For the quadratic function show below the coordinates of its vertex are

v₁ = [[-1], [-2], [-2]] and v₂ = [[-4], [8], [-6]] are the vectors that satisfy the given conditions.

To write vector y as the sum of a vector v₁ in W and a vector v₂ orthogonal to W, we need to find the orthogonal projection of y onto the subspace W spanned by u₁ and u₂.

y = [[-5], [6], [-8]]

u₁ = [[1], [2], [2]]

u₂ = [[6], [2], [-5]]

To find v₁, we'll use the formula for the orthogonal projection

v₁ = ((y · u₁) / (u₁ · u₁)) × u₁

where "·" represents the dot product.

Calculating the dot products

y · u₁ = (-5 × 1) + (6 × 2) + (-8 × 2) = -5 + 12 - 16 = -9

u₁ · u₁ = (1 × 1) + (2 × 2) + (2 × 2) = 1 + 4 + 4 = 9

Substituting the values

v₁ = ((-9) / 9) × [[1], [2], [2]] = [[-1], [-2], [-2]]

Now, to find v₂, we'll subtract v₁ from y

v₂ = y - v₁ = [[-5], [6], [-8]] - [[-1], [-2], [-2]] = [[-4], [8], [-6]]

Therefore, we can write y as the sum of v₁ and v₂

y = v₁ + v₂ = [[-1], [-2], [-2]] + [[-4], [8], [-6]] = [[-5], [6], [-8]]

To know more about vectors here

https://brainly.com/question/24256726

#SPJ4

The formula for the n+1 points where the Chebyshev polynomials Tn(x), for n >= 2, alternate between 1 and -1, can be expressed as follows: x_k = cos((2k - 1)π / (2n)), where k ranges from 1 to n+1.

These points are known as the Chebyshev nodes and are commonly used in polynomial interpolation and numerical analysis. They are distributed in a way that minimizes the interpolation error, making them ideal for approximating functions. The Chebyshev polynomials, denoted as Tn(x), are a set of orthogonal polynomials defined on the interval [-1, 1]. They can be recursively generated using the formula Tn(x) = 2xTn-1(x) - Tn-2(x), with initial values T0(x) = 1 and T1(x) = x. These polynomials have the property that their roots, called the Chebyshev nodes, alternate between 1 and -1.

To find the n+1 Chebyshev nodes, we can use the formula x_k = cos((2k - 1)π / (2n)), where k ranges from 1 to n+1. This formula generates the values of x at which the Chebyshev polynomials Tn(x) alternate between 1 and -1. The nodes are evenly distributed along the interval (-1, 1], with denser clustering towards the endpoints.

Learn more about polynomials click here:

brainly.com/question/11536910

#SPJ11

Answer:

Brian will have $12 dollars left.

Step-by-step explanation:

30 - 18 = 12

Answer: 95%

Step-by-step explanation: 0.9 = 90%

The similarity between the z-test and the one-sample t-test is that they are both statistical tests used to make inferences about population parameters based on sample data.

The z-test and the one-sample t-test are both hypothesis tests used to determine if a sample mean significantly differs from a hypothesized population mean. The main similarity between the two tests is that they are both used when the population standard deviation is known for the z-test or estimated from the sample for the t-test. Both tests involve comparing the observed sample mean to the hypothesized population mean and considering the variability in the data. They both calculate a test statistic that measures the difference between the observed and hypothesized means relative to the variability in the data. The test statistic is then compared to a critical value or p-value to determine the significance of the difference. However, the main difference between the two tests is that the z-test assumes a known population standard deviation, while the one-sample t-test uses the sample standard deviation to estimate the population standard deviation. This makes the t-test more appropriate when the population standard deviation is unknown.

To know more about hypothesis testing here: brainly.com/question/30701169

#SPJ11

Answer:

Answer is D

Step-by-step explanation:

hope that helps

Answer:

7/8 if u want more if u want less then it 4/9

Step-by-step explanation:

The sum of the series [infinity] (−1)n − 1/n^2 * (13^n), where n starts from 1, can be approximated. The sum of this series is approximately -3.2891 when rounded to four decimal places.

To calculate this approximation, we can use the concept of an alternating series. Since the series alternates between positive and negative terms, we can apply the Alternating Series Test to determine its convergence.

By evaluating the terms of the series, we observe that the absolute value of each term decreases as n increases. This indicates that the series converges.

To approximate the sum, we can calculate the partial sums of the series until we reach a desired level of accuracy. By adding up a significant number of terms, we find that the sum is approximately -3.2891 when rounded to four decimal places.

learn more about sums of the series here: brainly.com/question/14383846

#SPJ11

The number 8.7104 belongs to the set of real numbers. The sets of natural numbers, whole numbers, integers, rational numbers, and real numbers are ordered from most specific to most inclusive.

Natural numbers: Also known as counting numbers, they include positive whole numbers starting from 1 (1, 2, 3, 4, ...).

Whole numbers: Similar to natural numbers, they include all positive integers starting from 0 (0, 1, 2, 3, ...).

Integers: This set includes both positive and negative whole numbers, including zero (-∞, ..., -3, -2, -1, 0, 1, 2, 3, ..., +∞).

Rational numbers: These are numbers that can be expressed as fractions, where the numerator and denominator are both integers. Rational numbers can be written as terminating or repeating decimals.

Real numbers: This set includes all rational and irrational numbers. Real numbers can be represented on the number line and include all possible decimal values, including non-terminating and non-repeating decimals.

In the case of the number 8.7104, it is a decimal number that can be expressed as a terminating decimal. Therefore, it falls within the set of real numbers. Real numbers encompass all possible decimal values, both terminating and non-terminating, making them the broadest set in terms of representation on the number line.

To know more about number system click here: brainly.com/question/31765900

#SPJ11

Answer:

graph is in the attachment

Step-by-step explanation:

y=-x²-4x-3=-x²-4x-4+1=-(x+2)²+1

Answer:

C. 1 13/18

Explanation:

Answer:

7. 8 I think (typing more for the limit)

Answer:

7.8

Step-by-step explanation:

The probability that a randomly selected man weighs less than 163 pounds is approximately 0.7422 or 74.22%.

We are given that the weights of adult males are normally distributed with a mean of 150 pounds and a standard deviation of 20 pounds.

(a) To find the probability that a randomly selected man will weigh less than 163 pounds, we need to calculate the area under the normal curve to the left of 163 pounds.

To do this, we can standardize the value using the formula for z-score:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, x = 163 pounds, μ = 150 pounds, and σ = 20 pounds.

Calculating the z-score:

z = (163 - 150) / 20

z = 13 / 20

z = 0.65

Now, we can use a standard normal distribution table or a calculator to find the corresponding probability for a z-score of 0.65. The probability of a man weighing less than 163 pounds is the area to the left of the z-score of 0.65.

Looking up the z-score in the standard normal distribution table, we find that the corresponding probability is approximately 0.7422.

Therefore, the probability that a randomly selected man will weigh less than 163 pounds is approximately 0.7422, or 74.22%.

To learn more about probability visit : https://brainly.com/question/13604758

#SPJ11

Answer:

9.1 units

Step-by-step explanation:

formula of a distance of two points:

[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex] where x and y indicate the coordinates of the points

[tex]\sqrt{(4+5)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} = 9.1 units[/tex]

Answer:

0.3475905 in league

Answer:

576

Step-by-step explanation:

6 papers an hour. 7 hours spent grading.

So 7•6 = 42

618-42

576

Hope this helps

Answer:

c

Step-by-step explanation:

Answer:

k = 3.

Step-by-step explanation:

If they are collinear the slope of AB = the slope of BC, so :-

(0- (-2)) / (2 - 0) = (k - 0) / (5 - 2)

2/2 = k/3

1 = k/3

k = 3.

Answer:

the second option

Step-by-step explanation:

pretty sure it's the second option

hope this helped ;)

Answer:

Step-by-step explanation:

[tex]\sf 30-24x[/tex]

30 → 6 * 5

24 → 6 * 4

[tex]\sf 6* \:5-6* \:4x[/tex]

[tex]\sf 6\left(5-4x\right)[/tex]

Answer:

10sqrt{2}

Step-by-step explanation:

This is a 45-45-90 right triangle. This means that the two legs are both the same length, call it x, and the hypotenuse is square root 2 times the given leg.  There's a proof for this, but it's long, and you can find it online.    

Answer:

2 real solutions

Step-by-step explanation:

x=6i, -6i

Answer:

1.5 °C

Step-by-step explanation:

-2.5, -1, -0.5, 0, 3, 4, 4.5, 5

median is the middle number in the list of numbers

Since there are a total of 15 shirts,

5 red shirts+4 white shirts= 9 shirts total

3 blue shirts+3 purple shirts= 6 shirts total

The odds that you would pick a red shirt and then a white are 3:2

3 being the 9 red and white shirts combined.

2 being the 6 purple and blue shirts combined.

9:6 simplified=3:2

9/3=3

6/3=2

3:2

Answer: The odds that you would pick a red shirt then a white shirt would be 3:2 or 60%

Answer:

One

Step-by-step explanation:

3x-5=-3 add 5 to each side.

3x-5+5=-3+5   simplify.

3x=2       divide each side by three.

3x/3=2/3     simplify

x=2/3

The interval of convergence, I, is (-∞, +∞), which means the series converges for all real values of x.

To find the radius of convergence, use the ratio test. The ratio test states that for a power series of the form:

Σ(aₙ × xⁿ)

where aₙ is the nth term of the series, the radius of convergence R is given by:

R = lim(n→∞) |aₙ / a_(n+1)|

In this case, the series:

Σ(n!) × xⁿ

Apply the ratio test to find the radius of convergence:

|aₙ / a_(n+1)| = |(n!) × xⁿ / ((n+1)!) × xⁿ⁺¹|

= |x / (n+1)|

Taking the limit as n approaches infinity:

lim(n→∞) |x / (n+1)| = |x / ∞| = 0

Since the limit is 0, the series converges for all values of x. This means that the radius of convergence, R, is infinite (R = ∞).

Now, let's find the interval of convergence, I. Since the radius of convergence is infinite, the series converges for all values of x. Therefore, the interval of convergence, I, is (-∞, +∞), which means the series converges for all real values of x.

learn more about interval of convergence: https://brainly.com/question/17019250

#SPJ4

Answer:

Lines m and n are parallel.

Step-by-step explanation:

< 6 and < 14 are both equal to 72 degrees and they are corresponding angles for lines m and n.

Answer:

Thank you so much

Step-by-step explanation: