47 mL is equivalent to 0.047 L (liters).
What is measurement refers to?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.
Define the term equivalent?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
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Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
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What is the equivalent to this
None of the given options A, B, C, or D is correct as they all provide different answers.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
The question asks for the equivalent of 6 × 2. This means that we need to find a number that is equal to the result of multiplying 6 and 2 together.
When we multiply 6 and 2, we get:
6 × 2 = 12
So, the equivalent of 6 × 2 is 12.
However, none of the answer options provided matches this answer.
Option A suggests that the equivalent of 6 × 2 is 2 × 1, which is equal to 2, not 12.
Option B suggests that the equivalent of 6 × 2 is 3 × 2, which is equal to 6, not 12.
Option C suggests that the equivalent of 6 × 2 is 9 × 3, which is equal to 27, not 12.
Option D suggests that the equivalent of 6 × 2 is 18 × 1/2, which is equal to 9, not 12.
Therefore, none of the options provided is correct.
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.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."
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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.
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
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
Use the graph to answer the question.
graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at 8 comma 5, 10 comma 1, 14 comma 1, 12 comma 5
Determine the translation used to create the image.
7 units to the right
7 units to the left
3 units to the right
3 units to the left
The translation used to create the image A'B'C'D', from the pre-image, ABCD is; 7 units to the right
What is a translation transformation?A translation transformation is one in which the location of the points on the pre-image is changes but the size, and orientation of the pre-image is preserved.
The coordinates of the vertices of the polygon ABCD are; (1, 5), (3, 1), (7, 1), (5, 5)
The coordinates of the vertices of the polygon A'B'C'D' are; (8, 5), (10, 1), (14, 1), (12, 5)
Whereby the vertices of the image and the preimage are;
A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5), the difference in the x and y-values indicates;
A' - A = (8 - 1, 5 - 5) = (7, 0)
B' - B = (10 - 3, 1 - 1) = (7, 0)
C' - C = (14 - 7, 1 - 1) = (7, 0)
D' - D = (12 - 5, 5 - 5) = (7, 0)
Therefore, the transformation used to create the image A'B'C'D' from the pre-image, ABCD is a translation; 7 units to the right
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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
Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.
1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.
Based on the results, which statements are true? (Pick all that apply)
A. Most students found a pine tree.
B. More students found a maple tree than a pine tree.
C. More students found a birch tree than an oak tree.
D. More students found a pine tree than a birch tree.
E. More students found a maple tree than an oak tree.
The statements that are correct concerning the outcome of events between Jasmine and her classmates include the following:
Most students found a pine tree.
More students found a pine tree than a birch tree. That is option A and D respectively.
How to calculate the number of students per tree?The quantity of students that found birch tree = 1/7 = 0.14
The quantity of students that found pine tree = 7/9 = 0.8
The quantity of students that found maple tree = 1/4 = 0.25
The quantity of students that found oak tree = 11/23 = 0.48
Therefore, the statement that are correct about the outcome of the event between Jasmine and her classmates is as follows:
Most students found a pine tree.
More students found a pine tree than a birch tree.
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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.
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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
Help me pleas whith this
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.
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solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +
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.
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solve for the unknown to find the unit rate
1/5 ?
----- = -----
1/20 1
Answer: 4
Step-by-step explanation:
To find the unit rate, we can cross-multiply the fractions.
Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5.
Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20.
Now we have the equation 1/5 = 1/20.
To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4.
Therefore, the unit rate is 4.
Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)
Answer:
...............................
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
… 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
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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.
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if m(x)= sin²(x), then m'(x)=? A. cos²x+sin²x. B.sinx²-cos²x C. 2cos²x-sinx D. cos²-sin²x
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
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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)
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PLEASE HELP MEE!!!!! I REALLY NEED TO PASS, 100 POINTS!!!
Answer:
Step-by-step explanation:
i believe it is nearly as hard as my usual amount of challenge
Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
verbal phrase can be represented by 7.16.
What is the verbal phrase?Part A:
The verbal phrase can be represented by the following expression:
[tex]2.19g + 0.59[/tex]
Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex] .
Part B:
To evaluate the expression when [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:
[tex]2.19g + 0.59[/tex]
[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]
[tex]= 6.57 + 0.59[/tex]
[tex]= 7.16[/tex]
Therefore, the correct answer is [tex]7.16.[/tex]
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The given question is incomplete. the complete question is given below:
Consider the verbal phrase.
Two and nineteen hundredths times a number g, plus fifty-nine hundredths
Part A
Enter an expression to represent the verbal phrase.
g +
Part B
Evaluate the expression when g = 3.
3.96
7.16
8.34
8.93
Which geometric term describes ∠ T A G ?
Answer:
angle
Step-by-step explanation:
since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!
Answer: i know it is acute
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]
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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.
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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: