Evaluate the integral: (sec2(t) i + t(t2 + 1)4 j + t8 In(t) k) dt

Answer what are the number lines for? please explain is it for the numbers

Step-by-step explanation:

Answer:

There should be 10 l of 25% orange juice and 5 l of 10% orange juice.

Step-by-step explanation:

Let the amount of the 25% orange juice be "x", while the amount of the 10% one be "y". The sum of these must be equal to 15 l, therefore:

\(x + y = 15\)

The sum of the concentration of juice on each can must be equal to the final product, therefore:

\(25\%*x + 10\%*y = 15*20\%\\0.25*x + 0.1*y = 3\)

We can now solve the system of equations as shown below:

\(\left \{ ({{x + y=15})*(-0.1) \atop {0.25*x + 0.1*y=3}} \right. \\\left \{ {{-0.1*x - 0.1*y=-1.5} \atop {0.25*x + 0.1*y=3}} \right. \\-0.1*x + 0.25*x = 3 - 1.5\\0.15*x = 1.5\\x = \frac{1.5}{0.15} = 10\\y = 15 - x = 15 - 10 = 5\)

There should be 10 l of 25% orange juice and 5 l of 10% orange juice.

Procedure

Similar triangles

SRF = ROF

Height h

The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle.

Answer:

\(\boxed{\textsf{ The slope of the line is $\bf{\dfrac{3}{2}}$.}}\)

Step-by-step explanation:

Two points are given to us and we need to find the slope of the line that passes through these two points . The two points are (3,-2) and (9,-2) .As we know that the slope of the line is given by \(\tan\theta\)

Slope of a line is :-

\(\qquad\boxed{\boxed{ \sf Slope =\dfrac{ y_2-y_1}{x_2-x_1}=\tan\theta }}\)

On using this formula we can find the slope of the line .

Putting the respective values :-

\(\sf\implies Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\\sf\implies Slope = \dfrac{ 9-3}{2+2} \\\\\sf\implies Slope =\dfrac{6}{4}\\\\\sf\implies\boxed{\pink{\sf Slope = \dfrac{3}{2} }}\)

Answer:

Its zero -w-

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

           = 2(x2 + 4x + 4) - 6(x + 2)

           = 2x2 + 8x + 8 - 6x - 12

           = 2x2 + 2x - 4

In total of 24 coins, Latanya has 10 nickels and 14 dimes altogether.

Given is that Latanya has $1.90 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether.

We can write the equation as -

(x/20) + (y/10) = 1.90

x + y = 24

Refer to the graph attached. On solving the equation graphically, we get-

x = 10, y = 14

Therefore, she has 10 nickels and 14 dimes in total.

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No, we cannot use the normal approximation in this scenario.The normal approximation relies on certain conditions being met, such as having a large sample size and a roughly symmetric distribution.

In this case, you flipped a coin 200 times and obtained 85 tails. Since the sample size is sufficiently large (n=200), that condition is met. However, the distribution of coin flips follows a binomial distribution, which is generally not symmetric unless the probability of success (getting a tail) is close to 0.5. In your case, the probability of success is 0.5 (assuming a fair coin), but the number of tails (85) is not close to half of the flips (100). This asymmetry indicates that the binomial distribution is not well-approximated by a normal distribution. Therefore, it would be more appropriate to use the binomial distribution itself or other methods specifically designed for analyzing binomial data, rather than relying on the normal approximation.

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Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

The graph of the function y = x²+ 6x + 7 is given in the attachment.

To graph the quadratic function y = x²+ 6x + 7:

Find the vertex using the formula -b/(2a), where a is the coefficient of x²and b is the coefficient of x.

The vertex will be at (-3, -2).

Plot the vertex (-3, -2) on the graph.

Choose additional x-values and calculate the corresponding y-values by substituting them into the equation.

Plot these points on the graph.

Connect the plotted points smoothly to form a U-shaped curve, which represents the parabola.

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Answer:

\(12\) cm

Step-by-step explanation:

If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!

Answer: Simplification of Fractions.

Step-by-step explanation:

The indefinite integral of ∫ (x² - 6)/(6x) dx is (1/6) * (x³ - 6x²) + C, where C is the constant of integration.

We have the integral:

∫ (x² - 6)/(6x) dx.

We can simplify the integrand by factoring out (1/6x):

∫ (x - 6/x) dx.

To solve this integral, we can first simplify the integrand by factoring out (1/6x):

∫ (x² - 6)/(6x) dx = (1/6) * ∫ (x - 6/x) dx.

Now, we can split the integral into two separate integrals:

∫ x dx - (1/6) * ∫ (6/x) dx.

Integrating each term separately, we get:

(1/6) * (x²/2) - (1/6) * (6 * ln|x|) + C.

Simplifying further, we have:

(1/6) * (x³/2) - ln|x| + C.

Finally, we can rewrite the expression as:

(1/6) * (x³ - 6x²) + C.

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The complete question is:

Find the indefinite integral of (x² - 6)/(6x) dx using the Log Rule. Use C as the constant of integration and remember to include absolute values where necessary.

Answer:

65.1 km/hr

Step-by-step explanation:

The car travelled 217km in 3 hours and 20 minutes.  We can divide the km by the time to obtain a speed that is km per a time value.  If we would like it expressed as km/hour, we will need to convert the 20 minutes into hours.

20 minutes is (20 minutes)*(1 hour/60 minutes) = (1/3) hour

The total time to travel 217km is 3 and 1/3, or (10/3)  hours.

The speed is (217 km/((10/3) hours)

Speed = 65.1 km/hr

We need the angle AOD to find the x value

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Missed data: ABCD is a QUADRILATERAL

'O'  is a point in the middle joining OA,OB,OC and OD , find the angle AOD  which is x here

Adding 3 angles we get 11x+22,

Equation is :

11x+22 + AOD = 360

=> AOD = 360 - 22- 11x

     AOD= 338- 11x  

We need the angle AOD to find the x value

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Answer:

1/3

Step-by-step explanation:

1/4 is equal to 3/12. So then we add the 3/12 and the 1/12 and get 4/12. 4/12 is equal to 1/3, so that is our answer. Hope this helps!

Answer:

Step-by-step explanation:

(-5+5i)+(4-4i)

=-5+5i+4-4i

=-1+i

Answer:

Kindly check explanation and attached picture

Step-by-step explanation:

Given the data on the number of pages read by each of 20 students last summer :

163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431

Using an online histogram plotter, the plotted histogram can be found in the picture attached.

With frequency on the y-axis and class on the x - axis.

Class 160 - 220 has the highest frequency of 6 students while 400 - 460 has the least with 2

Answer:

1.28 * 10^10

Step-by-step explanation:

Area Code:  8 * 2 * 10

7 digit number: 8 * 10 * 10 * 10 * 10 * 10 * 10

The total number of area codes is 160

8,000,000 * Area Codes

1.28*10^10

Answer:

a)

h(1.2) =52.8

h(5)=125

b) h(10)=0 .Este valor es lo que tarda el cohete en tocar el suelo.

Step-by-step explanation:

Para contestar esta pregunta debemos reemplazar el valor de t (segundos) por los valores requeridos en la siguiente ecuación:

h(t) =50 t -5t ²

a)

h(1.2) =50 (1.2) -5(1.2)²

h(1.2) = 60-5(1.44)

h(1.2) = 60-7.2 = 52.8

h(5) =50 (5) -5(5)²

h(5) =250-5(25)

h(5)=250-125=125

b)

h(10) =50 (10) -5(10)²

h(10)= 500-5(100)

h(10) = 500-500=0

Este valor es lo que tarda el cohete en tocar el suelo, en 10 segundos la altura h es 0.

Answer:

its c.7

Step-by-step explanation:

I took the quiz

Answer:

c. 7

Step-by-step explanation:

i had this quiz also

Given statement solution is :- The correct statement describing the number of possible solutions to the system is:

D. The system may have no, 1, or infinite solutions.

Because when a quadratic function and a linear function are set equal to each other, the resulting system of equations may have no solution, one solution, or infinite solutions.

A Linear Equation is an equation of a line. A Quadratic Equation is the equation of a parabola. and has at least one variable squared (such as x2) And together they form a System. of a Linear and a Quadratic Equation.

A linear equation is a polynomial equation of the form y = mx + d, where m and d are constants, and a quadratic equation is a polynomial equation of the form y = ax2 + bx + c, where a, b, and c are constants.

The correct statement describing the number of possible solutions to the system is:

D. The system may have no, 1, or infinite solutions.

In general, when a quadratic function and a linear function are set equal to each other, the resulting system of equations may have no solution, one solution, or infinite solutions. The specific number of solutions depends on the nature of the quadratic and linear functions and their relationship.

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Answer:

Step-by-step explanation:

a) Input = -9   ⇒ x = -9

y = x² + 3

Plugin x = (-9),

y = (-9)² + 3  

  =  81 +  3                {(-9)² = -9 * (-9) = 81}

y = 84    ---> Output

y = √x - 2

  = √-9 - 2          { i² = -1}

  \(= \sqrt{3*3 * i^{2}}-2\\\\=3i -2\)    

y = 3i - 2  ------> Output

b) Output = 0

y  = x² + 3

x² + 3 = 0

x² = -3

\(x = \sqrt{-3}=\sqrt{3i^{2}}\\\\x = i \sqrt{3}\)

y = √x -2

0 = √x - 2

√x = 2

Take square,

\((\sqrt{x})^{2}=2^{2}\\\x = 4\)

Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

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By using trigonometric relations, we will see that the distance between Carlos and the tree is:

D = 781.23 ft

We can model this with a right triangle. We know that Carlos is 6ft tall, and the height of the tree is 275ft.

Then one of the cathetus of the triangle is equal to:

275ft - 6ft = 269ft.

That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.

Then we can use the relation:

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

Replacing that, we get:

tan(19°) = 269ft/D

Solving for D, we get:

D = 269ft/tan(19°) = 781.2ft

So we conclude that Carlos is at 781.23 ft of the tree.

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True. The statement "if the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25" is true.

When a range of feasibility is given, the lower and upper bounds of the values that can be chosen for the variables in a linear programming problem are given. The range of feasibility reflects the range within which the optimum answer can be found. It is a parameter that measures the extent to which the variables can change and still allow the same optimal answer to be obtained. In this case, the range of feasibility suggests that the initial amount of a resource was 20 and could be increased by 5, implying that the total amount of the resource can be 25. Therefore, statement is true.

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The value of the rate of growth in Japan is - 0.55.

From the question above, :Birth rate = 7.7 per thousand

Death rate = 9.8 per thousand

Net migration = 0.55 per thousand

The rate of growth can be calculated using the following formula:

r = (birth rate - death rate) + net migration

Where,r = rate of growth

birth rate = number of live births per thousand in a population in a given year

death rate = number of deaths per thousand in a population in a given year

net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year

Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.

Therefore, the rate of growth in Japan is - 0.55.

Your question is incomplete but most probably your full question was:

thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total

population • 100 but im not sure how to do it with net migration.

Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan

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