Gillian has a board that is 2 meters long. She cuts the board into 5 equal pieces, and then measures them with a tape measure that only measures in customary units. To the nearest inch, what is the length of each piece?

The matrix A of T with transformation T: R²→R² and is reflection of the line y = -x is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

T: IR²→IR² is reflection of the line y = -x.

It is known that e1 = (1,0) and e2 = (0,1) is the standard basis of IR².

So, the transformation is T(e1) = e1' and T(e2) = e2'.

T(e1) = e1' = (0,1)

= 0(1,0) + (-1)(0,1)

= 0 · e1 + (-1) · e2

T(e2) = e2' = (-1,0)

= (-1)(1,0) + 0(0,1)

= (-1) · e1 + 0 · e2

So, now the matrix A becomes [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

Therefore, the new matrix is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

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Find the matrix A of T for the following transformation. T: R²→R² is a reflection in the line y = -x.

The length of side x obtained using trigonometric ratios is 5 units

Trigonometric ratios are expressions that indicate the relationship between the lengths of two of the sides of a right triangle and the interior angles of the right triangle.

The specified triangle is a right triangle, therefore, if the interior angles, and the length of one of the sides is known, the lengths of the other sides can be found.

The right triangle is a 30°-60°-90° right triangle

The length of the hypotenuse side = 10

The length of the leg with measurement x, can therefore, be found using trigonometric ratios follows;

sin(θ) = Opposite/Hypotenuse

sin(30°) = x/10

Therefore; x = 10 × sin(30°)

x = 10 × 0.5 = 5

The length of the side x in the right triangle is 5 units

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10 mg of carbon-14 would still be present in the sample after 17,190 years.

The formula: A = A θ * (1/2)(t/t 1/2)

can be used to determine how much carbon-14 is still present in a sample after a specific number of years.

where A is the remaining carbon-14, A 0 is the initial carbon-14 concentration, t is the passing of time, t 1/2 is the carbon-14 half-life (5,730 years), and 1/2 is the decay factor.

By entering the specified values, we obtain:

A = 80 mg * (1/2)^ 5,730 years / 17,190 years

A = 80 mg * (1/2)^3

A = 80 mg * (1/8)

A = 10 mg

Therefore, 10 mg of carbon-14 would still be present in the sample after 17,190 years.

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The products that result in a difference of squares or a perfect square trinomial are Quadratic Equations, Perfect Square Binomials, and Difference of Squares. Difference of Cubes is incorrect.

Those apply:

All three of these products can be used to solve a variety of problems involving algebraic equations.

The task:

Which products result in a difference of squares or a perfect square trinomial?

Check all that apply:

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The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation dy/dx = y^2 - 4y are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

y² - 4y = 0

y(y - 4) = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation [tex]\frac{dy}{dx} = y^{2} - 4y[/tex] are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

[tex]y^{2} - 4y[/tex]= 0

[tex]y(y-4)[/tex] = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The truth value of a is False and after seeing the result of 1st statement b is true.

A mathematical statement like "3 is bigger than 4," "an infinite set exists," or "7 is prime" is referred to as a proposition.

A statement that is presumptively true is known as an axiom. Although there are several exceptions, mathematical logic can typically classify a claim as true or false given enough information (e.g., "This statement is false").

let p(x):x^2<=4

the domain for x is all positive integers (1, 2, 3, . . .).

(a) p(5)

p(5):25 not equal or less than 4

hence the truth value of a is False

(b)  negation for x;p(x)

after seeing the result of 1st statement b is true.

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Answer:

neither

Step-by-step explanation:

line T: m = -2/3

If line U was parallel to T it would have the same slope (-2/3)

If line U was perpendicular to T it would have a slope that is the negative reciprocal of the slope of line T  (3/2)

The probability of randomly drawing a vowel is 2/7, option C is correct.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given a set of cards spell P, E, R, C, E, N, T, S

total cards = 8

so total outcome = 8

to find  the probability of randomly drawing a vowel,

set contains 2 vowels,

a favorable outcome for vowel = 2

probability =  favorable outcome/total outcome

P(vowel) = 2/7

Hence option C is correct.

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Answer:

113

Step-by-step explanation:

the formula is: π(d/2)^2

so:

π(12/2)^2=113.09...

Rounded that equals 113.0

Hope that helped! Let me know if you have any other questions.

Answer:

113.0 ft²

Step-by-step explanation:

Solution Given:

diameter(d) :12 ft

radius(r) = d/2= 12/2=6 ft

now

we have

area of the circle= πr²=22/7*6²= 113. 14 ft² =113 ft²

You are right

The remaining ratios for the angle are:

sin θ = 2/√7

cos θ = √3 /√7

tan θ = 2/√3

sec θ = √7 /√3

cot θ = √3 /2

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Trigonometry is used to determine the lengths of the sides of a triangle when one or more angles and/or the lengths of one or more sides are known.

The remaining ratios are as follows

csc θ = √7 /2

Since sin θ = 1/cscθ

sin θ = 2/√7

Remember: sin θ= opposite/hypotenuse  = 2/(√7)

adjacent =  √((√7)² - 2²) = √3

cos θ = √3 /√7   (adjacent/hypotenuse)

tan θ = 2/√3  (opposite/adjacent)

sec θ = 1/cos θ

sec θ = √7 /√3

cot θ = 1/tan θ

cot θ = √3 /2

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Answer: The FOIL method (First, Outer, Inner, Last) is a mnemonic used to help solve and simplify multiplication problems by using the distributive property. To use FOIL, you simply multiply the first term of the first factor with the first term of the second factor, the outer terms of the two factors, the inner terms of the two factors, and the last terms of the two factors. Then, you add the results together to obtain the final answer.

For example, in the first problem, (a + b)(2a - 3b^2), we FOIL by first multiplying "a" and "2a": 2a^2. Next, we multiply "a" and "-3b^2": -3ab^2. Then, we multiply "b" and "2a": 2ab. Finally, we multiply "b" and "-3b^2": -3b^3. Now, we add the four results together to get the final answer: 2a^2 + (-3b^2 + 2b)a - 3b^3.

a. (a + b)(2a - 3b^2) = 2a^2 - 3ab^2 + 2ab - 3b^3 = 2a^2 + (-3b^2 + 2b)a - 3b^3.

b. (k - 8)(4k + b) = 4k^2 + bk - 32k - 8b = 4k^2 + (b - 32)k - 8b.

c. (7x^15)(2x + 2) = 14x^16 + 14x^15 = 14x^15 (x + 1).

d. (3ab - 1)(2ab + 6) = 6a^2 b^2 + 2ab - 3ab + 6 - 2ab = 6a^2 b^2 + 4ab +

Step-by-step explanation:

Answer:

The expression 2a^2b^2 + 2b^2c^2 + 2a^2c^2 - a^4 - b^4 - c^4 can be factored as:

(2ab^2 + 2bc^2 + 2ac^2)(a^2 - c^2) - (a^2 - b^2)(a^2 - c^2)

= (a^2 + b^2 + c^2)(2ab^2 + 2bc^2 + 2ac^2) - (a^2 - b^2)(a^2 - c^2)

Answer:

-1, 6

0, -3

1, -3.9

2, -3.99

f(x) = 5^2x+1

Step-by-step explanation:

for the first question, after plugging in the values of x, we get our answer to be the 2nd table

-1, 6

0, -3

1, -3.9

2, -3.99

for the second question

f(x) = 5^2x+1

after graphing, we can see it never passes x = 2

Just put your name on the check's back to complete a blank endorsement. The teller at the bank will ask if you want to cash it or deposit it after you arrive.

The three types of endorsements available for checks are blank, special, and restriction. When the payee signs their name on the check's top back, it becomes a blank endorsement.

To accomplish this, you just sign the check on the back and inform the bank teller whether you want to deposit it into a certain account or cash it. When depositing a check using mobile deposit or an ATM, a blank endorsement is also acceptable.

To be accepted for deposit, a check needs to have an endorsement on the back. Therefore, always add your signature to the document right before bringing it to the bank in the place provided next to the X.

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The x-intercept of the function is given by x=±9

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function y=x²-81

To find x-intercepts of the functions we set y=0

Thus y=x²-81

x²-81=0

x=√81

x=±9

Hence, The x-intercept of the function is given by x=±9

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Using Scalar multiplication, If all the conditions are satisfied, then the set is a subspace of R³

The result of multiplying a real number by a matrix is known as a scalar multiplication. Each entry of the matrix is multiplied by the specified scalar in scalar multiplication.

The following requirements must be met in order to establish whether a set is a subspace of R3 under addition and scalar multiplication:

Closure under addition: If elements u and v are present, then u plus v must also be present.

If u is a member of the set and k is any scalar, then ku must likewise be a member of the set. Closure under scalar multiplication.

The zero vector is contained in: The set must contain the zero vector (0, 0, 0).

includes all negative vectors; if u is in the set, then -u must also be.

These conditions must be checked for each set, and your response must be supported.

The set is a subspace of R³ if all the conditions are met.

The set is not a subspace of R³ if any of the requirements are not met.

Consequently, the set is a subspace of R³ if all of the conditions are met.

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Complete question -

Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.

Conditional Probability:

P(A|B)=P(A∩B)/P(A)

where:

P(B|A) is the probability of event B happening, given that A happened.

P(A∩B) is the probability of both A and B happening

P(A) is the probability of A happening.

Event A: Positive test.

Event B: Body attempting to reject the kidney.

The percentages associated with a positive test are:

80% of 30%(experience kidney rejection).

9% of 70%(do not experience kidney rejection).

Hence:

P(A)=0.8*0.3+0.09+0.7

P(A)=0.303

The probability of both a positive test and the body attempting to reject the kidney is:

P(A∩B)=0.8*0.3=0.24

Hence, the conditional probability is:

P(B|A)=0.24/0.303

P(B|A)=0.7921.

0.7921 = 79.21% probability that the body is attempting to reject the kidney.

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The Intermediate Value Theorem (IVT) states that for any continuous function f(z) and any real number a, if f(a) and f(b) have opposite signs, then there exists a number c in the interval (a,b) such that f(c) = 0.

The IVT states that if a continuous function has different signs (positive or negative) at two points in its domain, then it must have a zero in between those two points. In the case of the function f(z) = 26z^53 + 3, we are asked to find an integer n such that there exists a zero of the function in the interval [n/4, (n + 1)/4].

To find the solution, we can use the IVT by considering two points in the interval with opposite signs. For example, if we take n = 1, then the interval is [1/4, 2/4]. We can evaluate the function at the two endpoints of the interval and look for opposite signs:

f(1/4) = 26 * (1/4)^53 + 3 > 0

f(2/4) = 26 * (2/4)^53 + 3 < 0

Since the function has opposite signs at the endpoints, the IVT guarantees that there exists a zero of the function in the interval [1/4, 2/4]. This means that for n = 1, the IVT is satisfied and the function has a zero in the interval [1/4, 2/4].

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Complete Question:

For which integer n, 0 < n < 3 , does the IVT say that f(z) 26 53 + 3 has & zero in the interval [n/4, (n + 1)/4]?

As t increases without bound. N(t) approaches:

N(t) is limited by the number of people who started the rumor.

The correct answer is option (A).

The given exponential model is defined as follows:

[tex]N(t)=5501+49e^{-0.7t}[/tex]

For t = 0

Substitute the value of t = 0 in the above equation,

[tex]N(t)=5501+49e^{-0.7\times0}[/tex]

N(t) = 5501 + 49 × 1

N(t) = 5501 + 49

N(t) = 5550

Thus, 5550 people started the rumor.

Since [tex]49e^{-0.7t}[/tex] is greater than zero for all real t.

Then, [tex]5501+49e^{-0.7t} > 5501\\[/tex]

So, as t increases without bound.

N(t) approaches:

N(t) is limited by the number of people who started the rumor.

Therefore, the correct answer is option (A).

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The complete question is as follows:

The equation [tex]N(t)=5501+49e^{-0.7t}[/tex] models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer.

How many people started the rumor?

N(t) approaches:

A. N(t) is limited by the number of people who started the rumor.

B. N(t) is limited by the carrying capacity of the town.

C. N(t) is limited by the number of days it takes for the entire population to hear the rumor.

D. N(t) is limited by the rate at which the rumor spreads.

E. N(t) is not limited by any value and increases without bounds.

By applying inverse function concept, it can be concluded that the table that could be used to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F) is option A:

C           -20      -15      -5

F(C)        -5         4       23

An inverse function can be defined as a type of function that is obtained by inverting (undoing) the operation of the given function f(x).

In Mathematics, if f(x) is a given function, its inverse function has the following property f⁻¹(f(x)) = x.

We already have this table:

F       -4        5       23

C(F)   20    -15      -5

By applying the concept of inverse function, we can form a new table to represent the inversion function of the above table:

C           20      -15      -5

F(C)        -4        5       23

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Full question attached.

The rate law is an equation that describes the rate of a reaction as a function of the concentrations of the reactants. The rate of a reaction is typically represented as the change in concentration of a reactant or product over time.

a) Rate = k[a]2 - Second Order Rate Law

b) Rate = k[a] - First Order Rate Law

c) Rate = k - No Match

The rate law is an equation that describes the rate of a reaction as a function of the concentrations of the reactants. The rate of a reaction is typically represented as the change in concentration of a reactant or product over time.

a) The rate law equation for a second order reaction is rate = k[a]2, where k is the rate constant and [a] is the concentration of the reactant.

b) The rate law equation for a first order reaction is rate = k[a], where k is the rate constant and [a] is the concentration of the reactant.

c) There is no rate law equation for a reaction with a rate of k.

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The angle in the sector formed in radian is 5/4 π

The length of an arc is defined as the part of the circumference of a circle which is bounded by two radii.

The length of an arc = tetha / 360 × 2πr

where( tetha) is the angle

r is the radius

360° = 2π

therefore :

15π/2 = tetha/2π × 2× 6 × π

15π/2 = 6 tetha

tetha = 15π/2 ÷ 6

tetha = 15/12 π

tetha = 5/4 π

therefore the value of the angle in radian Is 5/4 π

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The solution to the equation are k = 2 or k = -3.5

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

2k^2 - 14 = -3k

Express properly

So, we have the following representation

2k^2 + 3k - 14 = 0

Expand the equation

2k^2 + 7k - 4k - 14 = 0

So, we have

k(2k + 7) - 2(2k + 7) = 0

This gives

k - 2 = 0 or 2k + 7 = 0

Evaluate

k = 2 or k = -3.5

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There are 187.425 pounds in 85 kilograms. The solution has been obtained by using the unit conversion.

What is unit conversion?

The same feature is expressed in a different unit of measurement using a unit conversion. For instance, you may represent time in minutes rather than hours or distance in feet rather than miles. It happens frequently when measurements are given in one set of units, like feet, but are demanded in another set, like chains.

We are given 85 kilograms which are to be converted into pounds.

We know that 1 kilogram = 2.205 pounds(approx)

So,

⇒85 kilograms = 85 * 2.205

⇒85 kilograms = 187.425 pounds

Hence, there are 187.425 pounds in 85 kilograms.

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The completed tiles are placed in the appropriate slots to prove that line j is parallel to k, as follows;

Statements         [tex]{}[/tex] Reasons

1. ∠6 ≅∠3 [tex]{}[/tex]          1. Given

2. ∠3 ≅∠2 [tex]{}[/tex]         2. Vertical ∠s ≅

3. ∠6 ≅ ∠2 [tex]{}[/tex]        3. Transitive Property

4. j ║ k       [tex]{}[/tex]         4. Corresponding ∠s ≅, lines ║

Parallel lines are are two lines that continue indefinitely and do not meet, such that they make the same or congruent corresponding angles with a common transversal.

The details of the reasons used to prove that line j is parallel to line k are as follows;

Vertical ∠s ≅

The vertical angles theorem states that vertical angles, which are angles formed by the intersection of two lines and which are located, opposite to each other are congruent.

Transitive property

The transitive property of congruency states that if a is congruent to b and b is congruent to c, them a is congruent to c

Corresponding ∠s ≅

The corresponding angles formed between parallel lines are congruent.

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The solution for the given initial-value is 6ty + t² - 9t + 4y² - y = 12

An initial value problem is a differential equation that is accompanied by an initial condition that specifies the value of one or more variables at a particular time or at a particular point in space. The initial value problem is to find the solution of the differential equation that satisfies the given initial condition. The solution of the initial value problem describes the behavior of the system over time or as a function of space based on the given initial conditions.

The given initial value problem is a non-linear ordinary differential equation and can be solved using numerical methods such as Runge-Kutta methods or numerical integration.

The solution to the initial value problem gives the function y(t) that satisfies the differential equation and the initial condition y(-1) = 2.

Given that

(6y + 2t − 9)dt = (8y 6t − 1)dy = 0

and y = -2

As both = 0 then (6y + 2t − 9)dt = (8y + 6t − 1)dy

that is

(6(-2) + 2t − 9)dt = (8(-2) + 6t − 1)d(-2)

−21dt + 2dt² = 34d−12dt

2dt² − 9dt - 34d

d(2t² −9t−34)

Integration both sides

6ty + t² - 9t + 4y² - y = c

Using y(-1) = 2

-12 + 1 + 9 + 16 - 2 = c

c = 12

Thus, the solution for the given initial-value is 6ty + t² - 9t + 4y² - y -12 = 0

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The area of a triangle is 43.8178 square centimeters

Let the triangle's third side measure "x" cm.

circumference = x+8+11 = 32;

or x = 32-19 = 13 cm.

If we are aware of all three sides of a triangle, we can use "Heron's Formula" to determine its area.

Triangle's surface area equals the square root of s(s-a) (s-b) (s-c);

where s is the triangle's semi-perimeter; a, b, and c are its three sides.

As a result, s = 32/2 = 16 cm; a= 8 cm; b= 11 cm; and c= 13 cm.

Therefore, the triangle's area is equal to the square root of 16 X (16-8) X (16--11) X (16—13).

= Square root of (1920) = (16 X 8 X 5 X 3).

=43.8178 square centimeters

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The question seems incorrect;

What is the area of a triangle, two sides of which are 8cm and 11cm and the perimeter is 32cm?

The coefficient of q in the sum of these two expression is 1/2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expressions are (2/3q −3/4) and (−1/6 q − 2).

We have to add these two expressions.

First arrange in such a way that like terms are together.

(2/3q −3/4) + (−1/6 q − 2) = (2/3q - 1/6q) + (-3/4 - 2)

                                        = (4/6q - 1/6q) + (-3/4 - 8/4)

                                        = 3/6q - 11/4

                                        = 1/2 q - 11/4

Hence the sum of the given expressions is 1/2 q - 11/4. And the coefficient of q is 1/2.

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The volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the given vertices we can write the equation of the base of the triangular region as:

x = 1 - y

The area of the triangular region is given as:

A = 1/2 (b)(h)

A = 1/2 (1-y)(3)

The volume of the region is calculated by taking the integration of the area:

[tex]V = \int\limits^1_0 {\frac{3}{2} [1 - y] } \, dx\\\\V = \frac{3}{2} [y - \frac{y^2}{2} ]_0^1[/tex]

Substituting the values of the limit we have:

V = 3/2 [ 1 - 1/2]

V = 3/2 [1/2]

V = 3/4

Hence, the volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

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