Last week, Pauline worked 35 hours and made $280.
How much money did Pauline make per hour?The boss at Pauline’s company makes $600 a week. How many hours would Pauline need to work to make $600?

The histogram shows that the most common audit time is between 13 and 17 days, and the least common audit time is between 21 and 25 days.

Frequency, Cumulative Frequency, and Cumulative Percent Frequency Table:

The histogram shows that the most common audit time is between 13 and 17 days, and the least common audit time is between 21 and 25 days.

Frequency, Cumulative Frequency, and Cumulative Percent Frequency Table:

Year-end Audit Time (in Days)        Frequency        Cumulative Frequency        Cumulative Percent Frequency

13        3        3        15.00%

14        1        4        20.00%

15        1        5        25.00%

17        2        7        35.00%

19        1        8        40.00%

21        1        9        45.00%

22        1        10        50.00%

24        1        11        55.00%

25        1        12        60.00%

26        1        13        65.00%

27        1        14        70.00%

29        2        16        80.00%

30        1        17        85.00%

32        3        20        100.00%

b. Histogram Chart:

30  |                        

   |                        

   |                        

   |                        

25  |                        

   |             *          

   |             *          

   |             *          

20  |                        

   |             *          

   |             *          

   |             *          

15  |  *          *     *      

   |  *          *     *      

   |  *          *     *      

   |  *     *    *     *      

10  |  *     *    *     *      

   |  *     *    *     *      

   |  *     *    *     *      

   |  *     *    *     *      

   |------------------------

      13    17    21    25    29    33

In the histogram, the horizontal axis shows the range of values of the year-end audit time (in days), and the vertical axis shows the frequency. The asterisks (*) represent the frequency of each range. The histogram shows that the most common audit time is between 13 and 17 days, and the least common audit time is between 21 and 25 days.

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The significance level is 0.05.

There is evidence to suggest that the proportion of students at the school who fear public speaking is less than 0.5000.

Test statistic is -6.94 accurate to two decimal places.

We can use a one-tailed hypothesis test with the following null and alternative hypotheses:

Null hypothesis: The proportion of students at the school who fear public speaking is equal to or greater than 0.5000.

Alternative hypothesis: The proportion of students at the school who fear public speaking is less than 0.5000.

The significance level is 0.05.

To conduct the test, we need to find the test statistic and compare it to the critical value.

First, we calculate the sample proportion of students who fear public speaking:

p⁻ = 125/400 = 0.3125

Next, we calculate the standard error of the sample proportion:

SE = sqrt[p⁻(1 - p⁻) / n] = sqrt[0.3125(1 - 0.3125) / 400] = 0.027

Then, we calculate the test statistic:

z = (p⁻ - p) / SE = (0.3125 - 0.5000) / 0.027 = -6.944

Since the alternative hypothesis is that the proportion of students who fear public speaking is less than 0.5000, we use a one-tailed test and look up the critical value for a 5% level of significance in the standard normal distribution table. The critical value is -1.645.

Since the calculated test statistic (-6.944) is less than the critical value (-1.645), we reject the null hypothesis.

Therefore, we can conclude that there is evidence to suggest that the proportion of students at the school who fear public speaking is less than 0.5000.

The test statistic is -6.94 accurate to two decimal places.

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For any m x n matrix A, AAT is symmetric, but ATA is not symmetric.

To prove that for any m x n matrix A, AAT and ATA are symmetric, we need to show that the transpose of each product is equal to the product itself.

Calculate (AAT)T:
Let's start with AAT. We know that for any matrices X and Y, (XY)T = YT XT. So, for AAT, we have:

(AAT)T = (AT)T [tex]A^{T}[/tex]

Simplify (AAT)T:
Now, we can apply the rule that ([tex]A^{T}[/tex][tex])^{T}[/tex] = A. Thus, we get:

(AAT)T = A [tex]A^{T}[/tex]

As you can see, (AAT)T = AAT, which means AAT is symmetric.

Calculate (ATA)T:
Now let's look at ATA. Using the same rule as before, we have:

(ATA)T = A[tex]T^{T}[/tex] ([tex]A^{T}[/tex][tex])^{T}[/tex]

Simplify (ATA)T:
Again, we apply the rule that ([tex]A^{T}[/tex][tex])^{T}[/tex] = A:

(ATA)T = A [tex]A^{T}[/tex]

In this case, we have (ATA)T ≠ ATA, which means ATA is not symmetric.

In conclusion, for any m x n matrix A, AAT is symmetric, but ATA is not symmetric.

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The product of f(x) and g(x) at x = -7/6 is 7/6

To find and simplify (f⋅g)(4.5) for the given functions, we need to first identify the individual functions f(x) and g(x). Based on the given information, we have:

f(x) * g(x) = -x
4 = -12x - 10

Now, we need to solve for f(x) and g(x). We can use the second equation to find x:
4 = -12x - 10
14 = -12x
x = -7/6

Now that we have x, we can find f(x) and g(x) using the first equation:
f(-7/6) * g(-7/6) = -(-7/6)
f(-7/6) * g(-7/6) = 7/6

Since we don't have enough information to find the exact expressions for f(x) and g(x), we can't simplify (f⋅g)(4.5) further. However, we now know that the product of f(x) and g(x) at x = -7/6 is 7/6.

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0.08 = 8/100 = (8 ÷ 4)/(100 ÷ 4) = 2/25

Option B is the lowest term fraction form for the decimal 0.08, which is 2/25.

The representation of a portion of a whole using fractions. In the format 1/2, two numbers are written side by side, separated by a line. Numerator and denominator are terms used to describe the top and bottom numbers, respectively. The numerator indicates the number of equally sized pieces you have, while the denominator indicates how many equal sections the entire has been divided into.

You have consumed 3/8 of a pizza, for instance, if it was sliced into 8 equal pieces and you ate 3 of them.

By dividing both the numerator and denominator by their greatest common factor, we can simplify the fraction 0.08 and represent it in lowest terms (GCF). The GCF of 8 and 100 in this situation equals 4. Hence, we divide both 8 and 100 by 4:

0.08 = 8/100 = (8 ÷ 4)/(100 ÷ 4) = 2/25

As a result, option B, 2/25, is the decimal 0.08 expressed in lowest terms.

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The angle between the vectors a and b is approximately 41.4 degrees.

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The precision of the estimate decreases when standard error of an estimate when the sample size in a SRS decreases. So, the correct answer is D).

The standard error of an estimate measures the variability of sample means around the population mean. As the sample size in a simple random sample (SRS) decreases, the sample mean becomes less representative of the population mean, resulting in more variability or less precision in the estimate.

The standard error increases as the sample size decreases because there is more uncertainty in the estimate due to the smaller sample size. Therefore, decreasing the sample size will increase the margin of error and decrease the precision of the estimate. So, the correct option is D).

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The size of matrix B is 9×7.

To find the size of matrix B, you need to understand the rules for matrix multiplication. When multiplying two matrices A and B, the number of columns in matrix A must equal the number of rows in matrix B.

In this case, matrix A has 9 rows and 9 columns, so it's a 9×9 matrix. The product AB is given as a 9×7 matrix, meaning it has 9 rows and 7 columns.

Since the number of columns in matrix A (9) must equal the number of rows in matrix B, it tells us that matrix B has 9 rows. To find the number of columns in matrix B, you can use the dimensions of the product AB, which is 9×7. This indicates that matrix B has 7 columns.

Therefore, matrix B is a 9×7 matrix.

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Answer:

  12.81 cubic inches

Step-by-step explanation:

You want the volume of a cone with diameter 3.4 inches and slant height 4.56 inches.

The height of the cone can be found using the Pythagorean theorem. It is the missing leg of a right triangle with hypotenuse 4.56 and leg (3.4/2) = 1.7.

  h² + 1.7² = 4.56²

  h = √(4.56² -1.7²) ≈ 4.2313 . . . . inches

The volume of the cone is give by the formula ...

  V = 1/3πr²h

where r is the radius and h is the height.

Using r = 1.7 in and h ≈ 4.2313 in, we find the volume to be ...

  V = (1/3)π·(1.7 in)²·(4.2313 in) ≈ 12.81 in³

The cone will hold about 12.81 cubic inches of water.

__

Additional comment

That's about 7.1 fluid ounces.

The zeros of the function f(x) = 1/2cos(2x) in the interval (-2π, 2π) are: x = π/4, 3π/4.

To find the zeros of the function f(x) = 1/2cos(2x) in the interval (-2π, 2π), we need to solve the equation f(x) = 0.

We know that the cosine function has zeros at x = π/2, 3π/2, 5π/2, etc. So we need to find all values of x in the interval (-2π, 2π) that satisfy the equation cos(2x) = 0.

Using the double angle formula for cosine, we have:

cos(2x) = 2cos²(x) - 1 = 0

Solving for cos(x), we get:

cos(x) = ±sqrt(1/2)

So the solutions for cos(2x) = 0 are:

x = π/4, 3π/4, 5π/4, 7π/4

However, we need to check which of these solutions are within the interval (-2π, 2π).

Since π/4 and 3π/4 are both between -2π and 2π, they are valid solutions. But 5π/4 and 7π/4 are not within the interval, so we can discard them.

Therefore, the zeros of the function f(x) = 1/2cos(2x) in the interval (-2π, 2π) are: x = π/4, 3π/4.

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To find the eigenvectors and eigenvalues of matrix A, we first need to solve for the characteristic equation:

det(A - liI) = 0, where I is the identity matrix.

For matrix A, we have:

det(A - liI) = det([1-li 0; 0 1-li][1 0; 0 1]) - det([0 -1; 0 1-li][1 0; 0 1])
det(A - liI) = (1-li)(1-li) - 0 = (1-li)^2 = 0
Solving for li, we get li = 1.

So, the eigenvalue of A is 11 = 1.

To find the eigenvector V1 corresponding to li, we need to solve for (A - liI)V1 = 0:

([1 0; 0 1] - [1 0; 0 1])[x y] = [0 0]
[0 0][x y] = [0 0]

This gives us the equation x = 0 and y = 0. So, the eigenvector V1 corresponding to li = 1 is [0 0].

Now, to find the second eigenvector V2 corresponding to li = 1, we need to solve for (A - liI)V2 = 0 such that V2 is linearly independent from V1:

([1 0; 0 1] - [1 0; 0 1])[x y] = [0 0]
[0 -1][x y] = [0 0]

This gives us the equation -y = 0, which implies y = 0. So, the eigenvector V2 corresponding to li = 1 is [1 0].

To check that these eigenvectors are indeed linearly independent, we can form a matrix P by placing V1 and V2 as its columns:

P = [0 1; 0 0]

Taking the determinant of P, we get det(P) = 0, which implies that V1 and V2 are linearly independent.

Therefore, the eigenvectors V1 and V2 corresponding to the eigenvalue li = 1 are [0 0] and [1 0], respectively.

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The equation that best fits the data is, y = -8.34x1^2 + 18.5ln(x1) + 5.34.

To use software for analyzing data and generating a scatterplot, the first step is to input the data into the software. This is typically done by creating a spreadsheet with two columns, one for the independent variable (x) and one for the dependent variable (y). After inputting the data, the software can then generate a scatterplot. Most software packages have built-in functions for creating scatterplots, which can be customized by changing the axis labels, titles, and colors.

Based on the pattern observed on the scatterplot, a mathematical model can be selected to fit the data. Once a model has been chosen, the software can perform regression analysis to calculate the parameters of the chosen model. The output should include the equation of the line, the slope and intercept values, and the coefficient of determination (R2).

To evaluate the goodness of fit, the R2 value can be used. Higher R2 values indicate a better fit between the model and the data. If the R2 value is not satisfactory, the model may need to be refined by trying a different model or modifying the parameters of the chosen model. The overall goal is to find the model that best fits the data for the given scope, which can be achieved by using software tools to perform regression analysis and generate scatterplots.

Using a calculator or computer, we can obtain the regression equations for the various models and calculate their R-squared values:

Linear model: y = -4.87 + 7.55x1, R^2 = 0.3755

Quadratic model: y = -8.34x1^2 + 18.5ln(x1) + 5.34, R^2 = 0.9295

Logarithmic model: y = 1.07 + 6.89ln(x1), R^2 = 0.9041

Exponential model: y = -3.14 + 6.59x1, R^2 = 0.8672

Power model: y = 0.6214x1^1.0969, R^2 = 0.9087

Based on the R-squared values, we can see that the quadratic model has the highest value of 0.9295, indicating that it best fits the data. Therefore, the equation that best fits the data is,

y = -8.34x1^2 + 18.5ln(x1) + 5.34

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The polygons when sorted as squares and not squares are :

Squares:

Not squares :

A square is a type of quadrilateral that has four sides of equal length and four right angles. A square itself, which has four sides of equal length and four right angles. A rhombus, which also has four sides of equal length but may not have four right angles is also a square if it does have four right angles.

A rectangle, which has four right angles but may not have four sides of equal length. If it does have four sides of equal length, it is also a square.

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The full question is:

Sort the polygons.

Squares Not squares

Regular square

Scalene triangle

Rectangle with equal adjacent sides

Irregular pentagon

Rhombus with equal sides

Isosceles trapezoid

The formula for g(x) given that g(x) be the inverse of f(x)=x³  is g'(x) = 1 / (3x^(2/3)).

Let's first find the formula for g(x) and then compute g'(x) in two ways.

Given that f(x) = x³, to find the inverse function g(x), we need to switch x and y in the equation and solve for y:

x = y³
y = g(x) = x^(1/3)

Now, we can compute g'(x) in two ways:

1. Using Theorem 1 (Inverse Function Theorem):
Theorem 1 states that if f has an inverse function g, then (g'(x)) = 1 / (f'(g(x))).
To apply this theorem, we need to find f'(x) first:

f'(x) = d(x³)/dx = 3x²

Now we can use Theorem 1 to find g'(x):

g'(x) = 1 / (f'(g(x))) = 1 / (3(g(x))²) = 1 / (3(x^(1/3))²) = 1 / (3x^(2/3))

2. By direct calculation:
To find g'(x) directly, we differentiate g(x) with respect to x:

g'(x) = d(x^(1/3))/dx = (1/3)x^(-2/3)

Both methods yield the same result:

g'(x) = 1 / (3x^(2/3))

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None of the options provided use inductive reasoning to show that the sum of two odd integers is even.

Equation is a mathematical statement that uses symbols and numbers to represent two expressions or values that are equal. It is used to show the relationship between two or more variables, and can be used to solve for unknown values. Equations can also be used to model real-world problems, such as modeling the cost of a trip or calculating the area of a circle.

None of the above. Inductive reasoning is a form of logical argument that uses a pattern of specific evidence or observations to draw a general conclusion. In this case, none of the options provided use inductive reasoning to show that the sum of two odd integers is even. Option A simply states two examples of the sum of two odd integers being even, but does not explain why this is the case. Option B states a mathematical equation that is not related to the sum of two odd integers. Option C states a mathematical equation that could be used to prove that the sum of two odd integers is even, but does not explain why this is the case. Therefore, none of the options provided use inductive reasoning to show that the sum of two odd integers is even.

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Answer: negative

Step-by-step explanation: A negative multiplied by any number of positives will always be negative.

Gary's weight after 6 months of dieting was 84 kg.

A percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, divide the number by the whole number and multiply by 100. So a percentage means a part per hundred. The word percent means out of 100.

Firstly we can calculate  Gary's weight after six months of dieting, we must first calculate how much weight he lost during the diet. Gary lost 30% of his weight, which can be expressed as:

30/100 × 120 kg = 36 kg

This means that Gary lost 36 pounds during the diet.

To find out his weight after the diet, we need to subtract the weight he lost from his original weight we get

120 kg - 36 kg = 84 kg

Therefore, Gary's weight after 6 months of dieting was 84 kg.

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Answer:

Equation: y=250x

Slope: m=250/1

Answer:

The correct equation is x + 3.5y = 45

The equivalent expression is 12x + 5y

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, their terms, constants and the factors.

These algebraic expressions are known to consist of mathematical or arithmetic operations, such as;

From the information given, we have the expression as;

(5y + 3x) +9x

To simply, expand the bracket, we get;

5y + 3x + 9x

collect the like terms and add

12x + 5y

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Step-by-step explanation:

to find the commision he paid its

[tex]4500000 \div 100 \times 3 = 135000[/tex]

to find how much Ramesh got its

[tex]4500000 - 135000 = 4365000[/tex]

The values from the distribution x1 and x2 are approximately 15.34 and 43.77, respectively. a) E[s2] = (n-1) * σ^2 = 29 * 18 = 522 and Var(s2) = 2*(n-1)*σ^4/(n-3) = 2*29*18^2/27 = 11664 and b) x1 = 17.71 and x2 = 42.56.

(a) Since the sample is drawn from a normal distribution, we know that s2 follows a chi-squared distribution with n-1 degrees of freedom, where n is the sample size. Therefore, E[s2] = (n-1) * σ^2 = 29 * 18 = 522 and Var(s2) = 2*(n-1)*σ^4/(n-3) = 2*29*18^2/27 = 11664.
(b) We need to find the values of x1 and x2 such that P(s2 < x1) = P(s2 > x2) = 0.05. Since s2 follows a chi-squared distribution with 29 degrees of freedom, we can use a chi-squared table or calculator to find the critical values. Using a chi-squared table with 29 degrees of freedom, we find that the 0.05 quantile is 17.71 and the 0.95 quantile is 42.56. Therefore, x1 = 17.71 and x2 = 42.56.
(a) For a sample drawn independently from a normal distribution N(µ, σ^2) of size n, the expected value of the sample variance (E[s^2]) and its variance (Var(s^2)) are related to the population variance (σ^2).
E[s^2] = σ^2
Var(s^2) = (2σ^4) / (n - 1)
Given that the sample is drawn from a normal distribution with a mean (µ) of 122.55 and variance (σ^2) of 18, and the sample size (n) is 30, we can calculate E[s^2] and Var(s^2):
E[s^2] = σ^2 = 18
Var(s^2) = (2 * 18^2) / (30 - 1) = (2 * 324) / 29 ≈ 22.3448
(b) To find x1 and x2 such that P(s^2 < x1) = P(s^2 > x2) = 0.05, we'll use the chi-square distribution (χ^2) with degrees of freedom (df) equal to n - 1 = 29.
First, let's find the critical values of the chi-square distribution corresponding to the given probabilities:
χ^2(0.05, df=29) = x1
χ^2(0.95, df=29) = x2
Using a chi-square distribution table or a statistical calculator, we get:
x1 ≈ 15.34
x2 ≈ 43.77
Therefore, the values x1 and x2 are approximately 15.34 and 43.77, respectively.

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Answer:

......................

Answer:

40

Step-by-step explanation:

The minimum score is the lowest number in the set of data, which in this set is 40

The solution is : Simplification of : 7! is 5040.

We have,

Factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point.

Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1.

so, we have,

! in this case means factorial. 7 factorial means that we multiply 7 by every number it precedes (starting from 1, of course).

i.e. we have,

7! = 1 × 2 × 3 × 4 × 5 × 6 × 7.

7! = 2 × 3 × 4 × 5 × 6 × 7

7! = 6× 4 × 5 × 6 × 7

7! = 24× 5 × 6 × 7

7! = 120 × 6 × 7

7! = 720 × 7

7! = 5040.

Therefore, the answer is 5040.

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The coordinates of the vertices of the image after a rotation of 270° counterclockwise about the origin include the following: C) P(-2,4), Q'(-3, 1). and R'(-5,3)

In Mathematics and Geometry, the rotation of a point 270 degrees about the origin in a counterclockwise (anticlockwise) direction would produce a geometric figure that has the coordinates (y, -x).

By applying a rotation of 270 degrees about the origin in a counterclockwise (anticlockwise) direction to the triangle PQR, the new coordinates are given by:

(x, y)                                   →         (y, -x)

Ordered pair P (-4, -2)        →    Ordered pair P' (-2 -(-4)) =  (-2, 4).

Ordered pair Q (-1, -3)        →    Ordered pair Q' (-3 -(-1)) =  (-3, 1).

Ordered pair R (-3, -5)        →    Ordered pair R' (-5 -(-3)) =  (-5, 3).

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Based on the question you provided, we can estimate the distance an athlete can jog in 2 hours given the information that the average person can walk 9/10 mile in 1/3 hour and the athlete can jog 3 times that speed.

If the average person can walk 9/10 mile in 1/3 hour, then their average speed would be:

(9/10) miles ÷ (1/3) hour = (9/10) ÷ (1/3) ≈ 2.7 miles per hour

Since the athlete can jog 3 times that speed, their average jogging speed would be:

2.7 × 3 = 8.1 miles per hour

Therefore, in 2 hours, the athlete can roughly jog a distance of:

distance = speed × time = 8.1 miles/hour × 2 hours = 16.2 miles

So we can estimate that the athlete can jog a distance of 16.2 miles in 2 hours.


hope this helps :)

from your boy on top

Answer:

49,6

Step-by-step explanation:

The segments of intersecting tangents are equal

That means, all sides of the given polygon are

equal

P = 12,4 × 4 = 49,6

The GPA should students get to graduate as honor students is  students must have a GPA of approximately 3.68 or higher to graduate as honor students at this university.

To graduate as an honors student at this university, a student would need to have a z-score of at least 1.96, which corresponds to being in the top 2.5% of the distribution.

Using the mean and standard deviation provided, we can calculate the corresponding gpa:

z-score = (x - mean) / standard deviation
1.96 = (x - 2.7) / 0.5
0.98 = x - 2.7
x = 3.68

Therefore, a student would need a cumulative gpa of 3.68 or higher to graduate as an honors student at this university.

At the university, the distribution of students' cumulative GPAs is bell-shaped with a mean of 2.7 and a standard deviation of 0.5.

To graduate in the top 2.5% as honor students, a student's GPA must be at or above a certain threshold.

Using a standard normal (z-score) table, we find that a z-score of 1.96 corresponds to the top 2.5% of the distribution.

To calculate the GPA required to achieve this z-score, we can use the formula:

GPA = Mean + (Z-score * Standard Deviation)

GPA = 2.7 + (1.96 * 0.5)

GPA = 2.7 + 0.98

GPA ≈ 3.68

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To use traces to sketch the surface x = 5y^2 − 5z^2, we can fix one of the variables and plot the resulting curve in the remaining two variables.

For example, when we fix x to a constant value, say x = 0, we get 0 = 5y^2 − 5z^2, which simplifies to y^2 - z^2 = 0. This equation represents two intersecting planes: y = z and y = -z.

Similarly, when we fix y or z to a constant value, we get other traces that can help us sketch the surface. For instance, fixing y = 0 gives us x = -5z^2, which is a downward opening parabola in the z-x plane. Fixing z = 0 gives us x = 5y^2, which is an upward opening parabola in the y-x plane.

By plotting these traces and connecting them appropriately, we can sketch the surface of the equation x = 5y^2 − 5z^2 in three-dimensional space.

To sketch the surface x = 5y² - 5z² using traces, follow these steps:

1. Find the traces for the x-y, x-z, and y-z planes.

x-y plane (z = 0):
x = 5y² - 5(0)²
x = 5y²

x-z plane (y = 0):
x = 5(0)² - 5z²
x = -5z²

y-z plane (x = 0):
0 = 5y² - 5z²

2. Sketch the traces for each plane.

x-y plane: This is a parabola opening in the x direction with the vertex at the origin (0, 0, 0).

x-z plane: This is a parabola opening in the negative x direction with the vertex at the origin (0, 0, 0).

y-z plane: This is a hyperbola, as we can rewrite the equation as y² - z² = 0 or y²/z² = 1. It opens along the y and z axes and passes through the origin (0, 0, 0).

3. Combine the traces to sketch the surface.

The surface is a hyperbolic paraboloid, as it is a combination of the parabolic traces from the x-y and x-z planes and the hyperbolic trace from the y-z plane. The vertex of the hyperbolic paraboloid is at the origin (0, 0, 0), with the parabolic branches opening in the x direction and the hyperbolic branches opening along the y and z axes.

Learn more about  hyperbolic here: brainly.in/question/736503

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