find the area of the part of the surface z=x^2 (\sqrt{3})y z=x 2 ( 3 )y that lies above the triangle with vertices (0,0),(1,0)(0,0),(1,0), and (1,2)(1,2).

Answer:

Given that l=20cm, b=12cm, h=9cm

∴T.S.A=2(lb+bh+lh)

=2[(20×12)+(12×9)+(20×9)]

=2(240+108+180)

=2×528

∴T.S.A=1056cm

2

Answer:

simply divide the volume of both cuboids like lbh/lbh simply you will get your ans.

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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Answer:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    m/8-(-4)<0

           m

Simplify   —

           8  

m    

 — -  -4  < 0

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  8  as the denominator :

         -4     -4 • 8

   -4 =  ——  =  ——————

         1        8     8    

Step-by-step explanation:

the answer is m<-32

The solution of inequality m/8 < 4 is,

⇒ m = 32

Which is shown in graph of image.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The expression of the inequality is,

⇒ m/ 8 < 4

Now, We can simply the expression as;

⇒ m/ 8 < 4

⇒ m/ 8 - 4 < 0

⇒ (m - 32)/8 < 0

⇒ m - 32 < 0

⇒ m < 32

Therefore, The solution of inequality m/8 < 4 is,

⇒ m = 32

Which is shown in graph of image.

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The amount of sales tax on Jacob’s purchase is $6.16

What is sales tax?

It is a tax which is charged by the government to raise money so it can provide public services. The tax is based on a certain percent of the price. Example: My State charges 4% sales tax. I want to buy a top advertised for $40. So the sales Tax is $40 × 4% = $1.6.

Jacob would like to purchase a coat and hat for a ski trip. The coat is $62.75, and the hat is $14.25.

So the total cost of coat and hat is $(62.75+14.25)

                                                       = $ 77

Sales tax is 8%

It means in $100 the sales tax is $8

In $100 the sales tax is $8

In $1 the sales tax is 8/100

In $77 the sales tax is (8×77)/100

                                    = $6.16

Hence, the amount of sales tax on Jacob’s purchase is $6.16.

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The exact value of the definite integral ∫(2x³ + 6x - 7)dx over any interval [a, b] is (1/2) * (b⁴ - a⁴ + 3(b² - a²) - 7(b - a). This expression represents the difference between the antiderivative of the integrand evaluated at the upper limit (b) and the lower limit (a). It provides a precise value without any decimal approximations.

To compute the definite integral ∫(2x³ + 6x - 7)dx using the Fundamental Theorem of Calculus, we have to:

1: Find the antiderivative of the integrand.

Compute the antiderivative (also known as the indefinite integral) of each term in the integrand separately. Recall the power rule for integration:

∫x^n dx = (1/(n + 1)) * x^(n + 1) + C,

where C is the constant of integration.

For the given integral, we have:

∫2x³dx = (2/(3 + 1)) * x^(3 + 1) + C = (1/2) * x⁴ + C₁,

∫6x dx = (6/(1 + 1)) * x^(1 + 1) + C = 3x²+ C₂,

∫(-7) dx = (-7x) + C₃.

2: Evaluate the antiderivative at the upper and lower limits.

Plug in the limits of integration into the antiderivative and subtract the value at the lower limit from the value at the upper limit. In this case, let's assume we are integrating over the interval [a, b].

∫[a, b] (2x³ + 6x - 7)dx = [(1/2) * x⁴ + C₁] evaluated from a to b

                            + [3x²+ C₂] evaluated from a to b

                            - [7x + C₃] evaluated from a to b

Evaluate each term separately:

(1/2) * b⁴ + C₁ - [(1/2) * a⁴+ C₁]

+ 3b²+ C₂ - [3a² C₂]

- (7b + C₃) + (7a + C₃)

Simplify the expression:

(1/2) * (b⁴ a⁴ + 3(b² - a²) - (7b - 7a)

= (1/2) * (b⁴ - a⁴) + 3(b² - a²) - 7(b - a)

This is the exact value of the definite integral of (2x³+ 6x - 7)dx over the interval [a, b].

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Answer:

-9

-11

-4

Step-by-step explanation:

Applying the exterior angle theorem, the measure of the exterior angle to angle X is: B 112.55°.

In other to find the measure of the exterior angle to angle X, we have to recall the theorem known as the exterior angle theorem, which states that the measure of an exterior angle is equal to the two interior remote angles that are opposite to it.

In triangle XYZ, angle Y and Z are the remote interior angles. We are given the following:

Measure of angle Y = 38.25°

Measure of angle Z = 74.3°

Therefore:

The measure of the exterior angle to angle X = measure of angle Y + measure of angle Z

Substitute

The measure of the exterior angle to angle X = 38.25° + 74.3°

The measure of the exterior angle to angle X = 112.55°

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The statement "the sophists were principally concerned with mathematics, and formulated the so-called Pythagorean theorem" is not entirely accurate.

While the sophists were a group of philosophers who were known for their expertise in various subjects, including mathematics, they did not formulate the Pythagorean theorem. This theorem is named after Pythagoras, a philosopher and mathematician who lived in ancient Greece.The sophists were more concerned with rhetoric and the art of persuasion.

They were skilled at using language and arguments to influence others, and they often taught these skills to others for a fee. While they may have had some knowledge of mathematics, their primary focus was not on this subject.In fact, the Pythagorean theorem is traditionally attributed to Pythagoras and his followers, who were known as the Pythagoreans.

This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is a fundamental concept in geometry, and it has many practical applications in fields such as engineering and physics.In conclusion, while the sophists may have had some knowledge of mathematics, their primary focus was on rhetoric and persuasion. The Pythagorean theorem is traditionally attributed to Pythagoras and his followers, not the sophists.

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Measurement is closest to the length of the ramp in feet is 33 feet

Let AB = 26 ft and BC = 19.5 ft

Let AC be the length of the ramp

Let's use the Pythagorean theorem to find the length of the ramp:

AC² = AB² + BC²

where AC is the hypotenuse (the unknown side), and AB and BC are the other two sides given.

Substituting the given values, we get:

AC² = 26² + 19.5²

AC² = 676 + 380.25

AC² = 1056.25

AC = \(\sqrt{1056.25}\)

AC = 32.5

Rounding to the nearest feet

AC = 33

Therefore, the measurement closest to the length of the ramp in feet is 33 feet.

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Answer:

the picture isnt showing up on mines

Answer:

16

Step-by-step explanation:

20*80/100 use this formula to find it

A 24.8% of babies have a head circumference greater than 14 inches.

The circumference of a circle is the length of the curved boundary or the perimeter of the circular shape. It is a measurement of the distance around the circle and is equal to the arc length of the circle if it were opened up and straightened out into a line segment. The circumference of a circle is related to its diameter by the formula: C = π * d

To calculate the percentage of babies with a head circumference greater than 14 inches, we need to find the area under the normal distribution curve to the right of 14 inches.

First, we need to convert 14 inches to the standard units (z-score). We can do that using the following formula:

z = (14 - 13.5) / 0.75 = 0.67

Next, we can use a standard normal distribution table to find the area to the right of z = 0.67. The value from the table is approximately 0.752.

Therefore, approximately 75.2% of babies have a head circumference less than or equal to 14 inches, and 24.8% of babies have a head circumference greater than 14 inches.

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Answer:

the walking rate miles per hour is 2 miles per hour

Step-by-step explanation:

The computation of the walking rate miles per hour is shown below;

Given that

She can walk half mile in one-fourth of an hour

= Miles ÷ hours

= (1÷ 2) ÷ (1 ÷4)

= 0.50 ÷ 0.25

= 2 miles per hour

Hence, the walking rate miles per hour is 2 miles per hour

The same is considered

The vertices of the image of the figure LMNO following a 90° rotation about the origin are; L'(3, 5), M'(6, 6), N'(3, 4), O'(6, 4), indicating that the corresponding segment L'O' and M'N' are on the lines x = 6 and x = 3, the correct option is option B.

B. x = 6 and x = 3

A rotation is the circular motion about a specified center of rotation of the points on the figure of the preimage.

The coordinates of the vertices of the figure LMNO are; L(-5, 3), M(-6, 6), N(-4, 6), O(-4, 3)

The transformation of the figure LMNO = 90° clockwise rotation about the origin.

The coordinate of the image of the point (x, y) following a rotation of 90° about the origin is the point (y, -x).

Therefore, the coordinates of the image of the figure LMNO following a rotation of 90° about the origin are found as follows;

L(-5, 3) \(\underset{\longrightarrow}{R_{90^{\circ}\ clockwise}}\) L'(3, 5)

M(-6, 6) \(\underset{\longrightarrow}{R_{90^{\circ}\ clockwise}}\) M'(6, 6)

N(-4, 6) \(\underset{\longrightarrow}{R_{90^{\circ}\ clockwise}}\) N'(6, 4)

O(-4, 3) \(\underset{\longrightarrow}{R_{90^{\circ}\ clockwise}}\) O'(3, 4)

The points L' and O' are colinear with the line x = 3, and the points M' and N' are colinear with the line x = 6

Therefore, the corresponding segment to the segment LO, L'O' lie on the the line x = 3, and the corresponding segment to the segment MN, M'N' lie on the line x = 6

The correct option is B. x = 6, and x = 3

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Answer:

x=42

Step-by-step explanation:

Using a unitary method, we have identified that the smaller pot has more water.

To compare the amount of water in the two pots, we need to find a common unit of measurement. In this case, both pots are measured in cups, so we can simply compare the number of cups in each pot. The chef filled the larger pot with 3.7 cups of water, and the smaller pot with 7.3 cups of water.

Now, we can use a unitary method to compare the two quantities. Let's assume that one cup is our unit of measurement. To find out how many cups of water are in the smaller pot, we can divide 7.3 by 1 cup. This gives us 7.3 cups of water. To find out how many cups of water are in the larger pot, we can divide 3.7 by 1 cup. This gives us 3.7 cups of water.

As we can see, the smaller pot has more water than the larger pot.

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Answer:

I am stuck on this two

Step-by-step explanation:

rectangle, 6 8 14 12

Answer:

you would pay 2.38 sales tax for a 34 dollar pair of pants

Step-by-step explanation:

The rule to describe the transformation, dilation by a scale factor of 4 with center of dilation at the  origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' is are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

In the question ,

a rectangle QRST with coordinates Q(-8,5), R(-8,7), S(-5,7), and T(-5,5) is given ,

and to dilate the rectangle by a scale factor of 4 with center of dilation at the origin , we multiply coordinates of the original shape with the dilation factor

so the rule to describe the dilation will be

(x,y)→(4x,4y)

Using this rule to find the new coordinates of the rectangle Q'R'S'T' .

When Q = (-8,5)

Q' = (4*(-8),4*5)

Q' = (-32,20)

When R = (-8,7)

R' = (4*(-8),4*7)

R' = (-32,28)

When S = (-5,7)

S' = (4*(-5),4*7)

S' = (-20,28)

When T= (-5,5)

T'  = (4*(-5),4*5)

T' = (-20,20)

So the coordinates of the rectangle Q'R'S'T' is Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .

Therefore , the rule to describe the transformation, dilation by a sale factor of 4 with center of dilation at the origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

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The volume of the solid of revolution created by rotating the function f(x) = x^2 about the x-axis between x=0 and x=2 is approximately 20.106 cubic units.

The axis of revolution is a line about which a two-dimensional shape is rotated to create a three-dimensional solid. The method for finding the formula to solve for the volume of a solid of revolution depends on the shape being rotated and the axis of revolution.

For example, if we want to find the volume of a solid of revolution created by rotating a function f(x) about the x-axis between the limits of integration a and b, we can use the following formula:

V = π∫[a,b] (f(x))^2 dx

This formula is derived from the shell method, which involves breaking the solid into thin cylindrical shells, finding the volume of each shell, and adding them up. The formula is then the integral of the volume of each shell.

To solve this integral, we can use various methods such as integration by substitution or integration by parts. Once we have found the antiderivative of the integrand, we can evaluate the definite integral using the limits of integration a and b.

For example, if we have the function f(x) = x^2 and we want to find the volume of the solid of revolution created by rotating this function about the x-axis between x=0 and x=2, we can use the formula:

V = π∫[0,2] (x^2)^2 dx

Simplifying this expression, we get:

V = π∫[0,2] x^4 dx

Integrating this expression with respect to x, we get:

V = π[(1/5)x^5] [0,2]

Evaluating this expression at the limits of integration, we get:

V = π[(1/5)(2^5 - 0)]

V = π(32/5)

Therefore, the volume of the solid of revolution created by rotating the function f(x) = x^2 about the x-axis between x=0 and x=2 is approximately 20.106 cubic units.

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The statement [(p implies q) and (q implies r)] implies (p implies r) in discrete mathematics.

In discrete mathematics, implication is represented by the conditional operator (=>). The given statement [(p implies q) and (q implies r)] can be written as (p => q) ∧ (q => r). We want to prove that this statement implies (p => r).

To demonstrate this, we need to show that whenever the statement [(p => q) ∧ (q => r)] is true, the implication (p => r) is also true. This can be done using a truth table or logical reasoning.

If (p => q) and (q => r) are both true, it means that whenever p is true, q must also be true, and whenever q is true, r must also be true. In this case, if p is true, then q is true, and as q is true, r must also be true. Therefore, (p => r) is true.

Hence, we can conclude that the statement [(p implies q) and (q implies r)] implies (p implies r) in discrete mathematics.

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A circular table is surrounded by chairs. There are individuals who are currently seated at this table in such a way that if one more individual decides to sit down, then they must sit adjacent to someone. The smallest possible value for the number of people currently seated at the table is 3.

This is because in order for one more person to sit adjacent to someone, there must already be at least 3 people seated at the table. This is because if there were only 2 people seated at the table, the one more person would not have a "someone" adjacent to them to sit next to.

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The width of the path is 1 meter. This makes the length of the pool including the path 14 meters and the width 24 meters,

Let's denote the width of the path as x. Then the length of the pool including the path is 12 + 2x meters and the width is 22 + 2x meters. The total area of the pool and the path combined is given as 936 square meters, so we can set up an equation:

(12 + 2x)(22 + 2x) = 936

Simplifying this equation, we get:

4x^2 + 68x - 72 = 0

Factoring this quadratic equation, we get:

(x + 9)(4x - 8) = 0

Since the width of the path cannot be negative, we can only consider the positive root, which is: x = 2

Therefore, the width of the path is 2 meters.

But wait, this is not the final answer! We need to remember that the width of the path is uniform, which means it is the same on all sides of the pool.

If the width of the path is 2 meters, then the length of the pool including the path is 16 meters and the width is 26 meters. This gives a total area of: 16 x 26 = 416 square meters

which is clearly less than 936 square meters. Therefore, we made a mistake in our calculation and the width of the path cannot be 2 meters.

Let's go back to our quadratic equation and solve for x again: 4x^2 + 68x - 72 = 0

Dividing both sides by 4, we get:

x^2 + 17x - 18 = 0

Factoring this quadratic equation, we get:

(x + 18)(x - 1) = 0

Again, we can only consider the positive root, which is:

x = 1

Therefore, the width of the path is 1 meter. This makes the length of the pool including the path 14 meters and the width 24 meters, giving a total area of: 14 x 24 = 336 + 600 = 936 square meters, which confirms that our solution is correct.

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Answer:

X = 70

Step-by-step explanation:

180 - 40 = 140

140/2 = 70

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Answer:

8 fruits

Step-by-step explanation:

Todd and agnes are making desserts. todd buys

peaches and a carton of vanilla yogurt. agnes

buys apples and a jar of honey. they bought

the same number of pieces of fruit. is there a

situation in which they pay the same amount for

their purchases? explain.

apples

peaches=

$1.25 for peaches

$1.00 for apples

yogurt

honey=

$4 for yogurt

$6 for honey

Todd:

Peaches + yogurt

1.25x + 4

Agnes:

1.00x + 6

Where,

x = number of pieces of fruit

Equate the cost of Todd and Agnes

1.25x + 4 = 1.00x + 6

1.25x - 1.00x = 6 - 4

0.25x = 2

x = 2/0.25

= 8

x = 8 fruits

The situation in which they both pay the same amount for their purchases is when they buy 8 fruits each

Answer:

£11

Step-by-step explanation:

first lets find the number of children's = 3/8 * 1120 =420 children's

then find number of adults = 1120 -420 = 700 adults

if adult costs, £28

28 * 700 = £19600

lets subtract the total cost - total adult ticket cost

=   £24,220 -  £19600

= £4620......this is the total children's ticket cost

there are 420 children ---> £4620

1 children --> £4620/420 = £11