sendo a função f(x) = 4x³ +8x² - 2 . x + 13, determine o valor de 9.f (3)

Answer:

46.80

Step-by-step explanation:

because 45/4%=1.80 and 45+1.80=46.80

Step 1:

50%= 50/100 = 0.5

Step 2:

50% of 50%= (50×0.5)/100= 0.25

Step 3:

50% of 50% of 50% = (50×0.25)/100= 0.125

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In this problem, we are given a second-order linear homogeneous differential equation, also known as an initial value problem. We need to find the solution to the given differential equation, satisfying the initial conditions y(0) = 9 and y'(0) = 1. Additionally, we are asked to determine the maximum value of the solution and find the point at which the solution is zero.

Let's solve the initial value problem step by step.

Step 1: Find the characteristic equation.

The characteristic equation is obtained by substituting y = \(e^{rt}\) into the differential equation, where r is an unknown constant:

9y" - 10y' + y = 0

Substituting y = c into the equation, we get:

9r²\(e^{rt}\)  - 10(r\(e^{rt}\) ) + \(e^{rt}\)  = 0

Step 2: Simplify the equation.

Divide the entire equation by \(e^{rt}\)  to simplify it:

9r² - 10r + 1 = 0

Step 3: Solve the quadratic equation.

We can solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, it is easier to use the quadratic formula:

r = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 9, b = -10, and c = 1.

Substituting these values into the quadratic formula, we have:

r = (-(-10) ± √((-10)² - 4 * 9 * 1)) / (2 * 9)

 = (10 ± √(100 - 36)) / 18

 = (10 ± √64) / 18

 = (10 ± 8) / 18

We have two possible solutions for r:

r₁ = (10 + 8) / 18 = 18 / 18 = 1

r₂ = (10 - 8) / 18 = 2 / 18 = 1/9

Step 4: Write the general solution.

The general solution of the differential equation is given by:

y(t) = c₁\(e^{r_{1} t}\) + c₂\(e^{r_2t}\)

where c₁ and c₂ are constants that will be determined using the initial conditions.

Step 5: Apply the initial conditions.

We are given y(0) = 9 and y'(0) = 1. Let's apply these initial conditions to find the specific solution.

When t = 0:

y(0) = c₁\(e^{{r_1} * 0}\) + c₂\(e^{{r_2} * 0}\)

      = c₁e⁰ + c₂e⁰

      = c₁ + c₂

Since y(0) = 9, we have:

c₁ + c₂ = 9 ---(1)

Differentiating y(t) with respect to t gives:

y'(t) = c₁r₁\(e^{r_2t}\) + c₂r₂\(e^{r_2t}\)

When t = 0:

y'(0) = c₁r₁\(e^{{r_1} * 0}\) + c₂r₂\(e^{{r_2} * 0}\)

= c₁r₁ + c₂r₂

Since y'(0) = 1, we have:

c₁r₁ + c₂r₂ = 1 ---(2)

Solving equations (1) and (2) simultaneously will give us the values of c₁ and c₂.

Step 6: Solve the system of equations.

We have the following system of equations:

c₁ + c₂ = 9

c₁r₁ + c₂r₂ = 1

Multiplying the first equation by r₁ and the second equation by 1, we can eliminate c₂:

c₁r₁ + c₂r₁ = 9r₁

c₁r₁ + c₂r₂ = 1

Subtracting the second equation from the first, we obtain:

c₂(r₁ - r₂) = 9r₁ - 1

Since r₁ - r₂ = 1 - 1/9 = 8/9, we can rewrite the equation as:

c₂ = (9r₁ - 1) / (8/9)

   = (9r₁ - 1) * (9/8)

   = (9r₁² - r₁) * (9/8)

Substituting this value of c₂ into equation (1), we get:

c₁ + (9r₁² - r₁) * (9/8) = 9

Simplifying the equation further, we have:

c₁ + (81r₁² - 9r₁) / 8 = 9

c₁ + 81r₁² - 9r₁ = 72

Rearranging the terms, we obtain:

81r₁² - 9r₁ + c₁ = 72

This equation relates the values of r₁ and c₁ that satisfy the initial conditions.

Step 7: Calculate the specific solution.

By solving the equation derived in step 6, we can find the values of r₁ and c₁. Once we have those, we can determine c₂ using equation (2).

After finding the values of c₁ and c₂, the specific solution of the initial value problem is given by:

y(t) = c₁\(e^{r_{1} t}\) + c₂\(e^{r_2t}\)

Step 8: Determine the maximum value of the solution.

To find the maximum value of the solution, we need to analyze the behavior of the function y(t) in the given range. Since we have the specific solution, we can analyze its properties using calculus. We need to find the critical points and classify them as local maximums, local minimums, or points of inflection.

Step 9: Find the point where the solution is zero.

To find the point(s) where the solution is zero, we need to solve the equation y(t) = 0. This can be done by setting the specific solution equal to zero and solving for t.

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The given set of constraints is 3x + 6y ≥ 18, x + 6y ≥ 12, and x ≥ 0, y ≥ 0. To find the minimum and maximum values of z = 7x + 3y, we can graph the feasible region determined by the intersection of these constraints .

Upon graphing the constraints, we observe that the feasible region is a triangular region with vertices at (0, 3), (0, 6), and (6, 0). Since the objective function z = 7x + 3y represents a straight line with a positive slope,

it is clear that the maximum value of z will occur at the vertex (6, 0) since it lies on the boundary of the feasible region. Plugging the values into z = 7x + 3y, we find the maximum value of z to be 7(6) + 3(0) = 42.

On the other hand, there is no minimum value for z since the feasible region extends infinitely in the positive direction. Therefore, the correct choices are A) There is no minimum value, and A) The maximum value is 42.

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Answer:

7) -8 , -4 , -3 , 3 , 4 , 9

8) -200 , -197 , -110 , -65 , 15 , 167

9) -5 , -2 , 2 , 4 , 7

Step-by-step explanation:

The larger the negative number the further away it is from zero so it is smaller.

Negative numbers are always smaller than positive numbers.

The numerical limits for A grade are 86 and B grade is 76, after rounding to the nearest whole number.

To find the numerical limit for grade A we need to rely on finding the z-scores concerning the top 14%.

here, we need to utilize the standard normal distribution table

the z-score for 14% is 1.08

therefore, using the formula of z-score to find the raw source

z = (X-μ)/σ

restructuring the formula concerning the raw materials

X = z x σ + μ

here,

X = raw source

μ = mean

σ = standard deviation

staging the given values into the formula

X = 1.08 x 7.3 + 78.3 => 86.4

The numerical limit for an A grade is 86.

To find the numerical limit for grade B rely on finding the z-scores concerning the bottom 55% of the z-score is -0.17.

using the formula of z-score to find the raw source

X = z x σ + μ

staging the given values into the formula

X = -0.17 x 7.3 + 78.3 => 76.0

The numerical limit for a B grade are 76.

The numerical limit for A grade are 86 and B grade is 76, after rounding to the nearest whole number.

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The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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Answer:

Step-by-step explanation:

Denominators of the fractions are 7 and 3, which are mutually prime numbers.

The LCD is the product of 7 and 3:

Simplify into mixed fraction

\(\\ \sf\longmapsto 6\dfrac{5}{7}=\dfrac{47}{7}\)

\(\\ \sf\longmapsto 6\dfrac{1}{3}=\dfrac{19}{3}\)

Find LCD

\(\\ \sf\longmapsto 7(3)\)

\(\\ \sf\longmapsto 21\)

Answer:

The answer is (3,-2)

Step-by-step explanation:

\( \frac{1}{3} x - 3 = - 2x + 4 \\ \frac{1}{3} x + 2x = 7 \\ \frac{7}{3} x = 7 \\ x = 3 \\ then \: \\ y = - 2\)

Therefore, the solutions to the given system of equations are: (2√2, -5) and (-2√2, -5).

Hence, option D (3, 0) and (−4, 7) are not solutions of the system of equations.

The given system of equations is: xy = 3.............(1)y = x² - 9..........(2) We have to solve the system of equations.

The value of y is given in the first equation. Therefore, we will substitute the value of y from equation (1) into equation (2).xy = 3x(x² - 9) = 3x³ - 27x  Now, we will substitute the value of x³ as a variable t.x³ = t

Therefore, t - 27x = 3t-24x=0t = 8x Substitute t = 8x into x³ = t.

We get:x³ = 8x => x² = 8 => x = ± √8 = ± 2√2. Substitute the value of x in y = x² - 9 to get the value of y corresponding to each value of x.y = (2√2)² - 9 = -5y = (-2√2)² - 9 = -5

A system of equations refers to a set of two or more equations that are to be solved simultaneously. The solution to a system of equations is a set of values for the variables that satisfies all the equations in the system.

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Answer:

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

We need to find the total surface area of a cylinder excluding its top.

Answer:

the answer is 245

Step-by-step explanation:

Answer:

245

Step-by-step explanation:

Answer:

x = 22/15

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 5x from both sides.

Step 3: Add 4 to both sides.

Step 4: Divide both sides by 30.

Therefore, the answer is 22/15.

Solving a product, we can see that Lorena must pay a total of $5.88

We know taht each kilogram of bananas costs $4.70, and Lorena bought a total of 1 and 1/4 kilograms, then to find the cost we just need to solve the following product:

C = (1 + 1/4)*$4.70

We can distribute it to get:

C = $4.70 + $4.70/4

C = $4.70 + $1.18

C = $5.88

That is the total amount that Lorena must pay.

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"complete question.

Lorena fue al supermercado y compró 1 1/4 de plátanos, cuyo kilogramo cuesta $4. 70.

¿Cuánto debe pagar?"

To find the rate at which the water level is rising when the depth at the deepest point is 5 ft, we can use related rates and the concept of similar triangles.

Let's denote the depth at the deepest point as \(\(h\)\) (in feet) and the rate at which the pool is being filled as \(\(\frac{dV}{dt}\)\) (in \(ft\(^3\)\)/min), where \(\(V\)\) represents the volume of water in the pool.

Since the cross-section of the pool is trapezoidal, we can use similar triangles to relate the change in water level \((\(\frac{dh}{dt}\))\) to the change in volume \((\(\frac{dV}{dt}\))\). The similar triangles are formed by the vertical side of the pool and the water level.

The ratio of the corresponding sides of the similar triangles is:

\(\(\frac{h - 3}{40} = \frac{h - 5}{20}\)\)

We can solve this equation for \(\(h\)\) to find the value of \(\(h\)\) when the depth at the deepest point is 5 ft:

\(\(\frac{h - 3}{40} = \frac{5 - 5}{20} = 0\)\)

Simplifying the equation, we have:

\(\(h - 3 = 0 \implies h = 3\) ft\)

Now, to find the rate at which the water level is rising \((\(\frac{dh}{dt}\))\) when \(\(h = 5\)\) ft, we can use the related rates formula:

\(\(\frac{h - 3}{40} = \frac{dh}{dt}\)\)

Substituting the values \(\(h = 5\)\) ft and \(\(\frac{dV}{dt} = 0.7\)\) \(ft\(^3\)\)/min, we have:

\(\(\frac{5 - 3}{40} = \frac{dh}{dt} \implies \frac{2}{40} = \frac{dh}{dt} \implies \frac{1}{20} = \frac{dh}{dt}\)\)

Therefore, the water level is rising at a rate of \(\(\frac{1}{20}\)\) ft/min when the depth at the deepest point is 5 ft.

(b) The period of motion refers to the time it takes for the pool to fill and empty completely. Since the pool is being filled at a constant rate and there is no mention of it being emptied, we can assume that the period is infinite.

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After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large, the best recommendation is c. Increase the sample size.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specific confidence level; the 95% confidence level is the most commonly used, but other levels, such as 90% or 99%, are also used.

Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. A researcher, for example, may randomly select different samples from the same population and compute a confidence interval for each sample to determine how well it may represent the true value of the population variable. The resulting datasets are all unique, with some intervals containing the true population parameter and others not.

In this case, the sample size should be increased when the results are meaningless because the width of the interval is too large.

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Complete questions

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

a. Increase the level of confidence for the interval

b. Decrease the sample size

c. Increase the sample size

d. Reduce the population variance

A reliable test is one that can measure what it is supposed to measure consistently, yield the same results when given a second time, and provide an unbiased score, ensuring that the results obtained are valid and reliable. Answer is D.

The reliability of a test refers to its consistency and stability over time and under different conditions. It is the extent to which a test is able to yield the same results repeatedly. A reliable test should be able to measure what it is supposed to measure consistently, without any errors or fluctuations. Additionally, it should provide an unbiased score, which means that it should not be influenced by any external factors such as personal biases or environmental factors. Therefore, the answer to the question is D, all of the above.

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A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

A function is a mathematical concept that assigns a unique output value for each input value.

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.

Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.

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The complete question is

The derivate of a function f(x) is determinated as:

For the function

First we have to determine de f ( x + h ) as follow:

Then we calculate and simplify the coeficient in the first formula

------------------------------------------------------------------------------------The equation of the tangent:

First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function

And the equation to thist tangent in a specific point will be find using the next formula:

We have to calculate the slope in the point x =4 using the derivate:

In the point x=4

Calculate the value of f(x0) substituting in the function the given point x:

Knowing that we put the value of m and f(x0) in the equation of the tangent:

---------------------------------------------------------------------------

The normal line

The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:

So in this situation is:

The equation of the normal line is given by the next formula:

Replacing the data we obtain:

Answer:

\(x\) = 4.9  (1 dp)

Step-by-step explanation:

Use trig ratio \(sin(\theta)=\dfrac{O}{H}\)

where \(\theta\) is the angle, O is the side opposite the angle and H is the hypotenuse of a right triangle.

Given:

\(\implies sin(55)=\dfrac{4}{x}\)

\(\implies x=\dfrac{4}{sin(55)}\)

\(\implies x = 4.9\)   (1 dp)

Answer:

392

Step-by-step explanation:

(10 x 25) = 250

250 + 54 + 100 - 12 = 392

Hope it helped! :)

Answer:64

Step-by-step explanation: i did the test

Answer:

Step-by-step explanation:

It is asking for the "mode" which is the data element you see the most, therefore it is 2.

To find the area of parallelogram MNOP, we can use the formula: Area = base × height. Since we are given NS = 16 and MR = 10, we can consider NS as the base and MR as the height. So, the area of parallelogram MNOP is 160 square units.

To find the area of parallelogram MNOP, we need to use the formula: area = base x height. In this case, we need to find the height of the parallelogram, which is perpendicular to the base.
First, we can use the fact that NS = 16 and MR = 10 to find the length of NO. We know that NS and MR are parallel sides of the parallelogram, so they have the same length. Therefore, NO = NS = 16.
Next, we can use the fact that RS = 3 to find the length of OP. We know that RS and OP are parallel sides of the parallelogram, so they have the same length. Therefore, OP = RS = 3.
Now we have the length of both base NO and base OP. To find the height, we need to draw a perpendicular line from O to line NO. Let's call the point where this line intersects NO point Q.
Using the Pythagorean theorem, we can find the length of QM. QM^2 + MR^2 = QR^2. We know that MR = 10 and QR = 16 - 3 = 13. Therefore, QM^2 + 10^2 = 13^2. Solving for QM, we get QM = √(169 - 100) = √69.
Finally, we can use the fact that QM is perpendicular to NO to find the height of the parallelogram. The height is the distance between lines NO and PQ, which is equal to QM. Therefore, the area of parallelogram MNOP is base x height = NO x QM = 16 x √69 ≈ 94.36 square units.
In conclusion, the area of parallelogram MNOP is approximately 94.36 square units. This answer is more than 100 words and includes the terms "answer more than 100 words" and "parallelogram".
To find the area of parallelogram MNOP, we can use the formula: Area = base × height. Since we are given NS = 16 and MR = 10, we can consider NS as the base and MR as the height. Therefore, the area of parallelogram MNOP is:
Area = NS × MR
Area = 16 × 10
Area = 160 square units
So, the area of parallelogram MNOP is 160 square units.

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A block hangs in equilibrium from a vertical spring. The equilibrium position sags by 6.00 cm when adding a second identical block. The oscillation frequency of the two-block system is approximately 1.44 Hz.

To find the oscillation frequency of the two-block system, we can use Hooke's Law and the formula for the frequency of simple harmonic motion.

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, it can be expressed as:

F = -kx

where F is the force applied by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

In the equilibrium position, the force exerted by the spring is balanced by the weight of the block(s), resulting in zero net force. Thus, we have:

mg = kx_eq

where m is the mass of one block, g is the acceleration due to gravity, and x_eq is the equilibrium displacement of the spring.

When a second identical block is added, the total mass becomes 2m. The equilibrium displacement increases to 2x_eq due to the additional weight. We are given that the equilibrium position sags by 6.00 cm, so we have:

2mg = k(2x_eq)

2mg = 4kx_eq

Dividing both sides by 2m, we get:

g = 2kx_eq / m

The angular frequency (ω) of the two-block system can be calculated using the formula:

ω = √(k / m)

The oscillation frequency (f) can be calculated as:

f = ω / (2π)

To find the oscillation frequency, we need to find k/m. From the equation above, we have:

k/m = (g / 2x_eq)

Substituting the given values, g = 9.8 m/s² and x_eq = 6.00 cm = 0.06 m:

k/m = (9.8 m/s²) / (2 * 0.06 m)

k/m = 81.67 N/m

Now, we can calculate the angular frequency and the oscillation frequency:

ω = √(81.67 N/m / m) = √(81.67 s⁻²) ≈ 9.04 rad/s

f = ω / (2π) ≈ 9.04 rad/s / (2π) ≈ 1.44 Hz

Therefore, the oscillation frequency of the two-block system is approximately 1.44 Hz.

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The scenario that illustrates an appreciation of the dollar against the euro is option D. Last week, 1 dollar was equal to 0.88 euros, but this week, 1 dollar is equal to 0.78 euros.

In this scenario, the exchange rate between the dollar and the euro has decreased from 0.88 to 0.78 euros per dollar. This means that the value of the dollar has increased relative to the euro. With fewer euros required to purchase one dollar, it implies that the dollar has appreciated in value.

Appreciation of a currency indicates that it can buy more of another currency. In this case, the dollar can buy more euros, which demonstrates an appreciation of the dollar against the euro. This would be beneficial for individuals or entities holding dollars who want to exchange them for euros, as they can now obtain more euros for the same amount of dollars compared to the previous week.

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Answer:

The answer is 1.1

Step-by-step explanation:

0.4

+0.7

____

1 . 1

Answer:

The answer to this question is the second choice.

Step-by-step explanation:

Step-by-step explanation:

product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20

3×x +5=20

3x+5=20

Subtract 5 from both sides

3x+5-5=20-5

3x=15

3x/3=15/3

x=5