Given f(x)=x-10tan ¹x, find all critical points and determine the intervals of increase and decrease and local max/mins. Round answers to two decimal places when necessary. Show ALL your work, including sign charts or other work to show signs of the derivative. (8 pts) 14. Given a sheet of cardboard that is 6x6 inches, determine the dimensions of an open top box of maximum volume that could be obtained from cutting squares out of the corners of the sheet of cardboard and folding up the flaps

Step-by-step explanation:

\( {9}^{ - 53} . {9}^{37} \)

To solve this question we use the rules of indices

Since the bases are the same and are multiplying we add the exponents using the formula

So for the above question we have

We have the final answer as

Which is the same as

Hope this helps you

Answer:

4/5

Step-by-step explanation:

3 x 5 get you 20 and 20 x 45 gets you 80 covert it into a fraction 4/5

Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

The correct answer is option (e). The sum of the lengths in inches of all of its interior diagonals is 40√2.

The surface area of a rectangular box can be expressed as 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the box, respectively. Since the total surface area is 94 square inches and the sum of the lengths of all its edges is 48 inches, we can write an equation using these variables. Solving for l, w, and h, we find that the length, width, and height are 6, 7, and 4 inches, respectively.

The sum of the lengths of all interior diagonals can then be found using the Pythagorean theorem. The result is,

√(l^2 + w^2 + h^2) = √(6^2 + 7^2 + 4^2)

= √(36 + 49 + 16)

= √101

= 10√2.

The sum of the lengths of all interior diagonals is then equal to 2(10√2) = 40√2.

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The amount accumulated after investing a principal P for t years at an interest rate compounded annually is  $46,057.58.

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

Therefore, let's find the amount accumulated after investing a principal P for t years at an interest rate compounded annually.

\(A = p(1 + \frac{r}{n} )^{nt}\)

where

p = 15,500

r = 9.5%

t = 12

n = 1

\(A = 15500(1 + \frac{0.095}{1} )^{1(12)}\)

A = 15,500.00(1 + 0.095)¹²

A = $46,057.58

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$46,057.58, answer for acellus

Answer:

  4 m

Step-by-step explanation:

The circumference of a circle is the product of π and the diameter.

  C = πd

  12.56 m = 3.14d

  d = 12.56 m/3.14 = 4 m

The rug's diameter is 4 meters.

Answer:

x2 + x + 1

Step-by-step explanation:

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial . Example 1: x2+x+1. (:

The area of the rectangle is 43.75 square centimeters, and we get that by using the area formula:

A = L*W

A rectangle is defined only by two dimensions, which are length and width if we define the variables:

L = length of the rectangle

W = width of the rectangle

Then the area of the rectangle is given by the formula:

A = L*W

Here we know that the dimensions of the rectangle are 12.5 cm and 3.5 cm, so we can define:

L = 12.5cm

W = 3.5cm

Replacing that in the formula for the area we get:

A = (12.5cm)*(3.5cm) = 43.75 cm^2

That is the area of the rectangle.

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Answer:

D

Step-by-step explanation:

one third of 15 is 5

15 + 5 = 20

Student B is 20 years old, 5 years older than student A

10 years ago, Student B was 10 and Student A was 5.

The number of years ago was student B twice as old as student A should be 10 when the student A age is given.

Since

Student A is 15 years old. Student B is one-third older

One-third of 15 should be 5

So, total be like

= 15 + 5

= 20

So, the number of years  be like

= 20 - 10

= 10

hence, The number of years ago was student B twice as old as student A should be 10.

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The probability that this ball is red after the jar is then shaken and one ball is randomly selected is 11/18.

There are four red balls and two white balls in a jar

P(white removed and then red is chosen)'

P = 2/6 * 5/6

= 10/36

P= 5/18

Probability that the white removed and then red is chosen is 5/18.

P(red removed and then white is chosen)

P = 4/6 * 1/2

= 4/12

= 1/3

P = 6/18

Probability that the red removed and then white is chosen is 6/18.

The probability that this ball is red,

P(red is chosen) = 5/18 +6/18 = 11/18

Therefore, The probability that this ball is red is 11/18.

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Answer:

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since the volume of oil in the tank is directly proportional to the depth of the oil, we can calculate the amount of oil left in the tank when it is 3 feet deep using a simple ratio.

First, we need to convert the tank's capacity from gallons to cubic feet because our measurements are in feet. According to the U.S. liquid gallon to cubic foot conversion, 1 gallon is approximately 0.133681 cubic feet. So, the tank's total volume in cubic feet is 620 gallons * 0.133681 cubic feet/gallon.

Let's denote the total volume of the tank as V_total and the remaining volume when the tank is 3 feet deep as V_remaining.

V_total = 620 * 0.133681 cubic feet.

Given that the total height (h_total) of the tank is 8 feet and the remaining height (h_remaining) is 3 feet, we can set up the following proportion:

h_remaining / h_total = V_remaining / V_total.

By cross-multiplying and solving for V_remaining, we can find the remaining volume in the tank when it's 3 feet deep. Then, we convert this volume back to gallons by dividing by 0.133681.

Let's calculate that.

Apologies for the confusion; I made a mistake. I can't execute calculations directly in this manner. I'll carry out the calculations below instead:

The total volume of the tank in cubic feet is:

V_total = 620 gallons * 0.133681 cubic feet/gallon = 82.9022 cubic feet.

The remaining volume when the tank is 3 feet deep can be calculated with the proportion:

h_remaining / h_total = V_remaining / V_total.

After cross-multiplying and solving for V_remaining, we have:

V_remaining = (h_remaining / h_total) * V_total = (3 ft / 8 ft) * 82.9022 cubic feet = 31.0941 cubic feet.

Then, we convert this volume back to gallons by dividing by 0.133681:

V_remaining_gal = 31.0941 cubic feet / 0.133681 = 232.63 gallons.

Rounding to the nearest whole number, approximately 233 gallons remain in the tank when the depth of the oil is 3 feet.

Answer:

2.88x=7.2

x=7.2/2.88

x=2.5

=)

Answer:

x=4

Step-by-step explanation:

btw that's what M a t h w a y.

Answer:

Option D) the same line.

Step-by-step explanation:

That's your answer. Have a good night.

The probability of winning by picking the number 30 in roulette is 1/38.

In the game of roulette, the wheel consists of 38 spaces, with numbers 0 through 36 and an additional space marked 00. When you pick a specific number, such as 30, the probability of that number coming up on the wheel can be determined by calculating the ratio of favorable outcomes to the total number of possible outcomes.

In this case, there is only one favorable outcome, which is the ball landing on the number 30. The total number of possible outcomes is 38 since there are 37 numbered spaces (0 through 36) and one additional space for 00. Therefore, the probability of winning by picking the number 30 is 1 out of 38.

To put it simply, if you were to play roulette many times, you would expect the number 30 to come up approximately once every 38 spins on average. This probability remains the same for each individual spin, as each spin of the roulette wheel is an independent event.

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Based on the projected sales of 1,400 total vehicles for the next year, the demand for each season can be determined. The demand for each season is as follows: 350 vehicles in winter, 350 vehicles in spring, 175 vehicles in summer, and 525 vehicles in fall.

To calculate the demand for each season, we can use the past sales data as a reference. In the past, the dealership sold an average of 1,200 vehicles each year. However, in the past two years, the sales figures were 220 and 260 in winter, 350 and 300 in spring, 150 and 160 in summer, and 300 and 660 in fall.

To estimate the demand for each season based on the projected sales of 1,400 vehicles for the next year, we can calculate the proportion of each season's sales compared to the total sales in the past. This gives us the following estimates: 350 vehicles in winter (25% of 1,400), 350 vehicles in spring (25% of 1,400), 175 vehicles in summer (12.5% of 1,400), and 525 vehicles in fall (37.5% of 1,400).

These estimates are based on the assumption that the sales distribution in the future will be similar to the past trends. However, it's important to note that actual market conditions and other factors may influence the demand for each season, so these estimates should be used as a rough guide and may require adjustment based on specific circumstances.

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Answer:

\(y=-3x^{2} +6x+18\)

Step-by-step explanation:

\(y=ax^{2} +bx+c\)

Substitute the three points we have.

\(21=a+b+c\\18=4a+2b+c\\9=a-b+c\\\)

Take the first less the third.

\(2b=12\\b=6\)

\(15=a+c\\6=4a+c\\15=a+c\\\)

Take the second and subtract the first.

\(-9=3a\\a=-3\)

Therefore, we can calculate c.

\(c=18.\)

Therefore, our equation is \(y=-3x^{2} +6x+18\)

The magnetic field $H$ in the interface between region 1 and region 2 is $2.7a$ mWb/m$^2$, and the angle it makes with the positive $x$-axis is $\arctan(\frac{1.8}{2.7}) = \boxed{33^\circ}$.

The magnetic field in region 1 is given by $B = 2.5a_x + 6a_z$ mWb/m$^2$, and the magnetic field in region 2 is given by $B = 4.2a_x + 1.8a_z$ mWb/m$^2$. The interface between the two regions is defined by $z = 0$.

We can use the boundary condition for magnetic fields to find the magnetic field at the interface:

B_1(z = 0) = B_2(z = 0)

Substituting the expressions for $B_1$ and $B_2$, we get:

2.5a_x + 6a_z = 4.2a_x + 1.8a_z

Solving for $H$, we get:

H = 2.7a

The angle that $H$ makes with the positive $x$-axis can be found using the following formula:

tan θ = \frac{B_z}{B_x} = \frac{1.8}{2.7} = \frac{2}{3}

The angle θ is then $\arctan(\frac{2}{3}) = \boxed{33^\circ}$.

The first step is to use the boundary condition for magnetic fields to find the magnetic field at the interface. We can then use the definition of the tangent function to find the angle that $H$ makes with the positive $x$-axis.

The boundary condition for magnetic fields states that the magnetic field is continuous across an interface. This means that the components of the magnetic field in the two regions must be equal at the interface.

In this case, the two regions are defined by $z = 0$, so the components of the magnetic field must be equal at $z = 0$. We can use this to find the value of $H$ at the interface.

Once we have the value of $H$, we can use the definition of the tangent function to find the angle that it makes with the positive $x$-axis. The tangent function is defined as the ratio of the $z$-component of the magnetic field to the $x$-component of the magnetic field.

In this case, the $z$-component of the magnetic field is 1.8a, and the $x$-component of the magnetic field is 2.7a. So, the angle that $H$ makes with the positive $x$-axis is $\arctan(\frac{1.8}{2.7}) = \boxed{33^\circ}$.

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Answer:

$500.92

Step-by-step explanation:

The question asks for the asking price of a three-acre lot on a lake, given that it is priced at $200 per front foot and has a depth of 1,000 feet. The options provided are A. $13,068, B. $19,666, C. $26,136, and D. $43,560. We need to calculate the total price based on the front footage of the lot.

To calculate the asking price of the lot, we need to determine the total front footage and multiply it by the price per front foot. Given that the lot has a depth of 1,000 feet, we can calculate the front footage by dividing the total area (in acres) by the depth and converting it to front feet.

Since three acres equal 3 * 43,560 square feet (one acre equals 43,560 square feet), the total area of the lot is 130,680 square feet. To find the front footage, we divide the total area by the depth:

Front footage = Total area / Depth = 130,680 / 1,000 = 130.68 feet.

Finally, we multiply the front footage by the price per front foot to determine the asking price:

Asking price = Front footage * Price per front foot = 130.68 * $200 = $26,136.

Therefore, the correct answer is C. $26,136, as it represents the asking price for the three-acre lot on the lake.

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Answer:

1a) 9+9+9+9=36

b) 9×9=81. Hope this helped

AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE

Translation is a type of transformation that involve a linear movement.

The translation rule is gotten by comparing the points as below

preimage point A (1, 7) and B (5, 4)

image points D(-6, -2) and E(-2,-5)

x coordinate

using point A and D = -6 - 1 = -7

using point B and E = -2 - 5 = -7

y coordinate

using point A and D = -2 - 7 = -9

using point B and E = -5 -  = -9

Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B

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To find the subtransient current in per unit for a three-phase fault on bus 4, we need to calculate the fault current using the bus impedance matrix.

Given bus impedance matrix Zbus:

| j0.15 j0.08 j0.04 j0.07 |

| j0.08 j0.15 j0.06 j0.09 |

| j0.04 j0.06 j0.13 j0.05 |

| j0.07 j0.09 j0.05 j0.12 |

To find the fault current on bus 4, we need to find the inverse of the Zbus matrix and multiply it by the pre-fault voltage vector.

The pre-fault voltage vector V_pre-fault is given as:

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Let's calculate the inverse of the Zbus matrix:

Zbus_inverse = inv(Zbus)

Now, we can calculate the fault current using the formula:

I_fault = Zbus_inverse * V_pre-fault

Calculating the fault current, we have:

I_fault = Zbus_inverse * V_pre-fault

Substituting the values and calculating the product, we get:

I_fault = Zbus_inverse * V_pre-fault

= Zbus_inverse * | 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Please provide the values of the Zbus matrix and the pre-fault voltage vector to obtain the specific values for the fault current and the per-unit current from generator 2.

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Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

The reciprocals of any two consecutive integers have a product that is equal to the reciprocal of the smaller integer minus the reciprocal of the larger integer is proved.

The reciprocal of n is 1/n, and the reciprocal of n+1 is 1/(n+1).

We want to prove that the product of the reciprocals is equal to the reciprocal of the smaller integer minus the reciprocal of the larger integer:

(1/n) × (1/(n+1)) = 1/n - 1/(n+1)

Let's find a common denominator for the right side of the equation:

(1/n) × (1/(n+1)) = (1/n) × (n+1)/(n+1) - (1/(n+1)) × n/n

= (n+1)/(n(n+1)) - n/(n(n+1))

Now, we can combine the fractions on the right side:

= (n+1 - n)/(n(n+1))

= 1/(n(n+1))

We have successfully simplified the right side of the equation to 1/(n(n+1)).

Now, let's compare it to the left side of the equation:

(1/n) × (1/(n+1)) = 1/(n(n+1))

Both sides of the equation are equal, so we have proven that the product of the reciprocals of any two consecutive integers is equal to the reciprocal of the smaller integer minus the reciprocal of the larger integer:

(1/n) × (1/(n+1)) = 1/n - 1/(n+1)

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Answer:

True

Step-by-step explanation:

The given statement "John Graunt is said to be the first to employ quantitative methods to describe population vital statistics" is true as he was interested in how various factors affected mortality rates and population growth.

Quantitative methods are used to quantify and assess data. These techniques are employed by statisticians and scientists in a variety of fields, including psychology, economics, and public health. Quantitative data can be transformed into statistical analyses to make sense of patterns, patterns, and relationships.

John Graunt was a London haberdasher who lived from 1620 to 1674. He is known as the father of vital statistics, and he was the first to employ quantitative methods to describe population vital statistics.

Graunt was interested in how various factors affected mortality rates and population growth, and he used statistical methods to investigate these issues.

In summary, John Graunt is said to be the first to employ quantitative methods to describe population vital statistics.

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