The correct answer will be option D. Y intercept will be greater and X will be less.
What is a coordinate system?A "coordinate system" is a mathematical framework that uses a set of coordinates to identify points in space or on a surface. It describes the location of a point in relation to a reference point or origin, often using numerical values. A coordinate system is made up of one or more axes, which are imaginary lines that cross at the origin, and units of measurement that run along each axis.
When the trucking firm starts paying a driver 0.25 cents per mile, it raises their operational expenditures, which has a direct influence on their profit (Y-axis). As a result, the Y-intercept (the point at which the profit crosses the Y-axis) will be larger since the company's costs will be bigger.
The X-axis, on the other side, displays the distance travelled by the vehicle. Because the corporation is now paying for a driver, it may decide to decrease the amount of kilometres the truck goes to save money. This indicates that the X-axis will be shorter, suggesting that the truck will drive fewer miles than previously.
As a result of the modification, the Y-intercept will be higher (showing higher costs) and the X-axis will be lower (meaning less kilometres travelled).
Learn more about coordinate system here:
https://brainly.com/question/30241634
#SPJ1
Write an equation for the polynomial graphed below
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
To learn more on polynomials: https://brainly.com/question/29260355
#SPJ1
Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
+
X
Ś
The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
To know more about graphs, visit:
brainly.com/question/17267403
#SPJ1
1. Suppose c = -11 + 3i. What two nonzero complex numbers could have been
added together to make c?
2. Find the value of iº.
Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:
a + b = -11
ai + bi = 3i
Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:
ai + bi = 3i
-ai - bi = 11i
0 + 10bi = 14i
Simplifying, we get b = 1.4. Substituting this into the first equation gives:
a + 1.4 = -11
a = -12.4
So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.
To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:
e^(iθ) = cos(θ) + i sin(θ)
So we have:
iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i
Therefore, iº = i.
Step-by-step explanation:
.6 1 and 2, write the expression using words. In 1. (23,000-789) x 19 In 3-4, read the expressio Donald's score is less. 2.6+(88×3³)
HELPP I NEED HELP WITH MATHH
Help me pleas whith this
How much money would an investment of 300 at rate of 12 percent compound monthly be after 4 years
Answer:
data given
principal 300
rate12%
time 4 years
Step-by-step explanation:
from
A=P[1+r/100]^n
where
A is amount
p is principal
r is rate
n is interest period
now,
A= 300[1+12/(100×12)]^(12×4)
A=300×1.01^48
A=483.67
: .would be 483.67
The diameter of a circle is 38 feet.what is the circles circumfrence. Use 3.14 for pi
Answer:
The circumference of the circle is 119.32 ft.
Step-by-step explanation:
The circumference of a circle can be solved through the formula:
C = πd
where d is the diameter
Given: d = 38 ft
π = 3.14
Solve:
C = πd
C = 3.14 (38 ft)
C = 119.32 ft
Triangle PQR is drawn with coordinates P(0, 2), Q(0, 5), R(1, 4). Determine the translation direction and number of units if R′(−7, 4).
8 units down
8 units up
8 units to the right
8 units to the left
It follows that the translation direction is 8 units to the left and 0 units up or down.
Describe translation?A translation is a geometric change in Euclidean geometry where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the origin of the coordinate system or as adding a constant vector to each point
The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.
We can use the following procedures to get the translation direction and number of units for R′(7, 4):
1. Determine the difference between R and R′'s x-coordinates: −7 − 1 = 8
2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0
It follows that the translation direction is 8 units to the left and 0 units up or down.
To know more about translation visit:
brainly.com/question/12463306
#SPJ1
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?
Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.
Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:
(x1, y1) = (35, 16.83)
(x2, y2) = (52, 18.87)
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27
Using point-slope form with the first point, we get:
y - y1 = m(x - x1)
y - 16.83 = 0.27(x - 35)
Simplifying, we get:
y = 0.27x + 7.74
Therefore, the monthly cost for 39 minutes of calls is:
y = 0.27(39) + 7.74 = $18.21
Step-by-step explanation:
Need help please
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
1. The initial mass of the sample was 32 mg. 2. The mass of the sample 7 weeks after the start is approximately 0.162 mg.
What is radioactive decay?An unstable atomic nucleus releases particles or electromagnetic radiation as it undergoes radioactive decay, changing into a different nucleus. Since this process is unpredictable and spontaneous, the decay's timing cannot be anticipated. The radioactive substance's half-life, or the amount of time it takes for half of its radioactive atoms to decay, is used to calculate the rate of decay. Radiometric dating, nuclear energy production, and medical imaging all employ radioactive decay, which can cause the emission of alpha particles, beta particles, or gamma rays. Understanding the behaviour of matter at the atomic and subatomic level requires knowledge of radioactive decay.
1. The radioactive decay is given by the formula:
[tex]N(t) = N_0 * (1/2)^{(t/T)}[/tex]
Now, for half-life of Palladium-100 is 4 days and t = 16 and N(t) = 2 we have:
[tex]2 = N_0 * (1/2)^{(16/4)}\\2 = N_0 * (1/2)^4\\2 = N_0* 1/16\\N_0 = 2 * 16\\N_0 = 32 mg[/tex]
2. Foe 7 weeks:
7 weeks = 7 * 7 days = 49 days.
[tex]N(49) = N_0 * (1/2)^{(49/4)}\\N(49) = 32 * (1/2)^{(49/4)}\\N(49) = 0.162 mg[/tex]
Learn more about exponential decay here:
https://brainly.com/question/14355665
#SPJ1
Camille opened a savings account and deposited $8,063.00 as principal. The account earns 14.69% interest, compounded quarterly. What is the balance after 10 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Save answer
Answer:$26,141.13.
Step-by-step explanation:
Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:
A = 8,063.00 * (1 + 0.1469/4)^(4*10)
A ≈ 26,141.13
Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.
PLEASE HELP
Find the Area
2cm
___cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
1. Find radius:
If diameter is 2, divide it by 2 to get radius = 1
2. Find formula:
A=πr^2
3. Plug in:
A = π(1)^2
4. Solve (multiply):
A = π(1)^2:
3.14159265359
Or
3.14 cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
r=2
2/2=1
A=[tex]\pi[/tex](1)^2
=[tex]\pi[/tex]1
≈3.14x1
≈3.14cm^2
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter. To the nearest inch, how many inches are in 4 inches?
To the nearest inch, there are 4 inches in 10.16 centimetres.
Describe Units Conversion?The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.
If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from metres to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilogrammes to pounds when measuring weight.
In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.
Since there are 2.54 centimetres in one inch, we may multiply 4 inches by 2.54 to convert them to centimetres:
4 inches * 2.54 centimeters per inch = 10.16 centimeters
We multiply by 2.54 to convert centimetres to inches:
10.16 centimeters / 2.54 centimeters per inch = 4 inches (rounded to the nearest inch)
Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimetres.
To know more about measurement, visit:
https://brainly.com/question/27233632
#SPJ1
In the Unit conversion,to the nearest inch, there are 4 inches in 10.16 centimeters.
Describe Units Conversion?
The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.
If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from meters to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilograms to pounds when measuring weight.
In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.
Since there are 2.54 centimeters in one inch, we may multiply 4 inches by 2.54 to convert them to centimeters:
=> 4 inches * 2.54 centimeters per inch = 10.16 centimeters
We multiply by 2.54 to convert centimeters to inches:
=> 10.16 centimeters / 2.54 centimeters per inch
=> 4 inches (rounded to the nearest inch)
Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimeters.
To learn more about Unit conversion refer the below link
https://brainly.com/question/13016491
#SPJ1
Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
The expression that represents the area of the remaining rectangular portion is given as follows:
A = -4x² + 12x + 6.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:
Area = Length x Width
The dimensions for the rectangle are given as follows:
Length of 4x + 2.Width of 3.Hence the area is given as follows:
A = 3(4x + 2)
A = 12x + 6.
Four squares of side length x -> area = x² are cut, hence the remaining area is given as follows:
A = -4x² + 12x + 6.
More can be learned about the area of a rectangle at brainly.com/question/25292087
#SPJ1
8. The population P (t) of a bacteria culture is given by P (t) = -1500t² + 60,000t + 10,000, where is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 460,000 organisms.
The time(s) at which the population will be greater than 460,000 organisms is between 10 and 30 hours after the culture is started.
What is inequality?An inequality is a comparison between two numbers or expressions that are not equal to one another. Symbols like, >,,, or are used to denote it, indicating which value is more or smaller than the other or just different.
To find the time(s) at which the population will be greater than 460,000 organisms, we need to solve the inequality:
P(t) > 460,000
Substituting the given equation for P(t), we get:
-1500t² + 60,000t + 10,000 > 460,000
Simplifying this inequality, we get:
-1500t² + 60,000t - 450,000 > 0
Dividing both sides by -1500 and flipping the inequality sign, we get:
t² - 40t + 300 < 0
We can solve this inequality by factoring the quadratic equation:
(t - 10)(t - 30) < 0
The roots of this equation are t = 10 and t = 30. Plotting these values on a number line, we can see that the solution to the inequality is:
10 < t < 30
Therefore, the time(s) at which the population will be greater than 460,000 organisms is between 10 and 30 hours after the culture is started.
Learn more about inequality on:
https://brainly.com/question/17448505
#SPJ1
if m(x)= sin²(x), then m'(x)=? A. cos²x+sin²x. B.sinx²-cos²x C. 2cos²x-sinx D. cos²-sin²x
25% of _ is 30 What is the answer
The value through which the given fraction that is 25% of something is 30 is 120.
What about fraction?A fraction is a numerical quantity that represents a part of a whole or a division of one quantity by another. It is written as a top number called the numerator, which represents the number of parts being considered, over a bottom number called the denominator, which represents the total number of parts in the whole. The numerator and the denominator are separated by a line or slash.
For example, the fraction 3/4 represents three parts out of a total of four parts, and can be read as "three-quarters". Fractions can be expressed as proper fractions (where the numerator is smaller than the denominator), improper fractions (where the numerator is greater than or equal to the denominator), or mixed numbers (which combine a whole number and a fraction).
According to the given information:The 25% of x through which we get 30 as a result
0.25x = 30
x = 120
To know more about fraction visit:
brainly.com/question/21010948
#SPJ1
Find the amount accumulated after
investing a principle P for t years and an
interest rate compounded twice a year.
P = $100 r = 3% t = 5
k=2
Hint: A = P(1 + E) kt
A = $[?]
Answer:
A= $116.05
Step-by-step explanation:
A=P(1+E)kt
A=100(1+0.03/2)^10
A= $116.05
… Approximate the area of the shaded region.
The approximated area of the shaded region is 92.54 square units
Approximating the area of the shaded region.From the question, we have the following parameters that can be used in our computation:
Two isosceles right trianglesCircleThe area of the shaded region in the figure is calculated as
Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2
Using the given dimensions, we have
Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2
Evaluate
Shaded region = 92.54
Hence, the shaded region is 92.54 square units
Read more about area at
https://brainly.com/question/24487155
#SPJ1
solve the system of equations below by graphing both equations. what is the solution? y=x+5 y=-2x-1
Answer:
To solve a system of equations by graphing, you need to graph each equation on the same coordinate system and find the point where the two lines intersect. If the equations are in slope-intercept form, you can identify the slope and y-intercept and graph them. If one of the equations is in slope-intercept form, you can rewrite the other one in that form and graph them. If both equations are in other forms, you can find the x- and y-intercepts and graph them.
In this case, we have two equations:
y = x + 5
y = -2x - 1
To graph these equations, we can start by finding their intercepts:
y = x + 5
0 = x + 5
x = -5
So the intercept for y = x + 5 is (-5, 0). Similarly,
y = -2x - 1
0 = -2x - 1
x = -1/2
So the intercept for y = -2x - 1 is (-1/2, 0). Now we can plot these points on a coordinate plane and draw a line through each point. The point where these two lines intersect is our solution.
Therefore, the solution to this system of equations is (-3, 2).
Step-by-step explanation:
Find each arc length. Round to the nearest tenth.
If FG = 27 yd, find the length of FED.
mFED= yards
(30 points) will give brainiest for effort
The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.
What is an arc length?The length of a section of a circle's circumference is known as an arc length.
The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.
To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:
m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)
m(EGD) = 360° - 80° - 47° - 90°
m(EGD) = 143°
The formula for arc length is:
Arc length = (central angle / 360) x (2πr)
We can use this information to find the radius of the circle:
FG = 2r
27 yd = 2r
r = 13.5 yd
Now we can use the formula for arc length to find the length of arc FED:
Arc length FED = ((∠FED) / 360) x (2πr)
We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):
∠(FED) = 360° - ∠(EGD)
∠(FED) = 360° - 143°
∠(FED) = 217°
Plugging in the values, we get:
Arc length FED = (217° / 360) x (2π x 13.5 yd)
Arc length FED = (0.6028) x (84.78 yd)
Arc length FED = 51.11 yd
To know more about circumference visit:
https://brainly.com/question/16422878
#SPJ1
Mr. Staten asks his student to name three favorite movies they have seen and wants to use a graphical representation that will allow them to see the overall shape of the data.
Which representation should Mr. Staten consider to best display the data?
Answer:
bar graph
Step-by-step explanation:
math nation
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = [tex]\frac{168}{7}[/tex] = 24
The first four terms of a sequence are given.
7, 11, 15, 19, ...
What is the 40th term of the sequence?
Answer:
To find the 40th term of the sequence, we first need to identify the pattern that generates the terms. We can see that each term is obtained by adding 4 to the previous term. So the sequence is an arithmetic sequence with a common difference of 4.
Using this information, we can find the formula for the nth term of the sequence using the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
Where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is a common difference.
In this case, we have a1 = 7 and d = 4. Substituting these values into the formula, we get:
an = 7 + (n - 1)4
Simplifying this expression, we get:
an = 4n + 3
Now we can use this formula to find the 40th term of the sequence:
a40 = 4(40) + 3
a40 = 160 + 3
a40 = 163
Therefore, the 40th term of the sequence is 163.
A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 10 feet. The slant height is 12 feet. What is the height of the heater? Round to the nearest tenth of a foot.
The height of the heater is approximately 6.6 feet.
What is Pythagoras theorem?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:
h² + 10² = 12²
Simplifying and solving for h, we get:
h² + 100 = 144
h² = 44
h ≈ 6.6 feet
Therefore, the height of the heater is approximately 6.6 feet.
Learn more about Pythagoras theorem on:
https://brainly.com/question/231802
#SPJ1
3 sigma n=1 (17n-25)
3 Σ n=1 (17n-25) = 3(27) = 81.The notation "3 sigma n=1 (17n-25)" represents a mathematical series. The Greek letter sigma (Σ) indicates
what is sigma ?
Sigma (Σ) is a Greek letter used in mathematics to represent the sum of a sequence of terms. The lowercase sigma (σ) is often used to represent standard deviation in statistics.
In the given question,
The notation "3 sigma n=1 (17n-25)" represents a mathematical series. The Greek letter sigma (Σ) indicates that we are adding up a sequence of terms, with "n=1" indicating that we start the series with n=1, and "3" indicating that we add up three terms in total.
The expression inside the parentheses, "17n-25", represents the general term in the series. To find each term in the series, we plug in the values of n=1, n=2, and n=3 into the general term and add them up:
17(1)-25 + 17(2)-25 + 17(3)-25 = -8 + 9 + 26 = 27
Therefore, 3 sigma n=1 (17n-25) = 3(27) = 81.
To know more about sigma , visit:
https://brainly.com/question/4302552
#SPJ1
find 3 ∑ n=1 (17n-25) and give the answer ?
Given that sin 0 = 20/29 and that angle terminates in quadrant III, then what is the value of tan 0?
The value of Tanθ is 20/21.
What is Pythagorean Theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: sinθ = -20/29 and that angle terminates in quadrant III.
We have to find the value of tanθ.
Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Sinθ = Perpendicular/hypotenuse
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Adjacent = - √Hypotenuse² - perpenducualr²
Replace the known values in the equation.
Adjacent = -√29² - (-20)²
Adjacent = -21
Find the value of tangent.
Tanθ = Perpendicular/base
Tanθ = -20/(-21)
Hence, the value of Tanθ is 20/21.
To learn more about the Pythagorean Theorem from the given link
https://brainly.com/question/28981380
#SPJ1
.6 In 1 and 2, write the expression using words. 1. (23,000-789) × 19 In 3-4, read the exproccia 2.6+(88×7)
1) the expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."
How to write the expression in words1) The expression (23,000-789) × 19 can be written in words using the following steps:
The expression inside the parentheses is the difference between 23,000 and 789, which is 22,211.
The expression is then multiplied by 19, which means it is being increased by 19 times.
So the final expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."
2) The expression 2.6+(88×7) can be read in words using the following steps:
The expression inside the parentheses, 88×7, means 88 multiplied by 7.
The result of the multiplication is 616.
The expression then becomes 2.6 added to 616.
So the final expression in words can be read as "Two point six plus six hundred and sixteen."
Learn more about expression at https://brainly.com/question/1718606
#SPJ1
See the photo below
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