Find the magnitude and direction of the vector u = <-4, 7>

when t=1, y is approximately equal to 5.

To solve for y when t=1 in the equation y=1.5 In(et.t+5), we first need to plug in t=1:

y=1.5 In(e(1)(1)+5)

We simplify the exponent e(1)(1) to just e:

y=1.5 In(e+5)

Using the properties of natural logarithms, we can simplify this further:

y=1.5(1+ln(5+e))

We can use a calculator to evaluate ln(5+e) to be approximately 2.063, so we can plug that in and simplify:

y=1.5(1+2.063)

y=1.5(3.063)

y=4.5945

Rounding this answer to the nearest whole number, we get:

y=5

Therefore, when t=1, y is approximately equal to 5.

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The image point of (6, 4) after the transformation R₉₀ T₁,₅ is (-3, 11).

The transformation R₉₀ T₁,₅  represents a rotation of 90° counterclockwise around the origin followed by a translation of 1 unit to the right and 5 units up.

To find the image point of (6, 4) under this transformation, we can apply the two transformations in order.

First, let's find the image of (6, 4) after rotating 90° counterclockwise around the origin.

Easy way to do this is by switching the x and y coordinates and negate the new x-coordinate. So, the image of (6, 4) after the rotation is (-4, 6).

Next, we apply the translation of 1 unit to the right and 5 units up. This moves the point (-4, 6) one unit to the right to get (-3, 6), and five units up to get the final image point:

Image point = (-3, 11)

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Answer: 4

Step-by-step explanation:

[tex]\frac{1}{3} \pi 3^{2} h=12\pi \\3h=12\\h=4[/tex]

The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.

Money spend =  $400

Time = 120 months

Loan amount = $30,000

Interest rate = 6.5%.

The formula is given P = [tex]PV*(i / (1 - (1+i)^{-n}))[/tex]

The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.

i = 0.065/12 = 0.00541667  

Substituting the values into the formula,

P = [tex]30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})[/tex]

P = $328.05

Therefore, we can conclude that the monthly payment for the loan is $328.05.

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Therefore, two possible values of α are approximately 138.19° and 221.81°.

Sin 180 has a precise value of zero. One of the fundamental trigonometric functions is sine, which is used to calculate the angle or sides of a right-angled triangle.

Given that cos = -8/17, we must determine two potential values for.

We can construct a right triangle with the adjacent side equal to -8 and the hypotenuse equal to 17, and then use the Pythagorean theorem to calculate the opposite side since cos = adjacent/hypotenuse.

The Pythagorean theorem gives us:

opposite² = hypotenuse² - adjacent²

opposite² = 17² - (-8)²

opposite² = 225

opposite = ±15

Both the x and y coordinates are negative in the second quadrant, resulting in:

cos α = -8/17

sin α = -15/17

Consequently, may have the following value: = 180° - arccos(-8/17) 138.19° (rounded to two decimal places)

The x coordinate is negative and the y coordinate is positive in the third quadrant, resulting in:

cos α = -8/17

sin α = 15/17

Therefore, another possible value of α is:

α = 360° - cos(-8/17)

≈ 221.81°

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Answer: 80

Step-by-step explanation: The question is tell us that a certain company  we don't know which one, but it says a certain company has 400 shoes. that is important to note. also 20% of the shoes are black. and One shoe is chosen and replaced. Then the second shoe is chosen. The question is What is the probability that the shoes chosen are black?

Well, take 400 and mutipy it by 20% which changes to 0.20 in decimal form then mutiply your answer by one and you get 80. so the answer is the probability that shoes chosen are black is 80%.

For question 2, the zoologists can conduct an analysis of variance (ANOVA) test to investigate whether the four different diets impact the weight gains of the 6-month baby elephants. The ANOVA test will compare the mean weight of each diet group to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the zoologists can conclude that the diets are impacting the weight gains of the baby elephants.

For question 3, the researchers can also conduct an ANOVA test to investigate whether the nursery locations affect the growth of oak trees. The test will compare the mean circumference growth of the oak trees at each nursery location to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the researchers can conclude that the nursery locations are impacting the growth of the oak trees.

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To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, you would need to compare the corresponding side lengths of the two parallelograms. For example, if the green parallelogram has a side length that is half of the black parallelogram's side length, the scale factor would be 1/2 (Option B).

If the green parallelogram's side length is twice the black parallelogram's side length, the scale factor would be 2 (Option C). And if the green parallelogram's side length is one-third of the black parallelogram's side length, the scale factor would be 1/3 (Option A). Without specific measurements or a visual representation, it is not possible to accurately identify the scale factor between the two parallelograms. Please provide the side lengths or a diagram to help determine the correct scale factor.

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To determin how many pint containers of chocolate milk Joey should buy, we need to know how much chocolate milk he wants in total.

Let's assume Joey wants to buy "x" pints of chocolate milk. Then, the total amount of chocolate milk he will get in quarts can be calculated as:

Total amount of chocolate milk = x pints/2 pints per quart = x/2 quarts

If Joey has a specific total amount of chocolate milk he wants to buy, we can solve for "x". For example, if Joey wants to buy 3 quarts of chocolate milk, we can set up the following equation:

x/2 = 3

Multiplying both sides by 2, we get:

x = 6

So, Joey needs to buy 6 pint containers of chocolate milk to get 3 quarts in total.

If Joey has a different desired amount of chocolate milk, we can adjust the equation accordingly to find the number of pint containers he needs to buy

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The measure of ∠L in Triangle JKL is 56.1 degrees.

In geometry, the measures in triangles refer to the angles and sides within a triangle. Triangles are three-sided polygons, and the measures of their angles and sides are important properties that determine their shape and characteristics.

In a triangle, the sum of the measures of all three angles is always 180 degrees. Therefore, to find the measure of ∠L in Triangle JKL, we can use the information given:

∠J is congruent to ∠L, which means they have the same measure.

∠K is given as 67.8 degrees.

Since ∠J is congruent to ∠L, we can denote their measure as "x".

So, the sum of the measures of ∠J, ∠K, and ∠L is 180 degrees:

∠J + ∠K + ∠L = 180

Substituting the given values:

x + 67.8 + x = 180

Simplifying the equation:

2x + 67.8 = 180

Subtracting 67.8 from both sides:

2x = 180 - 67.8

2x = 112.2

Dividing both sides by 2:

x = 112.2 / 2

x = 56.1

Hence, the measure of ∠L in Triangle JKL is 56.1 degrees.

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The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.

- Vertical stretch by a scale factor of 2: Multiply the output by 2.

- Shift 3 units to the left: Replace x with x + 3.

- Shift 1 unit down: Subtract 1 from the output.

Thus, the function g(x) can be written as:

g(x) = 2 * f(x + 3) - 1

Substituting f(x) = 5^x, we get:

g(x) = 2 * 5^(x + 3) - 1

Simplifying:

g(x) = 2 * 125 * 5^x - 1

g(x) = 250 * 5^x - 1

The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.

The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.

Therefore, the function g(x) is g(x) = 250 * 5^x - 1.

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Answer: x intercepts = (-1.5,0) and (-1,0)

Step-by-step explanation: Graphed it in desmos :)

The angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s

To calculate the angular velocity of the elbow during an elbow flexion exercise, we'll use the information given about the relative angle at different times. Here's the step-by-step explanation:
First, find the change in relative angle: Δθ = Final angle - Initial angle = 120 degrees - 10 degrees = 110 degrees.
Next, find the change in time: Δt = Final time - Initial time = 0.71s - 0.5s = 0.21s.
Now, calculate the angular velocity: ω = Δθ / Δt = 110 degrees / 0.21s ≈ 523.81 degrees/s.
So, the angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s.

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The solution of the exponents is shown below.

Exponents are mathematical shorthand for multiplying a number by itself a certain number

We have that;

5^n = 1

5^n = 5^0

n = 0

2) 2^-7/2^n = 2^2

2^-7 - n = 2^2

-7 - n = 2

-n = 2 + 7

n = -9

3) 6^5 * 6^n = 6^1

6^ 5 + n = 6^1

5 + n = 1

n = 1 - 5

n = -4

4) (8^n)^7 = 8^21

8^7n = 8^21

7n = 21

n = 3

5) 4^n = (1/4)

4^n = 4^-1

n = -1

In each of the cases, we have applied the laws of the exponents as we know them.

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The equation of the forms are matched as;

2⁻⁷/2ⁿ = 2², n = -9

6⁵ * 6ⁿ = 6. n = -4

(8ⁿ)⁷ = 8²¹, n = 3

4ⁿ = 1/4 , n = -1

Index forms are simply described as mathematical forms that are used to represent numbers of variables that are too large or small.

To multiply index forms, you need to add the exponents of the same bases.

To divide index forms, you need to subtract the exponents of the same bases.

From the information given, we have that;

2⁻⁷/2ⁿ = 2²

cross multiply the values

2⁻⁷ = 2²⁺ⁿ

Then,

-7 = 2 + n

n = -9

6⁵ * 6ⁿ = 6

take the exponents

5 + n= 1

n =- 4

(8ⁿ)⁷ = 8²¹

We have;

7n = 21

Make 'n' the subject

n = 3

4ⁿ = 1/4

4ⁿ = 4⁻¹

n =-1

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After 50 minutes, you will have placed 675 pieces

Given, you are doing a 5000 piece puzzle. You have already placed 175 pieces, and every minute you place 10 more pieces. After 50 minutes, we need to find how many pieces you will have placed.

We can start by finding the number of pieces you place in 50 minutes.

Every minute, you place 10 more pieces, so in 50 minutes, you will place:

10 x 50 = 500 pieces

Adding the pieces you have already placed, we get:

175 + 500 = 675 pieces

Therefore, after 50 minutes, you will have placed 675 pieces

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the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters. So the dimensions of the rectangle are 10 meters by 11 meters.

what is  rectangle ?

A rectangle is a geometric shape that has four straight sides and four right angles (90-degree angles) between them. The opposite sides of a rectangle are parallel and have the same length, so the shape is symmetrical along its horizontal and vertical axes.

In the given question,

Let's assume that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is x + 1 meters, since the length and width are consecutive integers.

The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 42 meters, so we can write:

2(length + width) = 42

Substituting the expressions for the length and width in terms of x, we get:

2(x + x + 1) = 42

Simplifying this equation, we get:

4x + 2 = 42

Subtracting 2 from both sides, we get:

4x = 40

Dividing both sides by 4, we get:

x = 10

Therefore, the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters.

So the dimensions of the rectangle are 10 meters by 11 meters.

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We know that the solutions to the quadratic equation are x=21 or x=-12.

To solve the quadratic equation x^2-19x-39=0 using the method of completing the square, the number that would have to be added to "complete the square" is 91.

First, move the constant term to the right side: x^2-19x=39.

Then, take half of the coefficient of x, square it, and add it to both sides: x^2-19x+90.25=129.25.

This can be factored as (x-9.5)^2=129.25.

Taking the square root of both sides, we get x-9.5=±√129.25.

Solving for x, we get x=9.5±√129.25, which simplifies to x=9.5±11.5.

Therefore, the solutions to the quadratic equation are x=21 or x=-12.

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Solving the equation, Joshua will reach 100,000 miles after approximately 1,760 days of work.

To model Joshua's truck mileage as a function of the number of days he has worked, we can use the following equation:

Mileage (M) = 14 * Number of days worked (D) + Initial Mileage (I)

First, we need to determine the initial mileage on the mail truck. To do this, we can use the information given for his 100th day of work:

76,762 = 14 * 100 + Initial Mileage
76,762 = 1,400 + Initial Mileage
Initial Mileage (I) = 76,762 - 1,400
Initial Mileage (I) = 75,362

Now we can rewrite the equation as:

Mileage (M) = 14 * Number of days worked (D) + 75,362

To find when Joshua will reach 100,000 miles, we can set M equal to 100,000 and solve for D:

100,000 = 14 * D + 75,362
24,638 = 14 * D
D ≈ 24,638 / 14
D ≈ 1,759.857

Since Joshua cannot work a fraction of a day, he will reach 100,000 miles after approximately 1,760 days of work.

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To find the production level that will minimize the average cost, we need to differentiate the cost function with respect to x and set it equal to zero. So:

C'(x) = 0.005x^2 + 242x + 6000
0 = 0.005x^2 + 242x + 6000
Using the quadratic formula, we get:
x = (-242 ± sqrt(242^2 - 4(0.005)(6000))) / (2(0.005))
x = (-242 ± sqrt(146416)) / 0.01
x = (-242 ± 382) / 0.01
x = -14,000 or 27,000

Since the production level cannot be negative, we can discard the negative solution and conclude that the production level that will minimize the average cost is 27,000 units.

To find the minimal average cost, we need to plug the production level back into the cost function and divide by the production level. So:

C(27,000) = 6000 + 242(27,000) + 0.005(27,000)^2
C(27,000) = 6,594,000
Average cost = C(27,000) / 27,000
Average cost = 6,594,000 / 27,000
Average cost ≈ 244.22

Therefore, the minimal average cost is approximately $244.22.
To answer your question, first, let's correct the cost function, which should be in the form of C(x) = Fixed cost + Variable cost. Assuming it is C(x) = 6000 + 242x + 0.005x^2.

A) To find the production level that will minimize the average cost, we need to first determine the average cost function, which is AC(x) = C(x)/x. So, AC(x) = (6000 + 242x + 0.005x^2)/x.

Now, find the first derivative of AC(x) concerning x, and set it equal to zero to find the minimum point:

d(AC(x))/dx = 0

The first derivative of AC(x) is:

d(AC(x))/dx = (242 + 0.010x - 6000/x^2)

Setting this to zero and solving for x will give us the production level that minimizes the average cost:

242 + 0.010x - 6000/x^2 = 0

Now, you can solve for x using numerical methods, such as Newton-Raphson or others. After solving for x, you will get the production level that minimizes the average cost.

B) To find the minimal average cost, plug the production level x you found in part A into the average cost function, AC(x):

Minimal Average Cost = AC(production level)

This will give you the minimal average cost for the given cost function.

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The serum be said to be effective can't be concluded, since the test statistic is less than the critical value, we fail to reject the null hypothesis.

Let [tex]n_A[/tex] denotes the number of mice which receiving treatment. Therefore,

[tex]n_A[/tex] = 5,

Let [tex]n_B[/tex] denotes the number of mice which do not receive treatment. Therefore, [tex]n_B[/tex] = 4

Survival times for the mice receiving the treatment are: 2.1; 5.3; 1.4; 4.6; 0.9

Survival times for the mice not receiving the treatment are: 1.9; 0.5; 2.8; 3.1

Let [tex]x_A[/tex] be the mean of survival time for the mice receiving the treatment and [tex]x_B[/tex] be the mean of survival time for the mice not receiving the treatment.

We have: [tex]x_A[/tex] = 2.86

[tex]x_B[/tex] = 2.075

Standard deviation be:

[tex]S_A=\sqrt{\frac{\sum (x_a-x_A)^2}{n_A-1} }[/tex]

[tex]=\sqrt{\frac{[(2.1-2.86)^2+(5.3-2.86)^2+(1.4-2.86)^2+(4.6-2.86)^2+(0.9-2.86)^2]}{4} }[/tex]

= 1.971

[tex]S_B=\sqrt{\frac{\sum (x_b-x_B)^2}{n_B-1} }[/tex]

[tex]=\sqrt{\frac{[(1.9-2.08)^2+(0.5-2.08)^2+(2.8-2.08)^2+(3.1-2.08)^2]}{3} }[/tex]

= 1.167

[tex]\mu_A[/tex] and [tex]\mu_B[/tex]  are population means for the groups receiving the treatment and not receiving the treatment respectively.

Level of significance is α = 0.05

If P-value is less then 0.05, we will reject [tex]H_o[/tex]

The test statistic is,

[tex]t=\frac{(x_A-x_B)-(\mu_A-\mu_B)}{s_p\sqrt{\frac{1}{n1} +\frac{1}{n2} } }[/tex]

[tex]=\frac{2.86-2.07)-(0)}{1.674388\sqrt{\frac{1}{5} +\frac{1}4} } }[/tex]

= 0.79/1.123

t = 0.70

Degrees of freedom is,

[tex]d_f=n_A+n_B-2[/tex]

= 5 + 4 - 2

= 7.

According to the value in the table, the test's critical value is 1.895.

We are unable to reject the null hypothesis since the test statistic is less than the threshold value.

We thus cannot draw the conclusion that the serum is working.

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2.25 liters of solution in all is there in the test tubes. So, the correct option is 2.25 l.

The total volume of solution in the 15 test tubes can be calculated by multiplying the volume of one test tube by the number of test tubes:

Total volume = 15 test tubes × 150 milliliters/test tube

Total volume = 2,250 milliliters

However, the question asks for the answer in liters, so we need to convert milliliters to liters by dividing by 1,000:

Total volume = 2,250 milliliters ÷ 1,000

Total volume = 2.25 liters

Therefore, there are 2.25 liters of solution in all the test tubes.

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For a normal distribution with a mean of 68 and a standard deviation of 9, the percentage of scores less than 50 is 2.28%.

It is given that scores on a psychology exam have a normal distribution with a mean of 68 and a standard deviation of 9. The percentage of scores less than 50 can be determined as follows.

1. Calculate the z-score for 50 using the formula:

z = (X - μ) / σ

where

X = 50 (the value we're comparing to)

μ = 68 (mean)

σ = 9 (standard deviation)

2. Plug in the values:

z = (50 - 68) / 9 = -18 / 9 = -2

3. Use a z-table or calculator to find the area to the left of z = -2. This represents the percentage of scores less than 50.

4. Based on the z-table or calculator, the area to the left of z = -2 is approximately 0.0228, which means that around 2.28% of scores were less than 50.

So, about 2.28% of scores on the psychology exam were less than 50.

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DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.

    D

   / \

  /   \

 /     \

E-------F

Given that XF = 10, YF = 5, and EF = 13, we need to find DY.

We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:

EF / ED = EY / EJ  (where J is the intersection of XY and DF)

EF / DF = EJ / EY

Substituting the given values, we get:

13 / ED = EY / EJ

13 / DF = EJ / (13 - EY)

Multiplying the above two equations, we get:

13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)

169 / (ED * DF) = EY / (13 - EY)

Substituting the values of XF = 10 and YF = 5, we get:

169 / (ED * DF) = 5 / 8

ED / DF = 135 / 169

Using the Pythagorean theorem on triangles DEX and DFY, we get:

ED^2 = EX^2 + DX^2

DF^2 = FY^2 + DY^2

Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:

ED^2 = EX^2 + (13 - EX)^2

ED^2 = 2EX^2 - 26EX + 170

Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:

DF^2 = FY^2 + DY^2

DF^2 = 170 - 26EY + EY^2 + DY^2

Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:

(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170

DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)

DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX)   (Substituting XF = 10)

Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:

FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY)   (Substituting YF = 5)

DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2

Substituting the given values, we get:

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

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It took Franny 5 minutes to walk each lap. The correct option is B.

Franny spent a total of 35 minutes walking around the track and made 7 laps around the track, so the total time for all 7 laps is 35 minutes. Let's assume it took Franny t minutes to walk each lap. Then, we can set up the following equation:

7t = 35

We can solve for t by dividing both sides of the equation by 7:

t = 35/7 = 5

Therefore, the correct option is B.

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The maximum value of s is 9261, which is obtained when x = y = z = 7.

To find the maximum value of s=xyz, we can use the AM-GM inequality, which states that the arithmetic mean of a set of non-negative numbers is greater than or equal to the geometric mean of the same set of numbers.

Mathematically, this can be represented as:[tex](1/3)(x + y + z) \geq (xyz)^(1/3)[/tex]Multiplying both sides of the inequality by[tex]3(xyz)^(1/3)[/tex],

we get: [tex](x + y + z) \geq 3(xyz)^(1/3)[/tex] Now,

we can substitute the given value of x + y + z = 21, to obtain: 21 ≥ [tex]3(xyz)^(1/3)[/tex]

Cubing both sides of the inequality, we get: [tex]21^3 \geq 27(xyz)[/tex]

Simplifying the expression, we obtain: s=[tex]xyz \leq (21^3)/27[/tex]= 9261.

The maximum value of s=xyz is obtained when x = y = z = 7, and the value of s is equal to 9261. This result is obtained using the AM-GM inequality, which is a useful tool for solving optimization problems involving non-negative numbers.

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Answer:

0 hrs 32 mins

Step-by-step explanation:

Answer:

x + x + 2 + x + 4 + x + 6 + x + 8 = 235

5x + 20 = 235

5x = 215, so x = 43

The integers are 43, 45, 47, 49, and 51.

The greatest of these integers is 51.

The height of the tower is: 274.7m

To find the height of the tower, we will use the tangent trigonometric function.

The tangent function relates the angle of elevation to the ratio of the opposite side (height of the tower) to the adjacent side (distance from the observer to the tower).

In this case, the angle of elevation is 70°, and the distance from the observer to the tower is 100 meters.

The formula we will use is:

tan(θ) = opposite / adjacent

tan(70°) = height / 100m

To calculate the height, we will rearrange the formula:

height = 100m * tan(70°)

Using a calculator, we find that tan(70°) ≈ 2.747.

Therefore, the height of the tower is: 274.7m

height ≈ 100m * 2.747 ≈ 274.7m

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The question in English is:

A person observes a tower from a distance of 100m with an elevation angle of 70, with which trigonometric function would you obtain the height of the tower? Calculate the height of the tower

The value of x in the variation is -2/9

y varies inversely as x and the value of y is 18 and x is 1/2

the first step is to calculate the constant k

k= y/x

k= 18 ÷ 1/2

k= 18 × 2/1

k= 36

From the calculation above the value of k which is the constant is 36

The next step is to calculate x. The value of x can be calculated as follows

k = y/x

36= -10/x

cross multiply

36x= -10

x= -10/36

x= -2/9

Hence the value of x in the variation is -2/9

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