For the function f(x)=5x 2+3x+(−2), determine the absolute maximum and minimum values on the interval [0,4]. Answer: Absolute maximum = x at x= Absolute minimum = x at x= Hint: Follow Example 1.

Answer:

6

Step-by-step explanation:

If you were scaling it by 1/6 it would be smaller.

Answer:

41

Step-by-step explanation:

The middle number is the median

They would meet 30 times after 10 minutes.

Since Nick and Sally run on the 100m straight track, Nicks's speed is 3m / s, Sally's speed is 2m / s, if they star from two sides of the track, running towards each other continuously, to determine how many times they would meet each other after 10 minutes the following calculation must be performed:

Therefore, they would meet 30 times after 10 minutes.

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Answer:

x=54°

...

...

.....

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There probability are 17,576,000 different ways to arrange the 26 letters of the alphabet so that the vowels a, e, I o, and u never appear back-to-back.

There are 21 consonants and 5 vowels (a,e,i,o,u) (all other letters).

The vowels can be arranged in 5! = 120 different ways.

The consonants can be arranged in 21! = 5,109,400,800 different ways.

The product of the two integers is 17,576,000, which is the total number of possible arrangements for all letters.

26 letters make up the alphabet, and 5 of them are vowels (a,e,i,o,u). We must determine how many ways there are to organize the vowels and consonants before we can determine how many ways there are to arrange the letters so that no two vowels appear consecutively.

There are 5! = 120 different ways to order the vowels. This is due to the fact that there are 5 vowels that must be grouped in various ways. Since there are 21 consonants that can be arranged, there are 21! = 5,109,400,800 different combinations that can be made. The product of the two integers is 17,576,000, which is the total number of possible arrangements for all letters.

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The derivative dy/dx of the function x^3 + xe^y = 2√(y + y^2) is (3x^2 + e^y) / (xe^y - 2y - 1).

To find dy/dx for the given function x^3 + xe^y = 2√(y + y^2), we differentiate both sides of the equation with respect to x using the chain rule and product rule.

Differentiating x^3 + xe^y with respect to x, we obtain 3x^2 + e^y + xe^y * dy/dx.

Differentiating 2√(y + y^2) with respect to x, we have 2 * (1/2) * (2y + 1) * dy/dx.

Setting the two derivatives equal to each other, we get 3x^2 + e^y + xe^y * dy/dx = (2y + 1) * dy/dx.

Rearranging the equation to solve for dy/dx, we have dy/dx = (3x^2 + e^y) / (xe^y - 2y - 1).

Therefore, the derivative dy/dx of the function x^3 + xe^y = 2√(y + y^2) is (3x^2 + e^y) / (xe^y - 2y - 1).

To find the derivative dy/dx for the given function x^3 + xe^y = 2√(y + y^2), we need to differentiate both sides of the equation with respect to x. This can be done using the chain rule and product rule of differentiation.

Differentiating x^3 + xe^y with respect to x involves applying the product rule. The derivative of x^3 is 3x^2, and the derivative of xe^y is xe^y * dy/dx (since e^y is a function of y, we multiply by the derivative of y with respect to x, which is dy/dx).

Next, we differentiate 2√(y + y^2) with respect to x using the chain rule. The derivative of √(y + y^2) is (1/2) * (2y + 1) * dy/dx (applying the chain rule by multiplying the derivative of the square root function by the derivative of the argument inside, which is y).

Setting the derivatives equal to each other, we have 3x^2 + e^y + xe^y * dy/dx = (2y + 1) * dy/dx.

To solve for dy/dx, we rearrange the equation, isolating dy/dx on one side:

dy/dx = (3x^2 + e^y) / (xe^y - 2y - 1).

Therefore, the derivative dy/dx of the function x^3 + xe^y = 2√(y + y^2) is (3x^2 + e^y) / (xe^y - 2y - 1).

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12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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The smallest possible angle that the path of the plane could make with the ground is 9.3 degrees to 1 decimal place.

To find the smallest possible angle that the path of the plane could make with the ground, we need to use trigonometry.

Let's assume that

We know that the height reached by the plane is 8 km, which means that:

tan θ = 8 / d

We also know that the distance traveled by the plane should be in the range 44 km to 49 km. This means that:

44 ≤ d ≤ 49

To find the smallest possible angle θ, we need to find the largest possible value of d that satisfies the above inequality.

tan θ = 8 / 49

θ = arc tan (8 / 49)

θ = 9.2726

θ ≈ 9.3°

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The height of the escalator is as calculated using trigonometric ratios.

We know that in a right angled triangle the trigonometric ratios are

tan θ = perpendicular ÷ base

For a right angled triangle the tanθ is defined as the ratio of the perpendicular to the base of the triangle . The side opposite the angle θ is the perpendicular and the side adjacent to the θ is the base .

Now it is given that for every 2 feet vertically moved the horizontal distance moved is 3 feet.

Now using the trigonometric ratio of tanθ

tan θ = 2 / 3

Now we will use this ratio to calculate the vertical height for horizontal movement of 90 feet .

Now, the height is given as h .

∴ tan θ = h / 90

or, 2 / 3 = h / 90

or, h = 60 feet

Therefore the height of the escalator is 60 feet.

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Answer:

∡B = 60°

Step-by-step explanation:

find BC using Pythagorean Theorem:

5² + BC² = 10²

25 + BC² = 100

BC² = 75

BC = \(\sqrt{75}\)

BC = \(\sqrt{25}\)\(\sqrt{3}\) which is 5\(\sqrt{3}\)

this indicates that ∡B must be 60° because the ratio of sides in a 30-60-90 triangle are 1 : \(\sqrt{3}\) : 2

Answer:

2/5

Step-by-step explanation:

Average is the ratio of the sum of the data to the sample size

Sum of data = 2/5-4/5+9/5/+1/5

Sum of data = (2-4+9+1)/5

Sum of data = 8/5

Sample size = 4

Average = 8/5÷4

Average = 8/5× 1/4

Average = 2/5

Hence the average monthly change in water level is 2/5

If marc r v = marc v u , the value of marc v u is given as 64°.

mArc R V = mArc V U, Angle S O R = 13 x degrees and angle T O U = 15 x - 8 degrees

∠SOR = ∠TOU  (Vertically opposite angles are equal). Therefore:

13 x = 15x - 8

solving by calculating the value of x to satisfy the equation: Subtracting 13x from both sides

13x - 13x = 15x - 8 - 13x

0 = 15x - 13x - 8

2x - 8 = 0

Adding 8 to both sides:

2x - 8 + 8 = 0 + 8

2x = 8

2x/2 = 8/2  

x = 4

∠SOR = 13x = 13(4) = 52°

∠TOU = 15x - 8 = 15(4) - 8 = 60 - 8 = 52°

Let a = mArc R V = mArc V U

Therefore:

mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)

Substituting:

a + a + 52 = 180

2a = 180-52

2a = 128

a = 128/2

a= 64°

mArc R V = mArc V U = 64°

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The ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.

We are given height of cylinders and the information that both the cylinders are same. So, the radius of cylinders will be same.

The formula for calculation of volume of cylinder is -

Volume = πr²h, where r is radius and h is height.

Ratio of the volume of the large cylinder to the volume of the small cylinder= πr²h(large):πr²h(small)

Ratio = πr²75:πr²25

Cancelling πr² from both numerator and denominator as it is common in both

Performing division by 25 to find the ratio

Ratio = 3:1

Hence, the ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.

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Answer:

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

Step-by-step explanation:

You are given the points (2, 1) and (0, 4).

(0, 4) represents the y-intercept ⇒ b = 4

Calculate the slope between the two points: \(m = \frac{y_{2} -y_{1}}{x_{2} -x_{1}} = \frac{4-1}{0-2} = -\frac{3}{2}\)

\(y = mx +b\) ⇒ \(y = -\frac{3}{2}x +4\)

Answer:

Question 9) \(y=\frac{-3}{2}x+2 \\\\\)

Question 10) \(y=-x-6\\\)

Step-by-step explanation:

Well there are two methods of determining an equation of line

Method 1 (Using the slope-intercept form):

\(y=mx+b\)

This method is mostly used when the y-intercept also known as b is given and the slope also known as m is given

Method 2 (Using the point-slope form):

\(y-y_1=m(x-x_1)\\\)

This method is used when a point is given also known as (x1 , y1) and the slope is given which is denoted by m.

Since in Question 9 there is no y-intercept given only two points we will use the second method so here goes,

Q9)

Two points are  (0 , 2) and (4 , -4) first step to find out the equation of line is to calculate the slope which is as follows:

\(m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-4-2}{4-0} \\\\m=\frac{-6}{4}\\\\m=-3/2 \\\)

Now we have our slope which is m = -3/2 now since we have two points we can use any point in the point-slope form equation because both of these points lie on the line hence satisfying the desired equation that we need so we select the point (0 , 2) [YOU CAN TRY OUT FINDING THE EQUATION OF LINE BY USING THE OTHER POINT THE ANSWERS WOULD BE SAME]

so now we have the point (0 , 2) and value of m = -3/2

\(y-y_1=m(x-x_1)\\y-2=\frac{-3}{2}(x-0)\\\\y-2=\frac{-3}{2}x\\\\y=\frac{-3}{2}x+2\\\\\)

Question 10)

Two points are (-2 , -4) and (-3 , -3) we use the same method as shown above,

First step calculate the slope:

\(m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-3-(-4)}{-3-(-2)} \\\\m=\frac{-3+4}{-3+2}\\\\m=1/-1\\\\m=-1\\\)

now we insert the value of m = -1 and take any point of the two points that are given, we select the first point (-2 , -4)

\(y-y_1=m(x-x_1)\\y-(-4)=(-1)(x-(-2))\\y+4=(-1)(x+2)\\y+4=-x-2\\y=-x-2-4\\y=-x-6\\\)

Answer:

15 + 0.05x ≤ 50

Step-by-step explanation:

The cost needs to be less than or equal to 50. Thus, the equation would be

15 + 0.05x ≤ 50

Answer:

  b) Jim

Step-by-step explanation:

Given the angle measures lf Jared's triangle, Jim can draw one that is similar. However he cannot draw one that is congruent without knowing the measure of at least one side.

__

Jim is correct that he needs more information.

Answer:

A, C, and D

Step-by-step explanation:

the calculation would be:  1 - 0.60 = 0.40

The value of r2, also known as the coefficient of determination, represents the proportion of variation in the dependent variable that can be explained by the independent variable. In this case, r2 is equal to 0.60, which means that 60% of the variation in the dependent variable can be explained by the independent variable.
To find the percentage of variation that is left unexplained, you simply subtract the r2 value from 1 (or 100%, if you prefer to work with percentages).
This means that 40% of the variation in the dependent variable is left unexplained by the independent variable. Therefore, the correct answer from the given choices would be .40

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Answer:

3. 8 feet

Step-by-step explanation:

To find the horizontal distance (x) in feet, we can use the following steps:

Step 1: Determine the vertical height that the box has been lifted.

The difference between the two points is:

9 ft - 3 ft = 6 ft.

Therefore, the box has been lifted 6 feet.

Step 2: Use the slope of the ramp to find the horizontal distance (x).

The slope of the ramp is given as 3/4. This means that for every 3 feet the ramp rises vertically, it moves 4 feet horizontally. We can set up a proportion to solve for x:

3/4 = 6/x

We can cross-multiply to get:

3x = 24

Dividing both sides by 3 gives us:

x = 8

Therefore, the horizontal distance (x) is 8 feet.

Answer:

c

Step-by-step explanation:

Starting price is $5.50. And for every mile it costs $1.50.

Answer: (x−2)(x−2)

The middle number is -4 and the last number is 4.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -4

Multiply together to get 4

Can you think of the two numbers?

Try -2 and -2:

-2+-2 = -4

-2*-2 = 4

Fill in the blanks in

(x+_)(x+_)

with -2 and -2 to get...

(x-2)(x-2)

Answer:

(x−2)(x−2)

so the answer is D.

Answer: 3 ovals and 3 rectangles and an even amount of rectangles and ovals

Answer:

as the figure the answer is

angles E and G are equal to each other because they are vertically opposite angle (V.O.A)

With the help of  application of derivatives we can solve our question.

What is application of derivatives?

Derivatives are often used in mathematics.

They can be used to determine a function's maximum or minimum, the slope of a curve, or even the inflection point.

Below are a few instances where we will use the derivative. And the following sections go into great detail about each of them. The application of derivatives is most frequently found in:

Finding a Quantity's Rate of Change, Finding the Approximation Value, Tangent and Normal Equation to Curve Equation, Finding the Approximation Value,

Identifying the Point of Inflection, the Maxima and Minima, and the Increasing and Decreasing Functions

According to our question-

As c=2πr, it's given that dc/dt=2πdr/dt=2. (given).

A=πr2 so dA/dt=2πrdr/dt by the chain rule.

dc/dt=2πdr/dt where we are given dc/dt=2cm/s.

Area as a function of the radius is a(r)=πr2, and, again, taking derivatives we write da/dt=π(2rdrdt).

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.

Population standard deviation, level of significance are same.

Margin of error increased.

With increase in margin of error sample size decreases.

By dividing the population's standard deviation by the sample size and then multiplying the resulting number by the crucial factor, the margin of error—a statistical expression used to estimate how much a result will deviate from the value of the full population—can be determined.

The standard deviation of the sample statistics, if we could take several samples of the same size, is the standard error.

Population standard deviation, level of significance are same.

Margin of error increased.

Margin of error increases leads to decrease in the sample size

as the margin of error is in denominator position in sample size formula. Hence with increase in margin of error sample size decreases.

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The radius of the oatmeal container is 0.2 inches.

The surface area of the plastic is 0.08π square inches

The base and lid are made of plastic and have a radius of R.

The base and lid have a combined surface area of:

πr² + πr² = 2πr² square inches

The total surface area of the oatmeal container is 40 square inches.

The surface area of the cardboard is 16πr square inches and the surface area of the plastic is 2πr² square inches.

Thus, we have the equation:

40 = 16πr + 2πr²

We can solve for R as follows:

16πr + 2πr² = 40

2πr^2 + 16πr - 40 = 0

2πr^2 + 20πr - 4πr - 40 = 0

20r(πr + 2) - 4(πr + 2) = 0

(20r - 4)(πr + 2) = 0

20r - 4 = 0 or πr + 2 = 0

20r = 4 or πr = -2

r = 0.2

Thus, the radius of the oatmeal container is 0.2 inches.

The surface area of the plastic is 2πr² = 2π(0.2)² = 0.08π square inches

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Answer:

20%

Step-by-step explanation:

as we add 10 +25 = 35

so if we subract 40 from 35 it is 5 so mangoes are 5

5

_ × 100 =20%

25

Answer:

35 square units

Step-by-step explanation:

Area of the parallelogram = 7*5 = 35 square units

Answer:

171 is the answer of that question