Please help and explain

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

Learn more about Logarithmic differentiation: brainly.com/question/30881276

#SPJ11

Answer:

Step-by-step explanation:

Answer:

The answer is Medium size

Step-by-step explanation:

The equation is simple

14.20 divided by 20 = 0.71

Answer:

5/2

Step-by-step explanation:

10 multiplied by 5/2 gives us 25, so the scale factor is 5/2.

The solution in terms of y is -e^(4x) + xe^(4x).

Given that the initial value problem is y" - 8y' + 16y = 0, y(0) = -1, y'(0) = -3. To find the unique solution for the second-order initial value problem, we solve the homogeneous differential equation first:y" - 8y' + 16y = 0Characteristics equation is r² - 8r + 16 = 0(r - 4)² = 0r = 4 (Repeated roots)

The general solution is given as yh = c1e^(4x) + c2xe^(4x)Here, c1 and c2 are constants. We apply the initial conditions y(0) = -1, y'(0) = -3 into the general solution to get the value of c1 and c2 at x = 0.(i) y(0) = c1 + 0c2 = -1....(1)(ii) y'(0) = 4c1 + c2 = -3....(2)Solving equations (1) and (2) for c1 and c2, we get,c1 = -1, c2 = 1

Therefore, the unique solution for the second-order initial value problem y" - 8y' + 16y = 0, y(0) = -1, y'(0) = -3 isy = yh + yp = c1e^(4x) + c2xe^(4x) = -e^(4x) + xe^(4x).

Hence, the solution in terms of y is -e^(4x) + xe^(4x).

Therefore, we have found the unique solution for the second-order initial value problem.

Know more about  initial value problem here,

https://brainly.com/question/30466257

#SPJ11

2.3 : 2.2

3x : 5y and 7 : 11

3x : 5y

7 : 11

To find x:

3x = 7

x = 7/3 (Bring 3 over to 7 to divide)

x = 2.3 OR 2/1/3

To find y:

5y = 11

y = 11/5 (Bring 5 over to 11 to divide)

y = 2.2 OR 2/1/5

So,

x = 2.3

y = 2.2

Therefore, the answer is:

x : y = 2.3 : 2.2

The test statistic (or standard score) would be 1.72.

To convert the outcome of the pulse rate data to a standard score, we would need to calculate the z-score. The formula for the z-score is: (sample mean - population mean) / (standard deviation / square root of sample size).

In this case, the sample mean is 76, the population mean (according to the report) is 72, the standard deviation is 13, and the sample size is 85. Plugging these values into the formula, we get:

(76 - 72) / (13 / sqrt(85)) = 1.72.

Therefore, the test statistic (or standard score) is 1.72. This indicates that the sample mean of 76 is 1.72 standard deviations above the population mean of 72. This information can be used to conduct a statistical test of significance and determine whether the difference between the sample mean and population mean is statistically significant.

More on test statistic: https://brainly.com/question/28957899

#SPJ11

The line that passes through the point (-2,-1) and has a slope of 5. The equation of the line is y + 1 = 5(x + 2).

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

Using the slope and 1 point format:   (y- y₁) = m(x - x₁)  

where m = slope = 5, and point is (x₁, y₁). In this case point (x₁, y₁) = (-2, -1)

x₁ = -2,  y₁ = -1

Using: (y- y₁) = m(x - x₁)

y - -1 = 5(x - -2)

y + 1 = 5(x + 2).

To learn more about slope refer to:

https://brainly.com/question/3493733

#SPJ13

Answer:

0.167π

Step-by-step explanation:

r = 0.5

\(Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 0.5^{3} = 0.167\pi\)

Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing.  I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

y = -(2/3) -(4/3)

y = -(6/3) or -2

The solution is (2,-2)

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

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

The triangle DEF is first reflected over the y-axis. This means that each point of the triangle is mirrored across the y-axis, resulting in a new triangle.

Next, the reflected triangle is translated down 4 units and right 3 units. This means that each point of the reflected triangle is moved 4 units downwards and 3 units to the right, resulting in a final triangle.

In congruency statements, the order of the vertices indicates the order in which the transformations are applied. So, the congruency statement that describes the figures is:

Triangle DEF reflected over the y-axis and then translated down 4 units and right 3 units is congruent to triangle RUS.

The reflection over the y-axis changes the sign of the x-coordinate of each point, while keeping the y-coordinate the same. The translation moves each point 4 units down and 3 units to the right. This combination of transformations results in a congruent triangle.

The congruency statement that describes the figures is δDEF → δRUS.

To know more about triangle visit

https://brainly.com/question/2773823

#SPJ11

Answer:

Triangle DEF is congruent to triangle SRU

Step-by-step explanation:

did the quiz

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

Graph in pic

(Credits: Symbolab)

Answer: a^3 sqrt(a)

Step-by-step explanation: just did it :)

No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.

To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:

1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.

2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.

3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.

4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.

Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.

Learn more about null hypothesis at: brainly.com/question/28098932

#SPJ11

Answer:

Step-by-step explanation:

Factor the numerator and the denominator to get

\(\frac{(x+2)(x-2)}{(x+2)(x+3)}\\ \\ \text{The (x+2) terms cancel out leaving}\\ \\ \frac{x-2}{x+3}\)

Answer:

Hey there!

Sam's Money=1.80 dollars + 0.75 dollars.

1.80+0.75-1.50=1.05

1.05/0.13= 8.08.

He will be able to buy 8 pieces of gum.

Let me know if this helps :)

Step-by-step explanation:

(Ryan+ castel)/2

(5+6)/2

11/2

5.5 hrs or 5½ hrs

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

For more such questions on algebraic, click on:

https://brainly.com/question/4344214

#SPJ8

Answer:

0.5

Step-by-step explanation:

Answer:

answer is 0.5 just got it right

Step-by-step explanation:

A card is drawn randomly from a standard 52-card deck. then the probabilities are a) 1/13 b) 3/13 and c) 10/13

There are four 3's in the deck. This means that, from 52 possible cards to drawn, we have 4 chances of drawing a 3. This means that the probability will be:

p = 4/52

p= 1/13

b.

For every suit, there are three face cards, J, Q and K. There are 4 suits, so, the total number of face cards its:

4*3 =12

The total possible cards are, still, 52, so, the probability will be

p= 12/52

p=3/13

c.

We know that the card drawn must be a face card, o not being a face card. There is no third choice here. So, the probability of drawing a face card OR not drawing a face card its:

p=52/52

p=1

so

p( the card is a face card ) + p( the card is not a face card) =1

but, we know that

p( the card is a face card ) =3/13

so

p( the card is not a face card) =1- 3/13

                                                 = 10/13

learn more about of probability here

https://brainly.com/question/13293035

#SPJ4

The quantity of water in the reservoir after 6 hours at a rate of 2000 + 5t gal/hour is 12,180 gallons.

The quantity of water in the reservoir after 6 hours can be found by integrating the rate of flow over the given time period.

To find the quantity of water in the reservoir after 6 hours, you need to integrate the flow rate function with respect to time and evaluate it from 0 to 6 hours.

The flow rate function is given by R(t) = 2000 + 5t gal/hour.

First, we find the antiderivative of the rate of flow:

∫(2000 + 5t) dt = 2000t + (5/2)t² + C

Then, we plug in t = 6:

Now, evaluate the integral from 0 to 6 hours:

(2000(6) + (5/2)(6)²) - (2000(0) + (5/2)(0)²)

= 12000 + 180

= 12180 gallons

To learn more about integral  click here

brainly.com/question/18125359

#SPJ11

Answer:

1. The estimate of the proportion of mosquitoes in the area that carry the disease is approximately 0.1606 or 16.06%

2. To check for accuracy of the of the value of proportion of disease carrying mosquito in the area

Step-by-step explanation:

The given parameters are;

The number of mosquitoes in the sample = 137

The number of mosquitoes that carry the disease = 22

1. The estimate of the proportion of mosquitoes in the area that carry the disease = (Number of mosquitoes with the disease)/(The number of mosquitoes in the sample)

The estimate of the proportion of mosquitoes in the area that carry the disease = 22/137 ≈ 0.1606 or 16.06%

2. The reason the scientist run the simulations to find additional possible proportions of mosquitoes in the area that carry the disease is to check for variability and accuracy of the proportion of disease carrying mosquito in the area.

1. The proportion of mosquitoes in the region that carry the illness is estimated to be 16.06%.

2. To ensure that the proportion of disease-carrying mosquitos in the region is accurate.

A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.

Given data;

There were 137 mosquitos in the sample,\(\rm N_s\)

The number of disease-carrying mosquitos is,\(\rm N_m\)=22

The estimated proportion of disease-carrying mosquitos in the region is found as;

\(\rm D_m=\frac{N_m}{N_s} \\\\ \rm D_m=\frac{22}{137} \\\\ D_m=16.06 \ %\)

2. The scientists used simulations to determine alternative probable proportions of disease-carrying mosquitos in the region in order to check for variability and accuracy in the proportion of disease-carrying mosquitos in the area.

Hence,the proportion of mosquitoes in the region that carry the illness is estimated to be 16.06%.

To learn more about the ratio, refer to the link;

https://brainly.com/question/14335762

#SPJ5

Answer:

In algebra, we begin to see variables or letters that are used to represent numbers. An example of a mathematical expression with a variable is 2x + 3. In the expression 2x + 3, the coefficient of x is number 2, and it means 2 times x plus 3.

The probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96%.

To find the probability that a randomly selected toaster will have a total resistance of 345 to 355 ohms, we need to know the distribution of total resistance and parameters such as mean and standard deviation.

Expecting that the dispersion of add up to resistance takes after a typical conveyance with cruel μ and standard deviation σ, ready to utilize the standard ordinary dispersion to calculate the likelihood that the entire resistance will be between 345 and 355 ohms.

 First, we need to normalize the 345 and 355 values ​​with the following formula:

z = (x - μ) / σ

where x=desired value, μ = mean, σ = standard deviation, and z =corresponding z-score.

For x = 345 ohms:

z1 = (345 - μ) / σ

For x = 355 ohms:

z2 = (355 - μ) / σ

Next, we need to find the area under the standard normal distribution curve between z-scores z1 and z2. This represents the probability that the total resistance will be between 345 and 355 ohms.

You can find this range using a standard regular table or calculator. For example, using the standard normal table, we can find the region between z1 and z2 like this:

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(z2) - Φ(z1)

where Φ(z) is the standard cumulative normal distribution function (CDF), the probability that a standard normal random variable is less than or equal to z.

For example, if z1 = -1.5 and z2 = 1.5, then

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(1.5) - Φ(-1.5) = 0.8664 - 0.0668 ≈ 0.7996

Therefore, the probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96% (assuming the distribution of total resistance follows a normal distribution with a known mean and standard deviation).

learn more about probability

brainly.com/question/30034780

#SPJ4

Answer:

11

Step-by-step explanation:

Three times an unknown number

= 3(n)

Added to

Two less than four times the same unknown number

= 4 - 2(n)

Total

= 3(n) + 4 - 2(n) = 15

= 3n + 4 - 2n = 15

Collect like terms

= 3n - 2n = 15 - 4

n = 11

Answer:

we have

C=(2,-1)

B=(-2,3)

since

BC is hypotenuse

length of BC=√[(-2-2)²+(3+1)²]=√32=4√2 units is your answer

Answer:

y= (x^2-3) + 2

Step-by-step explanation:

It is plus two on the end to go up 2 on the y axis since the question says up two units and in the parenthesis is where you can move the start of and line, exponential line, or parabola to the left or to the right. When in the parenthesis, if you do however many x's and whatever exponent there is if you plus it will go into the negatives, ot left, and minus will go positive, or right. Therefore the answer is y= (x^2-3) +2.

BTW, when writing exponents,  this: ^, is an exponent sign but working on certain platforms will allow you to write them like in the image, and if it can then you should write it like that.

Hope this helps!

The probability that the first nonzero digit in the decimal expansion of √x is 3 is,

⇒ P (A) = 2/3

Now, Let A be the event that the first nonzero digit in the decimal expansion of √√{x} is 3.

We want to find P(A).

First, notice that A occurs if and only if 0.3² \leq x < 0.4².

That is, A occurs if and only if √{x} lies between 0.3 and 0.4.

The probability that √{x} lies between 0.3 and 0.4 is the area of the region between the curve y=√{x} and the horizontal lines y=0.3 and y=0.4 over the interval [0, 1].

This area can be found by integrating the function √x over this interval:

∫₀¹ √{x} dx = 2/3

Therefore, P(A) is the ratio of the area of the region between the curve y=√{x} and the horizontal lines y=0.3 and y=0.4 over the interval [0, 1] to the area of the entire rectangle, which is equal to 1.

Hence,

⇒ P(A) = 2/3

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ4