Solve the system of linear equations.
1/3x+y=1
2x+6y=6
Solve using a graph and explain the steps.

The statements are classified as Exponential decay and Linear growth.

a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.

c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.

Learn  more about Exponential decay here: https://brainly.com/question/25802424

#SPJ1

Answer:

The area of the shape is 56 to the nearest tenth

Step-by-step explanation:

r=d/2

d=2r

d=2×3=6

Area of shape=Area of rectangle+Area of semi circle

A=L×B+1/2pir²

A=7×6+1/2×22/7×3²

A=42+11/7×9

A=42+99/7

A=42+14.14

A=56.14

A=56 to the nearest tenth

Equations with a single unknown can be powerful tools in helping us understand complex phenomena and make predictions about how they will behave.

Yes, equations with a single unknown can be very helpful in understanding various phenomena. Mathematical equations allow us to express relationships between different variables and make predictions about how they will behave under different conditions. By solving equations, we can find the values of unknown variables and gain a deeper understanding of the system we are studying.

Other examples of equations with a single unknown that have had a significant impact include Newton's second law of motion, F=ma, which relates force (F) to mass (m) and acceleration (a), and the ideal gas law, PV=nRT, which relates pressure (P), volume (V), number of moles (n), and temperature (T) of a gas.

equations with a single unknown can be powerful tools in helping us understand complex phenomena and make predictions about how they will behave.

To know more about complex visit:

https://brainly.com/question/29377605

#SPJ1

The linear regression model from a set of data is y =5.2956+4.0946*X.

A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.

The regression line is determined using the formula:

y = bo + b1 X

Now, using the table we have:

sum of (x) = ∑x = 103

sum of (y) = ∑y = 480

Calculating the squares we have:

sum of (x^2)= ∑x² = 1073

sum of (y^2)= ∑y² = 22868

Multiplying the variables we have:

sum of (x*y)= ∑x*y = 4939

mean(x)= ∑x/n = 9.3636

mean(y)= ∑y/n = 43.6364

Now, the intercept is given as:

intercept (bo) = (∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²

Substituting the values we have:

intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2

intercept (bo) = (515040-508717) / (11803-10609)

intercept (bo) = 5.2956

The slope is given as:

slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²

Substituting the values we have:

slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2

slope (b1) = (54329-49440)/(11803-10609)

slope (b1) = 4.0946

regression equation is, y = bo + b1 X

Substituting the values we have:

y =5.2956+4.0946*X

Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.

Learn more about linear regression model here:

https://brainly.com/question/29855836

#SPJ1

The complete question is:

Therefore, the graph of the given set is: closed circles on 1 and 4 with a line segment between.

A common form for an algebraic expression is one of the following: addition, subtraction, multiplication, or division. Simplify the values to determine the result.

The expression (x I x ≤ 1) U (x I x ≥ 24) represents the set of all values of x that are less than or equal to 1 or greater than or equal to 24.

the graph of this set will have a closed circle at x=1 and a closed circle at x=24

The arrows pointing outward indicate that the set continues indefinitely in both directions.

To know more about line segment visit:-

https://brainly.com/question/30072605

#SPJ1

Answer: the perimeter of the figure is 30 m and the area of the figure is 71.2 m².

Step-by-step explanation: Perimeter = 9 m + 4.1 m + 9.5 m + 3.4 m + 2m + 2m

Perimeter = 30 m

To find the area of the figure, we can divide it into two rectangles and a triangle

+-------------------+

|         9         |

+---------+---------+

|    4.1  |    9.5   |

+---------+---------+

   3.4     2     2

f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).

An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.

According to the given information:

To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.

First, we find the first derivative of f(x):

f'(x) = (14x)/(7x²+6)²

Then, we find the second derivative of f(x):

f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4

Simplifying the expression, we get:

f''(x) = 28(42x² - 72) / (7x^2+6)³

To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.

Setting f''(x) = 0, we get:

42x² - 72 = 0

Solving for x, we get:

x = ±√(6/7)

These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.

We can use a sign chart to determine the sign of f''(x) on each interval.

Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.

Here is the sign chart for f''(x):

x  |   -∞   | -√(6/7) | √(6/7) |   ∞

f''(x)|   -    |     +      |     -     |   +

From the sign chart, we can see that:

a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).

b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).

c) The inflection points occur at x = -√(6/7) and x = √(6/7).

Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).

To know more about inflection point visit :

https://brainly.com/question/30760634

#SPJ1

The f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).

What is inflection Point?

An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.

According to the given information:

To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.

First, we find the first derivative of f(x):

f'(x) = (14x)/(7x²+6)²

Then, we find the second derivative of f(x):

f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4

Simplifying the expression, we get:

f''(x) = 28(4x² - 72) / (7x^2+6)³

To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.

Setting f''(x) = 0, we get:

42x² - 72 = 0

Solving for x, we get:

x = ±√(6/7)

These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.

We can use a sign chart to determine the sign of f''(x) on each interval.

Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.

Here is the sign chart for f''(x):

x  |   -∞   | -√(6/7) | √(6/7) |   ∞

f''(x)|   -    |     +      |     -     |   +

From the sign chart, we can see that:

a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).

b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).

c) The inflection points occur at x = -√(6/7) and x = √(6/7).

Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).

To know more about inflection point visit :

https://brainly.com/question/30760634

#SPJ1

Therefore, Miranda saves approximately 22.96 meters by cutting across the diagonal instead of walking around the perimeter of the field.

Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a square, rectangle, triangle, or circle. It is the distance around the shape, and is measured in units such as centimeters, meters, feet, or inches. To find the perimeter of a shape, you simply add up the lengths of all its sides. For example, the perimeter of a square with sides of length 5 cm would be 4 × 5 cm = 20 cm. The perimeter of a rectangle with length 6 cm and width 4 cm would be 2 × (6 cm + 4 cm) = 20 cm.

If Miranda walks around the perimeter of the field, she will travel a distance equal to the perimeter of a rectangle, which can be calculated as follows:

[tex]Perimeter = 2(Length + Width) = 2(7m + 11m) = 2(18m) = 36m[/tex]

To cut across the diagonal of the field, Miranda will travel a distance equal to the length of the diagonal of the rectangle. This can be found using the Pythagorean theorem:

[tex]Diagonal = \sqrt(Length^2 + Width^2) = \sqrt(7m^2 + 11m^2) = \sqrt(170m^2) \approx 13.04m[/tex]

So, the distance Miranda saves by cutting across the diagonal is:

[tex]36m - 13.04m \approx 22.96m[/tex]

Rounding to the nearest hundredth of a meter gives:

≈ 22.96m to 2 decimal places

Therefore, Miranda saves approximately 22.96 meters by cutting across the diagonal instead of walking around the perimeter of the field.

To know more about diagonal visit:

https://brainly.com/question/12274248

#SPJ1

Using division operation, if a Meat-E-Um pizza is cut into 6 pieces and the total cost is $36.60, the cost per slice is $6.10.

Division operation is one of the four basic mathematical operations. Other mathematical operations are addition, subtraction, and multiplication.

Division operation involves the following parts: dividend, divisor, and quotient.

The total cost of the Meat-E-Um pizza = $36.60

The number of pieces the pizza is cut = 6

The unit cost of each slice = $6.10 ($36.60 ÷ 6)

Thus, a slice of a Meat-E-Um pizza cut into 6 pieces will cost $6.10 per slice.

Learn more about division operation at https://brainly.com/question/4721701.

#SPJ1

The total cost of a Meat-E-Um pizza is $36.60.

Thus, the linear equation in terms of x  that shows the sum of all three ages of Rebecca , Mary and Jill : 5x + 32 = 67.

Any pattern of numbers that consistently increases or decreases in value by the same amount is known as a linear equation. As a result, the only two elements we require to establish a linear equation are the point at which the pattern starts and the distance it travels.

The linear equation y = mx + b, with the m value representing the slope and the b value representing the y-intercept, is what is left.

Given that-

Then,

age of Jill = 3(x + 8) years

Sum of all is 67.

Linear equation:

x + x + 8 + 3(x + 8) = 67  ...eq 1

2x + 8 + 3x + 24 = 67

5x + 32 = 67

3x = 67 - 32

3x = 35

x = 35/3

Thus, the linear equation in terms of x  that shows the sum of all three ages of Rebecca , Mary and Jill : 5x + 32 = 67.

Know more about the linear equation:

https://brainly.com/question/2030026

#SPJ1

The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.

When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.

Given:

Width of the set of shelves = 5 times the height of the set of shelves

Number of shelves = 3

Total amount of wood available = 80 feet

Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".

Using the first given information, we can write the equation:

Width (w) = 5 times the height (h) ==> w = 5h

Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.

Finally, we are given that we have 80 feet of wood available to build the shelves.

Using these equations, we can substitute w = 5h into the equation for the total amount of wood:

3w + 4h = 80

Substituting w = 5h, we get:

3(5h) + 4h = 80

15h + 4h = 80

19h = 80

h = 80/19

So, the height of the set of shelves is approximately 4.21 feet.

Now, substituting this value of h back into w = 5h, we get:

w = 5(4.21)

w = 21.05

So, the width of the set of shelves is approximately 21.05 feet.

Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.

Learn more about Linear equation here:

https://brainly.com/question/11897796

#SPJ1

If Mr. Wang and Mrs. Wang have 3 sons and every son has 1 wife, 1 son, and 1 sister, the total number of people in the family, based on mathematical operations, is 14.

The total number of people in the family can be determined using the mathematical operations of multiplication and addition.

Multiplication and addition are two of the four basic mathematical operations.

Multiplication involves the multiplicand, the multiplier, and the product, while addition involves two or more addends added to get the sum.

The number of parents = 2

The number of sons = 3

The number of additional family members for each son = 3

The total number of additional family members = 9 (3 x 3)

The total number of persons in the family = 14 (9 + 3 + 2)

Thus, there are 14 people in the family of Mr. Wang and Mrs. Wang.

Learn more about mathematical operations at https://brainly.com/question/4721701.

#SPJ1

The line graph of Greg's data wood look like "It would move upward."

A graph is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data

If Greg is measuring the height of the plant each day and the plant is continuing to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."

To know  more about graph visit:

https://brainly.com/question/29629845

#SPJ1

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.

The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.

Given data:

surface area of pentagonal prism = 2* base area + 5*rectangle area

surface area of pentagonal prism = 2* B + 5*L*w

surface area of pentagonal prism = 2* 84.3 + 5*7*4

surface area of pentagonal prism = 168.6 + 140

surface area of pentagonal prism = 308.6 sq. ft

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

Know more about the pentagonal prism:

https://brainly.com/question/15637173

#SPJ1

We have to find the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$.

The Taylor Polynomial is given by:

(x)=∑

k=0

n

​k!

f

(k)

(a)

​(x−a)

k

where $f^{(k)}(a)$ is the $k$th derivative of $f(x)$ evaluated at $a$.

Using this formula, we can find the Taylor Polynomial as follows:

\begin{align*}

f(x) &= e^x \

f'(x) &= e^x \

f''(x) &= e^x \

f'''(x) &= e^x \

\end{align*}

Evaluating each derivative at $x=0$, we get:

\begin{align*}

f(0) &= e^0 = 1 \

f'(0) &= e^0 = 1 \

f''(0) &= e^0 = 1 \

f'''(0) &= e^0 = 1 \

\end{align*}

Substituting these values into the formula for the Taylor Polynomial, we get:

\begin{align*}

P_3(x) &= \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3 \

&= 1 + x + \frac{x^2}{2} + \frac{x^3}{6}

\end{align*}

Therefore, the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$, is $P_3(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}$.

Answer: To find the median credit score, we need to arrange the three scores in order from lowest to highest:

748, 758, 765

The median is the middle value in this ordered list. Since there are three scores, the median is the second score, which is 758.

Therefore, Christine's median credit score is 758.

Step-by-step explanation:

It should be noted that to find the net price of a product or service, you need to subtract any discounts or deductions from the gross price.

Here are the steps you can follow:

Determine the gross price: The gross price is the original price of the product or service before any discounts or deductions are applied.

Identify any discounts or deductions: Look for any discounts or deductions that apply to the gross price. These may include promotional discounts, coupons, or taxes.

Subtract the discounts or deductions: Subtract the total amount of discounts or deductions from the gross price. The result is the net price.

For example, let's say you want to buy a laptop that costs $1000. You have a 10% discount coupon, and there is a 5% sales tax. Here's how you can calculate the net price:

Gross price = $1000

Discount = 10% of $1000 = $100

Subtotal = $1000 - $100 = $900

Sales tax = 5% of $900 = $45

Net price = $900 + $45 = $945

So the net price of the laptop after applying the discount and sales tax is $945.

Based on the information provided, Happy Valley appears to be the strongest option for psychology undergraduate studies.

Learn more about net price on

https://brainly.com/question/26740879

#SPJ1

47 mL is equivalent to 0.047 L (liters).

Measurement refers to the process of quantifying or determining the amount, size, or degree of something using a standard unit of measurement. It is a way of expressing the quantity or magnitude of a physical property, such as length, mass, volume, time, temperature, etc.

Equivalent means having the same value, function, or meaning as something else. In mathematics, two values are said to be equivalent if they have the same numerical value or satisfy the same equation or inequality. In chemistry, equivalent refers to the amount of a substance that can react with or replace a given amount of another substance in a chemical reaction. In general, equivalent is used to indicate that two things are equal in some way or have the same effect or significance.

1L =1000mL

1mL=1/1000L

Therefore 47 mL=.047 L

Learn more about volume here:

https://brainly.com/question/12237641

#SPJ1

Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:

x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923

Using the formula for the sum of a geometric series, we have:

x(1 - (1.1)^7)/(1 - 1.1) = 56.923

x(1 - 1.1^7)/(-0.1) = 56.923

x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles

Therefore, the hiker traveled approximately 4 miles on the first day.

Sn = x(1 - r^n)/(1 - r)

where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.

S14 = x(1 - 1.1^14)/(1 - 1.1)

S14 ≈ 167.63

Therefore, the hiker will travel approximately 167.63 miles in 14 days.

More on geometric series can be found here: https://brainly.com/question/4617980

#SPJ1

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.

Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.

Here we have

DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.

Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.

Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.

From the problem,

We can set up a system of equations based on the information given:

DeShawn's purchase: 1d + 12g = 80 ---- (1)

Ndiba's purchase: 5d + 2g = 52 --- (2)

We can solve this system of equations using substitution or elimination.

Here, we will use substitution:

Solving for d in terms of g from Deshawn's equation:

1d = 80 - 12g --- (3)

Substituting into Ndiba's equation:

=> 5(80 - 12g) + 2g = 52

=> 400 - 60g + 2g = 52

=> - 58g = - 348

=>  g = 6

From (3)

1d = 80 - 12(6)

1d = 80 - 72

d = 8

Therefore,

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

Learn more about System of equations at

https://brainly.com/question/12895249

#SPJ1

Answer:

90 cubic feet

Step-by-step explanation:

3 feet × 5 feet × 6 feet = 90 cubic feet

The function is f(x)=115.[tex](1.58)^x[/tex] and number of people after 6 months is 1789.

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here according to the table initial people f(0) = 115

Now using exponential formula

=> f(x) = f(0).[tex](1+r)^x[/tex]

If x = 1 then f(1)= 182 then,

=> 182 = 115.[tex](1+r)^1[/tex]

=> 1+r = 182/115

=> 1+r = 1.58

=> r = 1.58-1=0.58

Then the exponential function is

=> f(x)=115.[tex](1.58)^x[/tex]

Now x=6 then,

=> f(6) = 115.[tex]1.58^6[/tex] = 1789

Hence number of people after 6 month is 1789.

To learn more about exponential function refer the below link

https://brainly.com/question/2456547

#SPJ1

Liam needs 0.25 yards of wire for the top of each sculpture.

Let's assume that Liam needs x yards of wire for the top of each sculpture.

Since Liam is making 8 sculptures, he will need 8x yards of wire in total for the tops of all the sculptures.

We also know that Liam needs one yard of wire for the base of each sculpture.

So he will need 8 yards of wire in total for the bases of all the sculptures.

Therefore, the total amount of wire Liam needs is:

8x yards for the tops + 8 yards for the bases = 10 yards in total

Simplifying this equation, we get:

8x + 8 = 10

Subtracting 8 from both sides, we get:

8x = 2

Dividing both sides by 8, we get:

x = 0.25

Therefore, Liam needs 0.25 yards of wire for the top of each sculpture.

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

Answer:

[tex]1. \: \: - 2 {a}^{2} [/tex]

[tex]2. \: \: 4ab[/tex]

[tex]3. \: \: - 2[/tex]

Step-by-step explanation:

-2a(a+b-5) +3(-5a+2b) +b(6a-b-8)

[tex] - 2 {a}^{2} - 2ab + 10a - 15a + 6b + 6ab + {b}^{2} - 8b[/tex]

collecting like terms

[tex] -2 {a }^{2} + {b}^{2} - 2ab + 6ab + 10a - 15a + 6b - 8b[/tex]

[tex] = - 2 {a}^{2} + {b }^{2} + 4ab - 5a - 2b[/tex]

Option 3 yielded the most money after 10 years is 171.7

Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

A solution of an equation is a value or set of values that satisfy the equation, meaning that when the value(s) is substituted for the variable(s) in the equation, both sides of the equation are equal.

Based on the given equations, Option 1 yielded the most money after 10 years, and Option 3 yielded the most total money by the time you were 60 years old.

After 10 years:

Option 1: 50×(1.09)¹⁰ - 30 =  88.36

Option 2: 50×(1.08)¹⁰ - 20 =  87.94

Option 3: 100×(1.07)¹⁰ - 25 =  171.71

Therefore, Option 3 yielded the most money after 10 years is 171.7

By the time you were 60 years old:

Option 1: 50×(1.09)⁶⁰ - 30 =  8,771.56

Option 2: 50×(1.08)⁶⁰ - 20 =  5,042.85

Option 3: 100×(1.07)⁶⁰ - 25 =  5,769.64

Therefore, Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

To know more about quadratic equation, visit:

https://brainly.com/question/1214333

#SPJ1

This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:

[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]

This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.

The problem involves some algebraic manipulation and the use of the linearity of the integral.

It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.

See the attached for the full solution.

Learn more about integration at:

https://brainly.com/question/18125359

#SPJ1

Therefore, the volume of the prism is 60 cubic feet.

Volume is the amount of space occupied by a three-dimensional object or the capacity of an object. It is typically measured in cubic units such as cubic meters, cubic feet, or cubic centimeters. The formula for finding the volume of a solid object depends on its shape. In general, the volume of a shape can be found by dividing it into smaller, more easily measured shapes and adding up their volumes. This is known as the method of integration in calculus, and it is used to find the volumes of irregularly shaped objects or fluids. Understanding the concept of volume is important in many fields, such as architecture, engineering, physics, and chemistry. In these fields, volume is used to determine the capacity of containers, the displacement of fluids, and the amount of materials needed for a construction project.

Here,

The volume of a prism is given by the formula:

V = Bh

where B is the area of the base and h is the height of the prism.

Substituting the given values:

V = (20 ft)(3 ft)

V = 60 cubic feet

To know more about volume,

https://brainly.com/question/28338582

#SPJ1

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To know more about interest rate visit:

https://brainly.com/question/14445709

#SPJ1

Answer: y=6x-1

Step-by-step explanation:

y=6x-1

x represents the time luke has been riding(hours) and the y represents the distance he has travelled (miles)