Find the derivative of the vector function
r(t)=ln(17−t^2)i+√16+tj−7e^{−8tk}

Variable - These are the unknown quantities that expected to estimate it as an output.

Example:- In an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a Decision variable.

Constraints - the restrictions on the variable open linear programming problem are called constraints.

The conditions x ≥ 0, y ≥ 0 called non negative restrictions.

Objective equation - the objective equation should be specified in a quantitative way.

It is of the form Z = ax + by

where x and y are decision variable.

Z is to be maximized or minimized to find the solution.

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Oh my gosh I hate math, do you

Step-by-step explanation:

thus the speed off the walk way is 5 ft/s

the speed of the moving walkway is 3 ft/s

Answer:

(-2,4)

Step-by-step explanation:

Hope this will help:)

Answer:

B (-2,4)

Step-by-step explanation:

The fractional equivalent of the repeating decimal 0.2 is 2/9

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

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

Two thirds of a bag.

Step-by-step explanation:

1/2 * 2 = 1

1/3 * 2 = 2/3

Hope this helped!

Answer:

slope is 4 over 7

Step-by-step explanation:

.......

Answer:

its b

Step-by-step explanation:

y being the total equals 9.50 times x beacause is how many cars he washed and the plus 50 is the money his mom gave him

Answer:

b

Step-by-step explanation:

Answer: =2x²y³+3y.

Step-by-step explanation:

\(\frac{14x^5y^4+21x^3y^2}{7x^3y} =\frac{7x^3y*(2x^2y^3+3y)}{7x^3y}= 2x^2y^3+3y.\)

Answer:

Step-by-step explanation:

2 × 2 = 4

4 + 3 = 7

denominator stays the same so 7/2 is the answer

When slave starting a disabled vehicle, the term that serves an important safety consideration is c. The slaving vehicle engine must be running while connecting the slave cable

The dead car is started while the live vehicle's engine is running by inserting a slave cable into the receptacle on each vehicle.

Vehicles with manual transmissions rely heavily on the clutch slave cylinder. When the pedal is depressed, the clutch is disengaged and the transmission is shifted thanks to the slave and clutch master cylinders.

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Answer: 6,192 paperclips, 3,826 paperclips

Step-by-step explanation:

a) To find the sum of all the children's paperclips, you must find each of them.

First, to start off, create some equations that represent this information:

k = j * \(\frac{6}{7}\)

m = 3k

m = j + 2552

Then, for starts you can use the equation m = 3k and plug in for the variables

m = 3k

(j+2552) = 3(j * 6/7)

j + 2552 = 3j + 2.57

2549.43 = 2j

j = 1274.715

j = 1274 (round down because you can't have a fraction of a paper clip)

Next, use j to solve the other equations

m = j + 2552

m = 1274 + 2552

m = 3826

k = j * 6/7

k = 1274 * 6/7

k = 1092

sum = k + j  + m

sum = 1092 + 1274 + 3826

sum = 6,192 paperclips

b) We already know m, which is 3826.

3,826 paperclips

Answer:

y = 3/2x-14

Step-by-step explanation:

      The given line is y=-2/3x. So, the slope of the given line is -2/3.

Now, we have to find the perpendicular line to y= -2/3x passing through the point (4,-8).

       The product of two perpendicular lines is -1.

m1.m2 = -1.

-2/3.m2= -1

m2 = 3/2

        Now, we need to find the equation of the line passing through the point (4,-8) with slope 3/2.

The equation of slope-point form is (y-y1) = m(x-x1)

        y-(-8) = 3/2 (x-4)

        y+8 = 3/2x -6

Now, we have to add 6 on both sides.

        y + 8 + 6 = 3/2x - 6 + 6.

        y + 14 = 3/2x

        y = 3/2x - 14.

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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The correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism.

A trisomic organism is one that has an extra copy of a chromosome in its genome. This means that it has three copies of a particular chromosome instead of the usual two, which can have significant implications for the organism's development and health.

In terms of algebraic notation, the chromosome number of a trisomic organism would be denoted as 2n+1, where "n" represents the normal diploid number of chromosomes for that organism. The "2n" represents the normal two sets of chromosomes, and the "+1" represents the extra chromosome.

Therefore, the correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism. It is important to note that trisomies can occur for any chromosome, not just the sex chromosomes, and can have varying effects depending on which chromosome is affected.

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A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, we can be multiply two polynomials step by step.

Distribute each term of the first polynomial to every term of the second polynomial.

Combine like terms by adding the coefficients of the terms that have the same variables raised to the same powers.

Simplify the result by arranging the terms in descending order of the exponent of the variable.

For example, let's say you want to multiply (2x + 3) and (x - 4):

(2x + 3) * (x - 4) = 2x * x - 2x * 4 + 3 * x - 3 * 4

Simplify the terms: 2x^2 - 8x + 3x - 12

Combine like terms: 2x^2 - 5x - 12

Therefore, the product of (2x + 3) and (x - 4) is 2x^2 - 5x - 12.

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The concentration of calcium in a water sample can be converted to meq/L and mg/L as CaCO3 by utilizing the molar mass of calcium and calcium carbonate.

Step 1: Calculate the moles of calcium present in the water sample.

Given:

Concentration of calcium, C_ca = 100 mg/L

Molar mass of calcium, M_ca = 40 g/mol

Convert mg to g:

Concentration of calcium, C_ca = 100 mg/L = 0.1 g/L

Calculate moles of calcium:

Moles of calcium = C_ca / M_ca

Step 2: Convert moles of calcium to meq.

Molar mass of calcium = 40 g/mol

Valence of calcium = 2 (since calcium forms Ca2+ ions)

Moles of calcium = Moles of calcium / Valence

Step 3: Convert meq/L to mg/L as CaCO3.

Molar mass of calcium carbonate (CaCO3) = 40 g/mol (for Ca) + 12 g/mol (for C) + 3 * 16 g/mol (for O) = 100 g/mol

Moles of calcium carbonate = Moles of calcium / Valence

Convert moles to mg:

Concentration of calcium carbonate = Moles of calcium carbonate * Molar mass of calcium carbonate

By following these steps and plugging in the appropriate values, you can calculate the concentration of calcium in meq/L and mg/L as CaCO3.

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Work Shown:

48w+23

48*3+23

144+23

167

It takes 167 minutes to cook 3 kg of meat.

Convert this to hours+minutes format.

167 min = 120 min + 47 min

167 min = 120/60 hr + 47 min

167 min = 2 hr + 47 min

Answer:

The partial sums are increasing in value.

The series converges to the same value as what the partial sums approach.

The partial sums appear to approach 0.33.

The series might converge to One-third.

Step-by-step explanation:

Answer:

The partial sums are increasing in value.

The series converges to the same value as what the partial sums approach.

The partial sums appear to approach 0.33.

The series might converge to One-third.

Step-by-step explanation:

A firm should record an impairment in the value of property, plant, or equipment by reducing the carrying amount of the asset and recognizing the impairment loss as an expense in the financial statements.

When the value of property, plant, or equipment is impaired, meaning its recoverable amount is lower than its carrying amount, a firm should recognize this impairment in its financial statements. The impairment is recorded by reducing the carrying amount of the asset to its recoverable amount, which is the higher of its fair value less costs to sell or its value in use. The difference between the carrying amount and the recoverable amount is recognized as an impairment loss and recorded as an expense in the income statement. This adjustment reflects the decrease in the value of the asset and allows the firm to accurately report its financial position and performance.

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Two sample t-tests are designed to learn if there is support for a relationship between variables when there are two independent groups and we want to compare their means.

Specifically, the two sample t-test is used to determine whether the means of two groups are significantly different from each other. The test is based on the assumption that the populations from which the samples are drawn are normally distributed, and that the variances of the two populations are equal.

If these assumptions are met, we can use the two sample t-test to test the null hypothesis that the means of the two groups are equal. The test produces a t-statistic and a p-value, which can be used to determine whether the null hypothesis should be rejected or not.

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\(x = - \frac{45}{2} \)

\( \frac{1}{2} x - \frac{1}{4} = \frac{3}{5} x + 2\)

\(20( \frac{1}{2} x - \frac{1}{4} ) = 20( \frac{3}{5} x + 2)\)

\(20 \times \frac{1}{2} x - 20 \times \frac{1}{4} = 20( \frac{3}{5} x + 2)\)

\(10x - 20 \times \frac{1}{4} = 20 \times \frac{3}{5} x + 20 \times 2\)

\(10x - 5 = 20 \times \frac{3}{5} x + 20 \times 2\)

\(10x - 5 = 4 \times 3x + 20 \times 2\)

\(10x - 5 = 4 \times 3x + 40\)

\(10x - 5 - 12x = 40\)

\(10x - 12x = 40 + 5\)

\( - 2x = 40 - 5\)

\( - 2x = 45\)

\(x = - \frac{45}{2} \)

3x1=3 add three 0's = 3000

If the new number is four times the reciprocal of the original number, then  the original number is 0.02.

Let us assume the original positive decimal number is = "x".

When we move the decimal point of x four places to the right,

We get,  "10000x", which is four times the reciprocal of x.

So, equation can be written as;

⇒ 10000x = 4(1/x),

On simplifying the equation,

We get,

⇒ 10000x² = 4,

Dividing both sides by 10000,

We get,

⇒ x² = 0.0004,

Simplifying further,

We get,

⇒ x = 0.02

Therefore, the original positive decimal number is 0.02.

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Answer:

Step-by-step explanation:

(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

Step-by-step explanation:

Approximate area is about 50 units²

The closest option is the last one

Answer:I have no clue

Step-by-step explanation:

So basically I have no clue