h(t) = -16t^2 + 200t + 3 find the max height, and time it needs to reach that height?


-b/2a and quadratic function formula

Answer:

i think the answer is this.. I don't have answer choices but here you go >>> -6>7

The maximum value of f(x,y) is 75/4√6 and the minimum value is -75/4√6, which confirms the given answer.

To find the maximum and minimum values of f(x,y) = xy on the ellipse 6x² + y² = 5, we can use the method of Lagrange multipliers.

We want to maximize and minimize f(x,y) subject to the constraint 6x² + y² = 5. So, we consider the function:

F(x,y,λ) = xy + λ(6x² + y² - 5)

We take the partial derivatives of F with respect to x, y, and λ and set them equal to zero:

∂F/∂x = y + 12λx = 0

∂F/∂y = x + 2λy = 0

∂F/∂λ = 6x² + y² - 5 = 0

From the first equation, we get y = -12λx. Substituting this into the second equation, we get x - 24λ²x = 0, which simplifies to:

x(1 - 24λ²) = 0

Since x cannot be zero, we have 1 - 24λ² = 0, or λ = ± 1/2√6.

Substituting y = -12λx into the constraint equation, we get:

6x² + (-12λx)² = 5

Solving for x, we get:

x = ± 5 / 2√6

Using y = -12λx, we get:

y = ± 15√2 / 2

Therefore, the critical points are:

(-5/2√6, -15√2/2), (-5/2√6, 15√2/2), (5/2√6, -15√2/2), and (5/2√6, 15√2/2).

To determine which of these points correspond to a maximum or minimum of f(x,y), we need to evaluate f(x,y) at each of these points.

f(-5/2√6, -15√2/2) = (-5/2√6)(-15√2/2) = 75/4√6

f(-5/2√6, 15√2/2) = (-5/2√6)(15√2/2) = -75/4√6

f(5/2√6, -15√2/2) = (5/2√6)(-15√2/2) = -75/4√6

f(5/2√6, 15√2/2) = (5/2√6)(15√2/2) = 75/4√6

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Answer:

t⁹

Step-by-step explanation:

Whenever you multiply the same base with 2 different exponents, you add the powers together.

t⁴(t⁵)

4 + 5 = 9

t⁹

Answer:

Hey there!

a^b(a^c)=a^b+c

t^4(t^5)=t^9.

Let me know if this helps :)

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = -2x - 10       ----------------------(I)

2x + 5y = 6      __________(II)

Substitute y = -2x - 10 in equation (II)

2x + 5 (-2x -10) = 6

2x  + (-2x) *5 + (-10) *5 = 6

2x - 10x - 50 = 6

-8x - 50 = 6

        -8x = 6 + 50

       -8x = 56

          x = 56/-8

x = -7

Plugin x = -7 in equation (I)

y = -2*(-7) - 10

  = 14 - 10

y = 4

Answer:

$216 or $162    (see below)

Step-by-step explanation:

If it's 18% for 9 months (and not per year)

then

1200x0.18=$216

If it's 18% per year then

1200x0.18x0.75=$162

Using the normal distribution, the project completion time with a 75% certainty is of 42 weeks.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given as follows:

\(\mu = 40, \sigma = \sqrt{9} = 3\)

The project completion time with a 75% certainty is the 75th percentile, which is X when Z = 0.675, hence:

\(Z = \frac{X - \mu}{\sigma}\)

0.675 = (X - 40)/3

X - 40 = 3 x 0.675

X = 42.

The project completion time with a 75% certainty is of 42 weeks.

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Answer:

B. 3/4

Step-by-step explanation:

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( -3 , 4 )

Let the second point be Q = Q ( 1 , 7 )

Now , the slope of the line between the two points is given by the formula ,

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 7 - 4 ) / ( 1 - ( -3 ) )

On simplifying the equation , we get

Slope m = 3 / 4

20=x

Simplify both sides of the equation, then isolate the variable

Answer:

#1. Fourteen divided by a number.

#2. Four times a number.

#3. A number divided by 14.

#4. A number minus 14.

Step-by-step explanation:

I hope this helps., I just need more points. So sorry.

Answer:

C = 50.26 cm

Step-by-step explanation:

The question says that, "What is the measure of the circumference of a tube with a radius of 8 cm".

The circumference of a circle is given by :

C = 2πr

Put r = 8 cm in the above formula.

C = 2π × 8

C = 50.26 cm

So, the circumference of the circle is 50.26 cm.

Answer and Step-by-step explanation:

We are given: 18x - 2(3x + 1) = 5x - 16

First, lets distribute the -2 to the 3x and 1.

18x - 6x - 2 = 5x - 16

Now, we combine like terms.

12x - 2 = 5x - 16

Next, we add 2 to each side.

12x = 5x -14

Now, we subtract 5x from both sides.

7x = -14

Finally, we divide by 7 on both sides.

x = -2

  Statements:                             Reasons:

  18x - 2(3x + 1) = 5x - 16            Given

  18x - 6x - 2 = 5x - 16                Distributive Property of Equality

  12x - 2 = 5x - 16                       Combine like terms

  12x = 5x -14                              Addition Property of Equality

  7x = -14                                     Subtraction Property of Equality

  x = -2                                        Division Property of Equality

#teamtrees #WAP (Water And Plant)

The symmetrical interval that includes 93% of the sample means is (3.2455 gallons per month, 3.5545 gallons per month) assuming the population follows a normal distribution.

To calculate the probabilities and identify the symmetrical interval, we'll use the provided information:

Given:

Population mean (μ) = 3.4 gallons per month

Population standard deviation (σ) = 0.85 gallons per month

Sample size (n) = 100

a. Probability that the sample mean will be less than 3.3 gallons per month: To calculate this probability, we need to use the sampling distribution of the sample mean, assuming the population follows a normal distribution. Since the sample size (n) is large (n > 30), we can approximate the sampling distribution as a normal distribution using the Central Limit Theorem. The mean of the sampling distribution is equal to the population mean (μ), which is 3.4 gallons per month. The standard deviation of the sampling distribution, also known as the standard error (SE), can be calculated as σ / √n:

SE = σ / √n

= 0.85 / √100

= 0.085 gallons per month

Now, we can calculate the z-score using the formula:

z = (x - μ) / SE

Substituting the values:

z = (3.3 - 3.4) / 0.085

= -0.1 / 0.085

= -1.1765

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -1.1765. The probability that the sample mean will be less than 3.3 gallons per month is approximately 0.1190. Therefore, the probability is 0.1190.

b. Probability that the sample mean will be more than 3.6 gallons per month:

Similarly, we can calculate the z-score for this case:

z = (x - μ) / SE

= (3.6 - 3.4) / 0.085

= 0.2 / 0.085

= 2.3529

Using a standard normal distribution table or calculator, we find the probability corresponding to a z-score of 2.3529. The probability that the sample mean will be more than 3.6 gallons per month is approximately 0.0096.

Therefore, the probability is 0.0096.

c. Identifying the symmetrical interval that includes 93% of the sample means:

To find the symmetrical interval, we need to determine the z-scores corresponding to the tails of 93% of the sample means.

Since the distribution is symmetrical, we can divide the remaining probability (100% - 93% = 7%) equally between the two tails.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a tail probability of 0.035 on each side. The z-score is approximately 1.8125.

The symmetrical interval is then given by:

=μ ± z * SE

=3.4 ± 1.8125 * 0.085

=(3.4 - 1.8125 * 0.085, 3.4 + 1.8125 * 0.085)

=(3.4 - 0.1545, 3.4 + 0.1545)

=(3.2455, 3.5545)

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Answer:

use ph0t03ath its answers every math question

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

rate of the boat is 10.5 and the rate of the current is 1.5

Step-by-step explanation:

Distance = rate x time

Let r = rate of the boat

Let c = current

Upstream:

Rate: r -c

Time: 4 hours

Distance: 36

36 = 4(r-c)  Divide both sides of the equation by 4

9 = r - c

Downstream:

Rate: r + c

Time: 3 hours

Distance: 36

36 = 3(r+c)  Divide both sides by 3

12 = r -c

Combine the two bold equations:

9 = r - c

12 = r + c

21 = 2r  Divide both side's by 2

10.5 = r This is the rate of the boat.

Rate of the current:

4(10.5 - c) =36

42 - 4x = 36  Subtract 42 from both sides

-4x = -6  Divide both sides by -4

x = 3/2 or 1.5

===================================================

Explanation:

Any triangle prism is composed of 2 parallel triangular faces (base faces), along with 3 rectangular lateral faces.

The bottom triangle face has a base of 10 cm and a height of 4 cm. The area is 0.5*base*height = 0.5*10*4 = 20 square cm. Two of these triangles combine to an area of 2*20 = 40 square cm. We'll use this later.

The lateral surface area of any prism can be found by multiplying the perimeter of the base by the height of the prism. The base triangle has side lengths 5, 8 and 10. The perimeter is 5+8+10 = 23. So the lateral surface area is (perimeter)*(height) = 23*9 = 207

Add this to the total base area we got earlier and the answer is 40+207 = 247. The units are in square cm, which we can write as cm^2.

The temperature change for sand is 0.0048°C

The temperature change for water  0.95°C

We have to note that we would use the specific heat capacity and the temperature change to obtain the heat that have been absorbed or evolved by a material.

Now the formula that we would have to use in this case would now be the formula that is given as;

H = mcdT

m = mass of the object

c = heat capacity

dT = temperature change

Then;

For water;

200 = 50 * 4.2 * dT

dT = 200/50 * 4.2

dT = 200/210

dT = 0.95°C

For the sand;

200 = 50 * 830 * dT

dT = 200/50 * 830

dT = 0.0048°C

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A, b and c can do a piece of work in 24, 30 and 40 days respectively. the work is completed in 13 days.

Let's calculate the work done by each person per day:

A completes 1/24 of the work per day.

B completes 1/30 of the work per day.

C completes 1/40 of the work per day.

Let's assume the total work is represented by "W".

When all three, A, B, and C, work together, their combined work rate per day is:

1/24 + 1/30 + 1/40 = (5 + 4 + 3) / 120 = 12/120 = 1/10

This means that when all three work together, they complete 1/10 of the total work per day.

Now, let's calculate the number of days it takes for them to complete the work. Let's represent this number of days by "D".

Since C leaves 4 days before the completion of the work, the remaining work is 1 - 1/10 = 9/10.

We can set up the equation:

(D - 4) * (1/10) = 9/10

Simplifying the equation:

D - 4 = 9

D = 9 + 4

D = 13

Therefore, the work is completed in 13 days.

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In Utah, if not directly involved in diving activity, motorized vessels and personal watercraft (PWCs) must remain 150 feet from the diver down flags.

The diver down flag is a banner that is used by vessels to indicate that divers are in the water. It is typically a red flag with a white diagonal stripe that is used to indicate the presence of divers in the water. The flag must be at least 12 x 12 inches in size and must be clearly visible from all directions. When the flag is raised, boaters are expected to keep a safe distance from the divers and to take extra precautions to ensure that they do not pose a hazard to the divers.The diver down flag should be used whenever there are divers in the water. This includes scuba divers, free divers, and anyone else who is swimming or diving underwater. The flag should be raised before the divers enter the water and should be lowered when they exit the water. In addition to the flag, divers are required to use other means of indicating their presence in the water, such as lights and audible signals, to ensure that boaters can see and hear them. Motorized vessels and personal watercraft (PWCs) must remain at least 150 feet from the diver-down flag. This means that they must keep a safe distance from the divers and take extra precautions to ensure that they do not pose a hazard to the divers. If a motorized vessel or PWC is directly involved in the diving activity, such as transporting divers to and from the dive site, they may operate closer to the flag, but they must still maintain a safe distance from the divers at all times.

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Answer:

Step-by-step explanation:

4 Tuan wants to add trim only around the edges of the

gate in problem 3. About how much trim does he need?

✘ O A 20.28 feet

✘ O C 34.56 feet

✘ O D 39.12 feet

The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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The height to the top of Mt. Kaala above the level of the road as required in the task content is; 2.72km.

It follows from the attached image which is a representation of the situation as described in the task content that the height of Mt. Kaala relative to the level of the road is represented by x.

Therefore, by trigonometric ratios where Tan(theta) = opposite/adjacent; we have;

Tan(10.83) = x/(y+7) and hence;

x = (y + 7) tan (10.83).

Also; Tan(20.67) = x/y and hence;

x = y tan 20.67

Since; x = x; we have;

y tan(20.67) = (y + 7) tan (10.83)

0.37727y = 0.19130y + 1.33912

0.18597y = 1.33912

y = 7.2007.

Therefore, since the value of y is as determined above, it follows that the height to the top of Mt. Kaala, x can be determined as follows;

x = 7.2007 (tan 20.67)

x = 7.2007 × 0.37727

x = 2.7166km.

Ultimately, when rounded to the nearest hundredth place; the height, x = 2.72 km.

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Answer:X is equal to -4 twice

Step-by-step explanation:

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:

2x² + 8x - x² + 16 = 0

Simplifying further, we get:

x² + 8x + 16 = 0

This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.

We can solve this equation by factoring it:

(x + 4)(x + 4) = 0

This gives us two solutions:

x + 4 = 0 or x + 4 = 0

x = -4 or x = -4

Therefore,

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

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If side JM = 30 and side LM = 8, the length of side KM is equal to 15.49 units.

In this exercise, we would assign the variable x to the length of side KM. Based on the information provided about triangle JKM and triangle KML, we can logically deduce the following parameters;

Side JL = [(30 + 8) × x]/2

Side JL = 38x/2

Side JL = 19x.

Since point M is the perpendicular bisector of both triangle JKM and triangle KML, the length of side KM can be calculated as follows;

19x = √[(30² + x²)(x² + 8²)]/2

38x = √[(30² + x²)(x² + 8²)]

By taking the square of both sides, we have:

38²x² = (900 + x²)(x² + 64)

38²x² = 900x² + 57,600 + x⁴ + 64x²

38²x² = 964x² + 57,600 + x⁴

(x² - 240)² = 0

x² = 240

x = √240

x = 15.49 units.

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Answer:

4 nickels

12 quarters

Step-by-step explanation:

If its wrong let me know