What substitution should be used to rewrite x8 â€"" 3x4 2 = 0 as a quadratic equation? u = x2 u = x4 u = x8 u = x16.

Answer:

f (x,y) = sin (x,y)  & points = (1,0)

Maximum  rate of change in f at given point & direction = 1

Step-by-step explanation:

The function & points are not given,

Considering them as general example : f (x,y) = sin (x,y) & points = (1,0)

Maximum rate of change in f (x,y) happens in direction of ∇ f (1,0)

∇  f (x,y) =  [ df / dx ,  df/ dy ]

= [ y cos (xy) , x cos (xy) ]

∇ f (1,0)  = [ 0, cos (0) ] = (0,1)

Magnitude at (1,0) = ∇ f (1,0)  = √ 0^2 + 1^2  = 1

Answer:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

SOLUTION :-

In ΔABC ,

\(=> 0.2588... = \frac{BC}{60}\)

\(=> BC = (0.2588....) \times 60 = 15.5291.....\) ≈ 15.5 ft

\(=> 0.9659..... = \frac{AC}{60}\)

\(=> AC = (0.9659.....) \times 60 = 57.9555.....\) ≈ 58 ft

Area of ΔABC = \(\frac{1}{2} \times 58 \times 15.5 = 449.5 \:ft^2\)

Answer:

you need to show the examples

Step-by-step explanation:

If Hilda has $210 worth of $10 and $12 stock shares and the number of $10 shares is 5 more than twice the number of $12 shares, then the number of $10 shares and $12 shares she has is equal to 15 and 5 respectively.

The number of $10 shares and $12 shares can be calculated by forming linear equations.

Consider the number of $10 shares to be x and the number of $12 shares to be y.

x = 2y + 5

10x + 12y = 210

Putting the value x = 2y + 5 in the second equation,

10x + 12y = 210

10 (2y + 5) + 12y = 210

20y + 50 + 12y = 210

32y + 50 = 210

32y = 210 - 50

32y = 160

y = 160 ÷ 32

y = 5

Putting y = 5 in the first equation,

x = 2y + 5

x = 2(5) + 5

x = 10 + 5

x = 15

Hence the number of $10 and $12 shares she has is calculated to be 15 and 5 respectively.

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Answer:

x^3 + 4x^2 - 9x-36

Step-by-step explanation:

Use long division to divide x-4 into it.....

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Therefore , the solution of the given problem of percentage comes out to be y = e(t + ln(1.03) - 1) - 1.

In mathematics, a number or number stated as a portion of 100 is referred to as a percentage. Also occasionally used are the abbreviations "pct.," "pct," as well as "pc." However, the "%" sign that is used to denote it is frequently used. The % sum is flat; there are no dimensions. Since percentages have a numerator of 100, they are basically fractions.

Here,

a)

We must determine the derivative of y with regard to t in order to determine the slope of the tangent line:

=> (Y+1)/(2t) = dy/dx

The following can be written using the chain rule:

Dy/dt = Dy/dx + Dy/dt

We can differentiate t with respect to itself to discover dx/dt and obtain dx/dt = 1 by doing so.

Consequently, (y+1)/(2t) = dy/dt = dy/dx * dx/dt = dy/dx.

Now that we have this equation, we can change t = 1 and y = 0.03 to obtain the slope of the tangent line:

dy/dt = (0.03+1)/(2√1) = 0.515

The tangent line to the y-axis graph at time t = 1 has the following expression as a result:

y - 0.03 = 0.515(t - 1) (t - 1)

We can use the tangent line equation with t = 1.2 to roughly calculate the proportion of the colony afflicted at that time:

y - 0.03 = 0.515(1.2 - 1) (1.2 - 1)

y - 0.03 = 0.257

y = 0.287 or 28.7% (estimate) (approx)

Consequently, 28.7% of the population was infected at time t = 1.2.

b) We can rewrite the given differential equation as y+1 = e(t + ln(1.03) - 1) in order to directly find y in terms of t.

If we condense this phrase, we get:

y = e^(√t Plus ln(1.03) - 1) - 1

As a result, the formula for the colony's infection rate as a function of time t is y = e(t + ln(1.03) - 1) - 1.

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Answer:

Johnny earns 50 cents each hour, x.

Step-by-step explanation:

Answer:

Ariana wanted to buy cashews at the grocery store. Cashews are $0.5 per ounce. If Ariana has $10 how many ounces of cashews can she buy

You can use linear equations and then can solve that system of linear equations to find the number of each type of coin Julio has got in the given condition.

The number of coin that Julio got in his pocket for each type are given as

Number of nickles = 12

Number of dimes = 14

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

Let Julio has got x amount of nickels and got y amount of dimes in his pocket. Then by the given description, we have got;

Number of dimes = twice the number of nickle - 10

\(y = 2x -10\)

Total amount in his pocket = $2.75

Total amount = amount by x nickles and amount by y dimes

\(2.75 = x \times 0.05 + y \times 0.1\) (since one nickle = $0.05, and one dime  = $0.1)

Thus, we got system of linear equations for given condition as:

\(y = 2x - 10\\0.05x + 0.1y = 2.75\)

Substituting value of y from first equation in the second equation, we get:

\(0.05x + 0.1(2x-10) = 2.75\\0.05x + 0.2x - 1 = 2.75\\0.25x = 3.75\\\\x = \dfrac{3.75}{0.25} = 12\)

Thus, there are 12 nickles in Julio's pocket

Putting this value in first equation, we get:

\(y = 2x - 10\\y = 2 \times 12 - 10\\y = 24 - 10 = 14\)

Thus,

The number of coin that Julio got in his pocket for each type are given as

Number of nickles = 12

Number of dimes = 14

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We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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The year it will take Mussman to reach a population of 27,000 resident is 10.7 years

Population growth is the increase in the number of people in a population or dispersed group.

We use exponential function when calculating increase in population per time

p(t) =p(o) e^kt

27000 = 13500 e^0.065t

e^0.065t = 27000/13500

0.065t = ln 2

0.065t = 0.693

t = 0.693/0.065

t = 10.7 years

therefore it will take 10.7years for the resident of Mussman to reach a population of 27000

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Answer: \(64\ ft^3\)

Step-by-step explanation:

Given

The dimension of the box is

\(\text{width w=}8\ ft\\\text{height h=}2\ ft\\\text{length l=}4\ ft\)

Space occupied by the box is equal to its volume i.e.

\(\Rightarrow V=l\times b\times h\\\Rightarrow V=4\times 8\times 2\\\Rightarrow V=64\ ft^3\)

The volume of the box is \(64\ ft^3\).

The present age of Kevin is 6 years.

Using the provided data, we can create two equations that specify the ages of Kevin and Daniel.

Let Kevin's present age be k and Daniel's present age be d.

As per the data given:

Kevin is 3 years older than Daniel. This can be written as:

k = d + 3

Two years ago, Kevin was 4 times as old as Daniel

Two years ago, Kevin was k - 2 years old, and Daniel was d - 2 years old.

k - 2 = 4(d - 2)

Now we have two independent equations, and we can solve for our two unknowns.

Solving our first equation for d.
We get:

d = k - 3

Substituting this into our second equation, we get the equation:

k - 2 = 4((k - 3) -2)

k - 2 = 4k - 12 - 8

k - 2 = 4k - 20

4k - k = 20 - 2

3k = 18

k = 6

Therefore the answer is 6 years.

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Answer:

12

Step-by-step explanation:

To determine the value of \( n \) such that the average rate of change of the function \( f(x) = x^2 - 3x + 7 \) on the interval \( -5 \leq x \leq n \) is \( -1 \), we need to find the average rate of change of the function and set it equal to \( -1 \). By using the formula for the average rate of change, \(\frac{{f(b) - f(a)}}{{b - a}}\), where \( a \) is the starting point of the interval and \( b \) is the ending point, we can set up the equation and solve for \( n \).

The average rate of change of a function on an interval is defined as the difference in the function values divided by the difference in the corresponding input values. In this case, we have the function \( f(x) = x^2 - 3x + 7 \) and the interval \( -5 \leq x \leq n \).

To find the average rate of change, we use the formula: \(\frac{{f(b) - f(a)}}{{b - a}}\), where \( a \) is the starting point of the interval and \( b \) is the ending point. In this case, \( a = -5 \) and \( b = n \).

We want the average rate of change to be \( -1 \), so we set up the equation: \(\frac{{f(n) - f(-5)}}{{n - (-5)}} = -1\). Substituting the function \( f(x) = x^2 - 3x + 7 \) and solving for \( n \), we can determine the value of \( n \) that satisfies the given condition.

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Answer and Step-by-step explanation:

Question 4:

We need to solve for y, so we need to use the cosine trig function, which is adjacent divided by hypotenuse.

\(cos(21) = \frac{y}{18}\\\\18(cos(21)) = y = 16.8\\\\\\\)

Question 5:

We need to use the sine trig function, which is opposite divided by hypotenuse.

\(sin(43) = \frac{31}{x} \\\\x = \frac{31}{sin(43)} = 45.45\)

#teamtrees #WAP (Water And Plant)

The height of the trapezoid is 98 units

The space enclosed by the boundary of a plane figure is called its area.

A trapeziod is a closed shape or a polygon, that has four sides, four corners/vertices and four angles

The area of a trapezoid is expressed as;

A = 1/2( a+b)h

where a and b are the bases length of the trapezoid.

245= 1/2 ( 14+21)h

490 = 35h

divide both sides by 35

h = 490/35

h = 98 units

Therefore the height of the trapezoid is 98 units

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Using Distributive Property, the product of 6x13 is 78.

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

The steps of distributive property are -

                                                 6 × 13

                                              6 × (10 + 3)

                                          (6 × 10) + (6 × 3)

                                  ((3 + 3) × (5 +5)) + ((3 + 3) × 3)

                 (3 × 5 + 3 × 5 + 3 × 5 + 3 × 5 ) + ((3 × 3) + (3 × 3))

                                     (15 + 15 +15 + 15 ) + (9 + 9)

                                                  60 + 18

                                                    = 78

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a) Based on the inflation rate, the $3 dues in 1916 would be worth $57.39 in 2023 dollars.
b) In 2023, after adjusting for inflation, the absolute change for the dues was $117.61.
c) In 2023, after adjusting for inflation, the relative change for the dues was  204.84%, rounded to the nearest percent.
d) The relative change is most meaningful, as it is the easiest to interpret. It shows the percentage of the dues increase over the time period, which gives a clear indication of the rate of inflation.

a) To find the value of the $3 dues in 1916 in 2023 dollars, we need to use the formula for inflation:

FV = PV(1 + r)^t

where FV is the future value, PV is the present value, r is the inflation rate, and t is the number of years.

Assuming an average inflation rate of 3% per year, we can plug in the values and solve for FV:

FV = 3(1 + 0.03)^(2023-1916)

FV = 3(1.03)^107

FV = 3(19.13)

FV = $57.39

So, the $3 dues in 1916 would be worth $57.39 in 2023 dollars.

b) To find the absolute change for the dues compared with the actual price, we need to subtract the value of the dues in 1916 in 2023 dollars from the actual price in 2023:

Absolute change = $175 - $57.39 = $117.61

c) To find the relative change for the dues compared with the actual price, we need to divide the absolute change by the value of the dues in 1916 in 2023 dollars and multiply by 100 to get a percentage:

Relative change = ($117.61/$57.39) * 100 = 204.84%

d) In my opinion, the relative change is the most meaningful measure of change because it takes into account the value of the dues in 1916 in 2023 dollars and shows how much the dues have increased relative to their original value. The absolute change only shows the difference in dollar amounts, but does not account for the effects of inflation.

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Answer:

3x^2 + 20x + 12 is (3x + 2)(x + 6)

Step-by-step explanation:

To factor the trinomial 3x^2 + 20x + 12, we look for two binomials in the form (ax + b)(cx + d) that multiply together to give the trinomial.

We can start by looking for factors of 3x^2, which are 3x and x. Then, we look for factors of 12, which are 1, 2, 3, 4, 6, and 12. We need to find a combination of these factors that will give us 20x when combined.

The factors of 12 are:

1, 2, 3, 4, 6, 12

We can try different combinations to see which one works:

(3x + 4)(x + 3) = 3x^2 + 9x + 4x + 12 = 3x^2 + 13x + 12

(3x + 6)(x + 2) = 3x^2 + 6x + 12x + 24 = 3x^2 + 18x + 24

(3x + 12)(x + 1) = 3x^2 + 3x + 12x + 12 = 3x^2 + 15x + 12

(3x + 2)(x + 6) = 3x^2 + 18x + 2x + 12 = 3x^2 + 20x + 12

From the combinations we tried, we see that (3x + 2)(x + 6) gives us the correct combination of factors. Therefore, the factored form of 3x^2 + 20x + 12 is (3x + 2)(x + 6).

Answer:

The first number is -6. The second number is -4.

Step-by-step explanation:

Let the second number be x.

"one number is 2 less than a second number"

Second number: x

First number: x - 2

"twice the second number is 22 more than 5 times the first"

2x = 5(x - 2) + 22

Distribute on the right side.

2x = 5x - 10 + 22

Subtract 5x from both sides. Combine like terms on the right side.

-3x = 12

Divide both sides by -3.

x = -4

x - 2 = -4 - 2 = -6

The first number is -6. The second number is -4.

Answer:

Exact Form:  x  =  1 /15

Decimal Form:  x  =  0.0 6

Answer:

1/3

Step-by-step explanation:

3/9 = 1/3

Answer:

16.34 yards of rope

Step-by-step explanation:

you need to do 4.67 x 2 and add 3.5 x 2 to get the total perimeter

Answer:

Step-by-step explanation:

\(\frac{7}{2} + \frac{14}{3} +\frac{7}{2} + \frac{14}{3}\)

\(\frac{21}{6} + \frac{28}{6} +\frac{21}{6} + \frac{28}{6}\)

\(\frac{98}{6}\) = \(\frac{49}{3}\) = 16 \(\frac{1}{3}\)

Answer:

Below

Step-by-step explanation:

For the x distance   -2 to 5   is 7 units

for the y distance   2 to 8 = 6 units

Pythagorean Theorem

 7^2 + 6^2 = d^2

  49 + 36 = d^2

  d^2 = 85       d = \(\sqrt{85}\)   =~ 9.2  units  

The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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Answer:

il faut diviser chaque nombre par 7/3

donc 2 divisé par 7/3

-5 divisé par 7/3 etc

Answer:

6 batches  

Step-by-step explanation:  

24 people x 4 cupcakes = 96 cupcakes  

96 cupcakes / 16 per batch = 6 batches  

Hope this helped, have a nice day! :)

Answer:

  D. f(1) = 4, f(n) = –1/2f(n – 1) for n > 1

Step-by-step explanation:

We assume your sequence is supposed to be ...

  4, -2, 1, -1/2, 1/4, ...

This has no common difference, but it has a common ratio of -1/2. That is, the first term is 4, and each successive term is -1/2 times the previous one. The function is described by the recursive formula ...

  f(1) = 4;

  f(n) = -1/2·f(n-1)