93°
65°
m X
finding the angle of x

The volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and [tex]y=1/\sqrt(1+x)[/tex] about the x-axis is πln(2),

(option A).

To find the volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and[tex]y=1/\sqrt(1+x)[/tex] about the x-axis, we need to use the formula for the volume of a solid of revolution.

The formula is ∫[a,b] [tex]π(f(x))^2dx[/tex], where a and b are the limits of integration and f(x) is the function that describes the distance between the axis of revolution and the curve being rotated.

In this case, we need to use the function f(x) = 1/sqrt(1+x), since this function describes the distance between the x-axis and the curve being rotated. The limits of integration are from x=2 to x=5, since these are the values of x that define the region being rotated.

Using the formula, we can set up the integral as follows:

[tex]∫[2,5] π(1/\sqrt(1+x))^2dx[/tex]

= π∫[2,5] 1/(1+x) dx

= π[ln(1+x)]|[2,5]

= π[ln(6) - ln(3)]

= πln(2) (option-A)

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area of A = πr² = π7² = 153.9 m²

area of B = πr² = π9² = 254.5 m²

The equation of the trigonometric function graphed is A) f(x) = 3 sin (x) - 2.

Given a graph of the trigonometric function.

We have to find the equation of the trigonometric function.

For x = π/2, y = 1

Also, when x = 3π/2, y = -5

A) If the function is,

f(x) = 3 sin (x) - 2,

When x = π/2

f(x) = 3 sin (π/2) - 2

     = 3(1) - 2

     = 1

When x = 5π/2

f(x) = 3 sin (5π/2) - 2

     = 3 (-1) - 2

     = -5

Hence the correct option is A.

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Any three lengths that satisfy the triangle inequality theorem can form the sides of a triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In order for three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's consider three lengths: a, b, and c.

To determine if they can form a triangle, we need to check the following conditions:

a + b > c

a + c > b

b + c > a

If all three conditions are true, then the lengths a, b, and c can form a triangle.

For example, let's consider the lengths 3, 4, and 5.

3 + 4 > 5 (True)

3 + 5 > 4 (True)

4 + 5 > 3 (True)

Since all three conditions are true, the lengths 3, 4, and 5 can form a triangle.

Therefore, any three lengths that satisfy the triangle inequality theorem can be the lengths of the sides of a triangle.

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Angle C of the triangle measures 68°.

Side AC = 22.90

Side BC = 14.26

Given triangle,

∠A = 37°

∠B = 75°

AB = 22

Now,

Sum of all the interior angles of triangle is 180.

So,

∠A + ∠B +∠C = 180°

37° + 75° + ∠C = 180°

∠C = 68°

Now,

According to sine rule,

Ratio of side length to the sine of the opposite angle is equal.

Thus,

a/SinA = b/SinB = c/SinC

Let,

BC = a

AC = b

AB = c

So,

a/Sin37 = b/Sin75 = c/Sin68

a/0.601 = b/0.965 = 22/0.927

Solving,

BC = a = 14.26

AC = b = 22.90

Thus with the properties of triangle side length and angles can be calculated.

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" Sum of area of Trapezoid and Semicircle "

its " 1/2 times (sum of parallel sides) times (perpendicular distance between them) "

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times ( 8+ 12) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times (20) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \times 5.5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 \: \: cm {}^{2} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi {r}^{2} }{2} [/tex]

[tex] \textsf{[ diameter (d) = 8 cm, radius (r) = d/2 = 8/2 = 4 cm ]} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{3.14 \times ( {4)}^{2} }{2}[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1.57 \times 16[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 25.12 \: \: cm {}^{2} [/tex]

- Area of Trapezoid + Area of Semicircle

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 + 25.12 = 80.12 \: cm²[/tex]

Answer:

Let’s solve this problem step by step. Since a + b = 28 and a = 2b + 7, we can substitute the value of a in the first equation to get 2b + 7 + b = 28. Solving for b, we get 3b + 7 = 28, which means 3b = 21 and b = 7. So, the second number is 7.

Answer:

The maximum value of the profit function occurs at the corner point with the highest value, which is P2 = 25.

Therefore, the maximum profit is $25.

Step-by-step explanation:

By algebra properties, the simplified form of the trigonometric equation cot² x / (csc x - 1) is  csc x + 1.

In this problem we find the case of a trigonometric equation, whose simplified form must be found. The simplification can be done both by algebra properties and trigonometric formulas. Now we proceed to determine the simplificated form:

cot² x / (csc x - 1)

(csc² x - 1) / (csc x - 1)

[(csc x + 1) · (csc x - 1)] / (csc x - 1)

csc x + 1

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Answer:

[tex]\huge\boxed{\sf h \approx 6.4\ cm}[/tex]

Step-by-step explanation:

Volume = v = 1280 cm³

Radius = r = 8 cm

π = 3.14

Height = h = ?

V = πr²h

Put the given data in the above formula.

Finding height of cylinder.

1280 = (3.14)(8)²(h)

1280 = (3.14)(64)(h)

1280 = 200.96 (h)

1280 / 200.86 = h

[tex]\rule[225]{225}{2}[/tex]

The new coordinates of the triangle after reflecting in the x-axis are:

(3, -1), (3, -3), and (-2, -3).

We have,

The triangle has the coordinates:

(3, 1), (3, 3), and (-2, 3)

Now,

To reflect a point or a shape in the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same.

Let's reflect each of the three given points in the x-axis:

Point (3, 1):

The reflected point in the x-axis will have the same x-coordinate of 3 but with the y-coordinate sign flipped:

Reflected point: (3, -1)

Point (3, 3):

The reflected point in the x-axis will have the same x-coordinate of 3 but with the y-coordinate sign flipped:

Reflected point: (3, -3)

Point (-2, 3):

The reflected point in the x-axis will have the same x-coordinate of -2 but with the y-coordinate sign flipped:

Reflected point: (-2, -3)

Therefore,

The new coordinates of the triangle after reflecting in the x-axis are:

(3, -1), (3, -3), and (-2, -3).

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Tom's estimated travel time is approximately 13.6 hours.

Based on the given scenario, Tom is traveling a distance of approximately 340 nautical miles from Houston to New Orleans by boat. He will be using a medium-sized recreational boat with an average speed of 25 miles per hour.

To estimate the time it will take for his journey, we can use the formula:

Time = Distance / Speed

Substituting the values, we have:

Time = 340 miles / 25 miles per hour

Calculating the division, we find that Tom's estimated travel time is approximately 13.6 hours.

However, it is important to note that this estimate assumes a continuous journey without considering other factors that may affect the travel time. Various elements can impact the actual duration, such as weather conditions, water currents, navigational challenges, refueling stops, and any necessary rest breaks.

Additionally, it is essential for Tom to adhere to all boating regulations and safety guidelines to ensure a smooth and secure voyage.

To obtain a more accurate estimate, Tom should consult local boating authorities, marinas, or experienced sailors familiar with the route.

They can provide valuable insights into the specific conditions and offer guidance on potential challenges that may affect the travel time. Planning for additional buffer time is also recommended to account for unforeseen circumstances and to prioritize safety during the journey.

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The complete question may be like:

Tom plans to travel by boat from Houston, Texas, to New Orleans, Louisiana. He wants to estimate the time it will take for his journey. The distance between the two cities by water is approximately 340 nautical miles. Tom will be traveling on a medium-sized recreational boat that has an average speed of 25 miles per hour. Considering normal weather conditions and assuming a continuous journey, how long will it take Tom to reach New Orleans?

Please provide an answer based on this scenario, taking into account the distance, average speed, and any other relevant factors.

Answer: $1.50 for every 1 pound

Step-by-step explanation:

If 2 pounds equal to $3.00 divide $3.00 by 2 and you end up with $1.50, you can also keep adding $1.50 to get the other prices.

Answer:

Step-by-step explanation:

Hello!

We want to know the area of the original circle - the now circle.

The original circle's diameter is 110 meters.

To figure out the area you use this formula: [tex]r^2*pi[/tex]

The diameter is 107 meters, so the equation is [tex]55^2[/tex][tex]*\pi[/tex].

The area is about 9503.3 meters.

The next area is the "now circle".

The now circle's diameter is 107 meters.

When you use this formula, you end up with  [tex]53.5^2*\pi[/tex].

The area is about 8892 meters.

So it's just basic subtraction!

I'll let you figure out the rest.

:)

Based on the assumption mentioned above, the dimensions of the open box would be:

Length: 5 units

Width: 3.75 units

Height: 2.5 units.

To create an open box as a prop for the school play, Jackson will need three dimensions: length, width, and height. The given dimensions provided are 5, 3.75, and 2.5, but it is not specified which dimension corresponds to which measurement.

To determine which dimension represents which measurement (length, width, or height), we need additional information or clarification. Typically, the length refers to the longest side of the box, the width is the shorter side, and the height is the vertical dimension.

If we assume that 5 represents the length, 3.75 represents the width, and 2.5 represents the height, we can proceed with those dimensions. However, it's important to note that without confirmation or further context, this assumption may not be accurate.

Therefore, based on the assumption mentioned above, the dimensions of the open box would be:

Length: 5 units

Width: 3.75 units

Height: 2.5 units.

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Answer: The value of x = 1  and y = -1

Step-by Step Explanation:

We have 5x + 2y = 3 -----(i)

and 2x + 3y = -1 -----(ii)

By substitution method,

from (i), x = 3-2y/5

Putting the value of x in equation (ii),

we get, 2(3-2y/5) + 3y = -1

6 - 4y/5 + 3y =-1

6 - 4y + 15y = -5

6 - 11y = -5

-11y = -5 - 6

-11y = -11

y = -1

And, x = 3-2(-1)/5

x = 3+2/5

x = 1

Therefore,  x=1 and y=−1

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The number of combinations of the 5 white balls and 1 red ball are possible is 1.

We are given that;

White balls=5

Red ball=1

Now,

To find the number of combinations of 5 white balls and 1 red ball, we can use the combinations formula12:

[tex]nCr = n! / (r! (n-r)!)[/tex]

where n is the total number of objects, r is the number of objects to be selected, and ! is the factorial operator.

we can plug in these values into the formula:

[tex]6C6 = 6! / (6! (6-6)!) 6C6 = 6! / (6! 0!) 6C6 = 1 / (1 1) 6C6 = 1[/tex]

So, there is only one combination of 5 white balls and 1 red ball. This makes sense because the order of selection does not matter in a combination. No matter how we arrange the balls, we will always have the same group of 5 white balls and 1 red ball.

Therefore, by combinations and permutations the answer will be 1.

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Answer:

15

Step-by-step explanation:

Answer: The Mode

Step-by-step explanation:

The mode is the data value that occurs the most often in a data set

Here are two significant advantages of a 401(k) over an IRA:

Higher Contribution Limits: 401(k) plans allow for higher annual contributions compared to IRAs. The contribution limit for a 401(k) is $19,500 (or $26,000 for individuals aged 50 and older), while the limit for an IRA is $6,000 (or $7,000 for individuals aged 50 and older).

Employer Contributions and Matching: 401(k) plans often offer employer contributions and matching programs. Employers may contribute to an employee's 401(k) account, adding to their retirement savings without any direct cost to the employee.

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$27.71 is the amount Steve spend if he shops at S2.

Given that Steve is going shopping

The shopping list of steve has 2 cereal, 4 soups , 2 soda, 1 milk and 4 candy.

We have to find the cost spend by Steve when he purchase in shop 2, S2.

In S2, the cereal cost 2.15, soup cost 2.75, soda cost is 3.00, Milk cost 3.25 and candy costs 0.79.
Total cost = 2×2.15 + 4×2.75+2×3+1×3.25+4×0.79

=4.3+11+6+3.25+3.16

=27.71

Hence, $27.71 is the amount Steve spend if he shops at S2.

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Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value [tex]= $50,000 - $10,000 = $40,000[/tex]

Year 2:

Book value = Initial investment - (2 [tex]\times[/tex] Depreciation expense per year)

Book value [tex]= $50,000 - (2 \times$10,000) = $30,000[/tex]

Year 3:

Book value = Initial investment - (3 [tex]\times[/tex] Depreciation expense per year)

Book value = $50,000 - (3 [tex]\times[/tex] $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 [tex]\times[/tex] Depreciation expense per year)

Book value [tex]= $50,000 - (4 \times $10,000) = $10,000[/tex]

Year 5:

Book value = Initial investment - (5 [tex]\times[/tex] Depreciation expense per year)

Book value [tex]= $50,000 - (5 \times $10,000) = $0[/tex]

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate [tex]\times[/tex] (Salvage value - Book value)

For Year 5:

Tax on salvage value[tex]= 0.30 \times ($10,000 - $0) = $3,000[/tex]

For Year 4 (if scrapped):

Tax on salvage value[tex]= 0.30 \times ($15,000 - $10,000) = $1,500[/tex]

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

[tex]PV = CF / (1 + r)^t[/tex]

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 [tex]= $10,000 / (1 + 0.12)^1 = $8,928.57[/tex]

PV Year 2 [tex]= $0 / (1 + 0.12)^2 = $0[/tex]

PV Year 3 [tex]= $0 / (1 + 0.12)^3 = $0[/tex]

PV Year 4 [tex]= $13,500 / (1 + 0.12)^4 = $9,551.28[/tex]

PV Year 5 [tex]= $7,000 / (1 + 0.12)^5 = $4,474.39[/tex]

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Total Surface Area of the Triangular prism = 30 ft².

Here, we have,

The triangular prism is attached.

The triangular prism shown has 2 triangular faces and 3 lateral faces.

here, we have,

Base of the triangle =2 ft

Height of the Triangle =3 ft

Area of one Triangular Face is:

A = 1/2 * 2 * 3 = 3 ft²

The dimensions of the lateral rectangles are:

2 ft by 3 ft

3 ft by height 3 ft

3 ft by height 3 ft

Therefore, total surface area of the triangular prism

=2(Area of one Triangular Face)+Area of 3 rectangular faces

= 2 *3 + ( 2*3 + 3*3 + 3*3)

= 6 + 24

= 30 ft²

Total Surface Area of the Triangular prism = 30 ft².

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Answer:

They would stop jumping rope at 12:46

Step-by-step explanation:

I'd probably say P.M considering the fact that I don't think kids would be having recess at midnight

The vertical asymptote of the function are x = ±1/2

Given that we need to determine what is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.

This is because division by zero is undefined, and the function may have vertical asymptotes at those points.

The denominator of the function is 4x² - 1.

To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:

4x² - 1 = 0

Adding 1 to both sides:

4x² = 1

Dividing both sides by 4:

x² = 1/4

Taking the square root of both sides:

x = ±√(1/4)

Simplifying further, we get:

x = ±1/2

Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.

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Translation =

What is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.

To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.

Given:

∠A = 50°

∠C = 90°

CB = 16

We can start by finding the measure of ∠B:

∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)

50° + ∠B + 90° = 180°

∠B + 140° = 180°

∠B = 180° - 140°

∠B = 40°

Now, using Sine law

CB/ sin A = AB / sin C

16 / sin 50 = AB / sin 90

16 / 0.766044 = AB

AB = 12.25

Again 12.25 = AC/ sin B

12.25 = AC / sin 40

AC = 19.068

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The value of x in the given right triangle HJK include the following: C. 10.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Hypotenuse, x = 5 × 2

Hypotenuse, x = 10.

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