Let r = 1+ cos be a polar curve. Find all values of 0 where the graph has vertical tangent lines.

The exact x-coordinate of the point  is frac{1163}{291}6

The curve is given by {x = t² + 1, y = t² - t}.

Let's find dy/dx in terms of t as follows:

frac{dy}{dx} = frac{dy/dt}{dx/dt} = frac{(2t - 1)}{(2t)} = 1 - frac{1}{2t}

Therefore, when dy/dx = 27, we have:

1 - frac{1}{2t} = 27

Rightarrow 2t - 1 = frac{2}{27}

Rightarrow t = frac{29}{54}

The x-coordinate is given by x = t² + 1, therefore, we have:

x = left(frac{29}{54}right)^2 + 1

= frac{1163}{2916}

Hence, the exact x-coordinate of the point on the curve where the tangent line has slope 27 is frac{1163}{291}6

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There are 800 million possible different 10-digit phone numbers that can be created in the USA.

In the NANP (North American Numbering Plan), the numbers are ten digits in length and follow the format nxx-nxx-xxxx. Here, 'n' can be any digit from 2 to 9, and 'x' can be any digit from 0 to 9.

The first three digits are known as the Numbering Plan Area (NPA) code, also referred to as the area code. There are currently 800 area codes available, meaning that not all three-digit combinations can be used as area codes. Some combinations are reserved for future use.

To calculate the number of possible different 10-digit phone numbers that can be created in the USA, we need to consider the possibilities for each digit:

- For the first digit (n): There are 8 possible choices (2 to 9).
- For the second and third digits (n): There are 10 possible choices for each digit (0 to 9).
- For the remaining seven digits (x): There are 10 possible choices for each digit (0 to 9).

Therefore, the total number of possible different 10-digit phone numbers in the USA can be calculated as follows:

8 (choices for the first digit) * 10 (choices for the second digit) * 10 (choices for the third digit) * 10^7 (choices for the remaining seven digits) = 8 * 10 * 10 * 10,000,000 = 800,000,000.

So, there are 800 million possible different 10-digit phone numbers that can be created in the USA.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The percentage rate of the discount is 11.11%.

To calculate the percentage discount, we need to find the difference between the original price and the marked down price and express it as a percentage of the original price.

The marked down price of the suit is:

$360 - $40 = $320

The discount amount is $40, and the original price is $360, so the discount rate is:

Discount rate = (discount amount / original price) x 100%

Discount rate = ($40 / $360) x 100%

Discount rate = 11.11%

Therefore, the percentage rate of the discount is 11.11%.

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Answer: -2

your welcome :)

Answer: 124.3%

Step-by-step explanation:

318.2/256=1.24296875

1.24296875*100=124.296875

124.296875=124.3%

Since 318.2 is greater than 256, the percent is going to be greater than 100, because the number 318.2 is more than 100 of 256 which basically translates to 318.2 being greater than 256.

1a)The values of l range from 0 to (n-1), so for n = 3, l can have the values 0, 1, and 2.

b) The values of m can be -2, -1, 0, +1, and +2

c) There are a total of 9 orbitals

The qualities and traits of quantum systems, like the electrons in atoms, are described by a set of numbers known as quantum numbers. They offer knowledge on the system's energy, angular momentum, orientation, and spin, among other characteristics.

Using the formula, number of electrons = \(n^2\)

Number of electrons =\(3^2 = 9\)

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The cafeteria earned $945 from all of the lunches sold on Friday.

percentage, a relative value indicating hundredth parts of any quantity.

Let us calculate the number of students who bought each pizza.

Number of students who bought cheese pizza = 50% of 270 = 0.5 x 270 = 135

Number of students who bought pepperoni pizza = 40% of 270 = 0.4 x 270 = 108

Total lunches sold = Number of cheese pizzas sold + Number of pepperoni pizzas sold + Number of fried chicken sold

= 135 + 108 + 27

= 270

Therefore, a total of 270 lunches were sold on Friday.

To calculate how much money the cafeteria earned from all of the lunches, we can multiply the total number of lunches sold by the cost of each lunch:

Total earnings = Total lunches sold x Cost per lunch

= 270 x $3.50

= $945

Therefore, the cafeteria earned $945 from all of the lunches sold on Friday.

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Fixed overheads are allocated to products on the number of litres of ice cream produced, irrespective of the size of the output. Liters Rands Expected Sales :500 ml ice cream = 60,000 litres

= 60,000 x R10

= R 600,0001 litre

ice cream = 80,000

litres = 80,000 x R 15 = R1,200,000

Total expected sales volume 140,000 litres R1,800,000 . From the given question, we are told that inventory is valued on the basis of equivalent units of inventory. Which means that two 500ml of ice cream is valued the same as one litre of ice cream. We are also told that variable overheads vary with direct labour hours. Fixed overheads are allocated to products on the number of litres of ice cream produced, irrespective of the size of the output.

Using this information we can prepare a sales budget for the company by estimating the sales volume in litres for each of the two sizes of ice cream containers and multiplying the sales volume by the respective sale price of each size. Since the number of litres is used to allocate fixed overheads, it is necessary to prepare the budget in litres as well. The total expected sales volume can be calculated by adding up the expected sales volume of the two sizes of ice cream products. The expected sales volume of 500 ml ice cream is 60,000 litres (500 ml x 0.12 million) and the expected sales volume of 1 litre ice cream is 80,000 litres (1 litre x 0.08 million). Adding up the two volumes, we get a total expected sales volume of 140,000 litres.

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In a tesselation of the plane with congruent equilateral triangles, each vertex is shared by six triangles.

This can be visualized by imagining a single equilateral triangle as the center, surrounded by six other equilateral triangles that share a common vertex with the central triangle. Therefore, in this type of tesselation, each vertex is surrounded by six neighboring triangles.

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The Domain is 0 ≤ x ≤ 4 and Range is 0 ≤ y ≤ 80.

The range of values that we are permitted to enter into our function is known as the domain of a function.  A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

We know that the domain of a function is the set of values that we are allowed to plug into our function.

From the Graph the x values ranges from 0 to 4.

So, domain is 0 ≤ x ≤ 4.

and, the range is the corresponding output for the input

From the Graph the y values ranges from 0 to 80.

So, Range is 0 ≤ y ≤ 80.

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Answer:

a: 6 b: 9 c: 6

Step-by-step explanation:

a: 10-2x2=6

b:10-2 1/2=9

c: 10-2x-2=6

Answer:

A. 6

B. 9

c. 14

Step-by-step explanation:

A. plug in 2 to x in the given equation: 10 - 2(2)

multiply first: 10 - 4

solve: 6

B. plug in 1/2 to the given equation: 10 - 2(1/2)

multiply first: 10 - 1

solve: 9

C. plug in -2 to the given equation: 10 - 2(-2)

multiply first (remember a - times a - is a +): 10 + 4

solve: 14

The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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Answer:

yes 1/6 is a rational number.

Answer:

400 students voted in the election

Step-by-step explanation:

Given:

Total number of votes received by Priscilla = 240

This was 60% of the students who voted in the election.

To find: Total number of students who voted in the election

Solution:

Total number of votes received by Priscilla = 60% of Total number of students who voted in the election

240 = 60% of Total number of students who voted in the election

240 = \(\frac{60}{100}\) × Total number of students who voted in the election

So,

Total number of students who voted in the election \(=\frac{240(100)}{60}=400\)

Answer:

16+2x is your answer

Step-by-step explanation:

2 Simplify 4\times 34×3 to 1212.

16-7x+12-2-3\times 2+9x-416−7x+12−2−3×2+9x−4

3 Simplify 3\times 23×2 to 66.

16-7x+12-2-6+9x-416−7x+12−2−6+9x−4

4 Collect like terms.

(16+12-2-6-4)+(-7x+9x)(16+12−2−6−4)+(−7x+9x)

5 Simplify.

16+2x16+2x

Done

Answer:

4, -3

Step-by-step explanation:

The quadratic formula is \(\frac{-b+-\sqrt{b^2-4ac} }{2a}\).

When using the formula for both the negative and positive value of the sqrt, you will get:

x = 4, -3

The probability that exactly 17 households own a DVD player is 0.0124.

Given:

The probability that a house hold in centercity owns a DVD player is = 53%.

So, p = 0.53

The probability that a house hold in centercity does not own a DVD player is = 100% - 53% = 47%

So, q = 0.47

The sample size is 22 households in the city.

So, n = 22

We have to calculate the probability that exactly 17 households own a DVD player.

So, r = 17

The formula to be used in binomial experiment is:

P (r) = \(\frac{n!}{r! (n -r)!}\) × \(p^{r}\) ×\(q^{n-r}\)

The probability that exactly 17 households own a DVD player will be,

= \(\frac{22!}{17! (22 - 17)!}\) × \(0.53^{17}\) ×\(0.43^{22-17}\)

= \(\frac{22!}{17! (5)!}\)× \(0.53^{17}\) ×\(0.43^{5}\)

= 0.0124

Therefore, the probability that exactly 17 households own a DVD player is 0.0124.

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Answer:33.cm

34cm

Step-by-step explanation:

yes

Answer:

\(\frac{20}{x^2 + 10x+24}\)

Step-by-step explanation:

common denominators : (x+6)(x+4)

numerators become difference of squares

\(x^2 -16\)   and   \(x^2-36\)  

\(x^2 -16\)   -   \(x^2-36\)   = 20

(x+6)(x+4) = \({x^2 + 10x+24}\)

Answer:

i hope it will help you thank u

Answer:

\(f(x)=\frac{4}{5}x-5\)

Step-by-step explanation:

Solution is below as well as graph for proof

Answer:

82 degrees

Step-by-step explanation:

The sum of all angle measurements of a 7 sided polygon is 900 degrees, and the sum of all expressed degrees is 818. 900-818= 82 degrees

Answer:

the 4th option is correct

Step-by-step explanation:

thank you

Answer:

x= -45

Step-by-step explanation:

Subtract 5 from both sides first

Simplify it

Multiply both sides by 3

Simplify it again

Divide both sides by -2

your answer would be x= -45

The estimation of the equation 1/6 + 5/6  is 1 (option C).

For rounding a fraction to the nearest whole number, use the "rounding half up" rule if necessary.

To estimate the solution for the equation 1/6 + 5/6, we can round each fraction to the nearest whole number.

The fraction 1/6 is closer to 0 than it is to 1, so we will round it to 0.

The fraction 5/6 is closer to 1 than it is to 0, so we will round it to 1.

Now we can estimate the solution for the equation as follows:

0 + 1 = 1

Therefore, the estimated solution for the equation 1/6 + 5/6 is 1.

The correct answer is C. 1.

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Equivalent expressions are expressions that have the same value.

The equivalent expression of \(g^{-3}h\) is: \(\frac{h}{g^3}\)

The expression is given as;

\(g^{-3}h\)

Apply law of indices to change the exponents

\(g^{-3}h = \frac{1}{g^3}h\)

Express as products

\(g^{-3}h = \frac{1}{g^3} \times h\)

Rewrite as

\(g^{-3}h = \frac{h}{g^3}\)

Hence, the equivalent expression is: \(\frac{h}{g^3}\)

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Answer:

Step-by-step explanation:

Step one:

given data

we are told that the total amount made is $700

If Frederick receives $175 from the amount made the balance left to share is

=700-175

=$525

Step two:

Hence the five band members will share $525

each of them will receive

=525/5

=$105

Answer:

3.8 foot

Step-by-step explanation:

with reference angle 31

perpendicular (p)= x

base(b) = 6.3

tan 31 = p/b

0.6 = x/6.3

x = 3.8 foot

Answer:

First number = 60 and another number = 48

Step-by-step explanation:

Let two numbers are 5x and 4x.

The two number are differ by 12. We need to find the numbers.

ATQ,

5x-4x = 12

x = 12

Now first number = 5x

= 5(12)

= 60

Other number = 4x

= 4(12)

= 48

Hence, the numbers are 60 and 48.

Answer:

The dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

Step-by-step explanation:

The formula for the perimeter of a rectangle = 2(L + W)

= 2L + 2W

The perimeter = 46 mm

L = 3x + 3

W = x - 4

P = 2L + 2W

46mm = 2(3x + 3) + 2(x - 4)

46 = 6x + 6 + 2x - 8

Collect like terms

46 +8 -6 = 6x + 2x

48 = 8x

x = 48/8

x = 6

Since the Length = 3x + 3

= 3(6) + 3

= 18 + 3

= 21mm

Since the Width = x - 4

= 6 - 4

= 2mm

Therefore, the dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.