 > 16

n > √16

n > 4

130n > n^2

130 > n^2/n

130 > n

130 > n > 4

Therefore the answer is the number of positive integers over 4 and 130 which is 129 - 5 + 1 = 125

Learn more about algebraic operations at: brainly.com/question/3927786

#SPJ4

Correctly written question:

How many positive integers n satisfy the following condition (130n)⁵⁰ > n¹⁰⁰ > 2²⁰⁰ ? (a)0 (b)7 (c)12 (d)65 (e)125

The matrix representation of the problem can be written as: ε = [ε1 ε2 ε3]'

The matrix representation of the linear regression problem can be expressed as Y = Xβ + ε, where Y is the n x 1 vector of the dependent variable (Yi),

X is the n x k matrix of the independent variables (xi),

β is the k x 1 vector of coefficients, and

ε is the n x 1 vector of errors.

In this case, n = 3 (number of observations), k = 2 (number of independent variables) and the matrix representation of the problem can be written as:

Y = Xβ + ε

Y = [0.3 0.8 -0.3]

X = [1 1 1; 1 2 0.1]

β = [β0 β1]'

ε = [ε1 ε2 ε3]'

For more questions on Matrix representation

https://brainly.com/question/13594851

#SPJ4

The volume and radius of the ice cream and the ice cream cone are;

(a) Volume of the ice cream is about 6.3 cubic inches

(b) Radius of needed for the cone to contain 14.5 cubic inches per serving is about 1.422 inches

The volume of a solid is the space the solid occupies, which is the amount of cube units that fills the solid.

Rotation of a quarter circle to form an hemisphere, by integration is presented as follows;

[tex]\int\limits^1_0 \pi \times ({\sqrt{1-x^2} })^2 \, dx = \frac{2}{3} \cdot \pi[/tex]

The volume of the cone carrying the hemisphere = (1/3)×π×1²×4 = (4/3)·π

The volume of the ice cream = The volume of the cone + The volume of the hemisphere

Therefore;

Volume of the ice cream = (2/3)·π + (4/3)·π = (6/3)·π = 2·π  ≈ 6.3

(b) Volume of ice cream contained in the new ice cream cone, V = 14.5 cubic inches

The formula for the volume of the ice cream, V = (2/3)·π·r³ + (4/3)·π·r²

Therefore;

V = (2/3)·π·r³ + (4/3)·π·r² (substitution property)

V = (2/3)·π·r³ + (4/3)·π·r²

14.5 = (2/3)·π·r³ + (4/3)·π·r²

(2/3)·π·r³ + (4/3)·π·r² - 14.5 = 0

Learn more on the volume of a solid by rotation of a plane figure here: https://brainly.com/question/12688268

#SPJ1

The length of the rectangular pool is 98 m.

The area of Rectangle is length times of width.

Given that the perimeter of a rectangular pool is 368m.

The width of the pool is 86m

We need to find the length of the pool.

Perimeter of rectangle=2(Length+width)

368=2(Length+86)

368=2Length+172

368-172=2length

196=2length

Divide both sides by 2

98=length

Hence, the length of the rectangular pool is 98 m.

To learn more on Rectangles click:

https://brainly.com/question/20693059

#SPJ1

Check the picture below.

Answer: $72.93

Step-by-step explanation:

$72.93

The equations that match the tape diagram.

Thus, the correct equations are: A, B, D and F

A diagram that resembles a piece of tape that is used to show how numbers relate to one another. Also known as length model, fraction strip, bar model, and strip diagrams. to use whole numbers, fractions, and ratios to answer problems that include the four operations. Students can improve their problem-solving abilities and algebraic reasoning with the use of tape diagrams.

A visual tool known as a tape diagram represents the components of a ratio using equal-sized boxes. The reason it is named a tape diagram is because it resembles the lengthy strips of sticky tape used to bind documents or wrap gifts.

Thus, from the above given data it is clear that, x = 4.5

Correct option: A, B, D, and F

To know more about tape diagram refer to:

https://brainly.com/question/26354395

#SPJ1

The probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music cannot be determined (E).

Here 'x' denotes the no. of puzzles completed by an individual within 5 minutes. Given that the probability distribution of 'x' as,

[tex]$$\begin{array}{ccccc}x: 1 & 2 & 3 & 4 \\p(x): & 0.2 & 0.4 & 0.3 & 0.1\end{array}$$[/tex]

'D' is the difference in the number of puzzles saved by two randomly selected subjects. Let [tex]X_{1}[/tex] be the number of puzzles solved by first individual and [tex]$X_2$[/tex] be the number of puzzles solved by [tex]$2^{n d}$[/tex] individual.

Then, D=[tex]X_1-X_2$[/tex] where [tex]$X_1$[/tex] and [tex]$X_2$[/tex] are independent and follow the above

[tex]$$\begin{aligned}& \therefore \text { Variance }(D)=V(D)=v\left(x_1-x_2\right) \\& =V\left(x_1\right)+v\left(x_2\right) \\& =2 \times v\left(x_1\right) \quad\left(\because v\left(x_1\right)=v\left(x_2\right)\right. \\& \text { Now, } V\left(x_1\right)=V(x)=E\left(x^2\right)-[E(x)]^2 \\& =0.2+0.8+0.9+0.4 \\& =2.3 \\&\end{aligned}$$[/tex]

[tex]$$\text { and } \begin{aligned}E\left(x^2\right) & =\sum_{R(x)} x^2 P[x=x] \\& =\sum_{x=1}^4 x^2 P[x \cdot x] \\& =\left(1^2 \times 0.2\right)+\left(2^2 \times 0.4\right)+\left(3^2 \times 0.3\right)+\left(4^2 \times 0.1\right) \\& =6.1 \\\Rightarrow V(x) & =k\left(x^2\right)-[k(x)]^2 \\& =6.1-(2.3)^2 \\& =0.81\end{aligned}$$[/tex]

[tex]$\therefore$[/tex] Variance of D,

[tex]$$\begin{aligned}V(D) & =2 \times v\left(x_1\right) \\& =2 \times 0.81=1.62\end{aligned}$$$\therefore$ Standard deviation of $D$ is,$$\sqrt{V(0)}=\sqrt{1.62} \simeq$$[/tex] 1.27.

Therefore, the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music is, 1.27.

For more such questions on Probability distribution

https://brainly.com/question/14210034

#SPJ4