The function below gives the cost in dollars to manufacturex items: C(x) = 10,000 + 5x – 10.000 Find the average cost per item over the interval (1,000,1,010]. Continuing with the previous problem find the average cost per item over the interval [999.5, 1000]. Continuing with the previous problem, what is the value of C' (1000) rounded to 1-decimal place?

The determinant of the given matrix is 0.

To find the determinant of a matrix, we do not need to reduce it to echelon form. However, if you specifically need to reduce the matrix to echelon form using row operations, I can guide you through the process.

Let's start with the given matrix:

[[1, -1, -3, 0],

[7, -6, 5, 4],

[1, 1, 2, 1],

[-3, 5, 14, 1]]

To reduce it to echelon form, we perform row operations to create zeros below the main diagonal:

1. Replace R2 with R2 - 7R1:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[1, 1, 2, 1],

[-3, 5, 14, 1]]

2. Replace R3 with R3 - R1:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[0, 2, 5, 1],

[-3, 5, 14, 1]]

3. Replace R4 with R4 + 3R1:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[0, 2, 5, 1],

[0, 2, 5, 1]]

4. Replace R4 with R4 - R3:

[[1, -1, -3, 0],

[0, 1, 26, 4],

[0, 2, 5, 1],

[0, 0, 0, 0]]

Now, the matrix is in echelon form. The determinant of this matrix is the product of the main diagonal elements: 1 * 1 * 5 * 0 = 0.

Therefore, the determinant of the given matrix is 0.

To learn more about determinant from the given link

https://brainly.com/question/24254106

#SPJ4

Answer:

A=

Step-by-step explanation:

This is Soh Cah Toa.

The angle opposite the right corner is always the hypoteneuse. The adjacent and opposite sides switch depending on what angle youre using.

for the side b use tan.

tan_of_angle=opposite/adjacent

tan_of_58=b/14

tan_of_58*14=b

1.6*14=b

22.4=b

for the side c use cos

cos_of_angle=adjacent/hypotenuse

cos_of_58=14/c

c=14/sin_of_58

c=14/0.5299

c=26.41

for the angle A use sin

sin_of_angle=opposite/hypoteneuse

sin_of_A=14/26.41

sin_of_A=0.5299

A=invsin_of_0.5299

A=32 degrees

The weight of the astronaut with gear on the moon is 80 pounds.

The pull of gravity is different on Earth than on the Moon as gravity depends on factors such as the mass of the celestial body, the radius of the celestial body, and the density of the celestial body.

The pull of gravity on Earth = 10 m/s²

Thus, Given:

Weight of object on Earth: 25 pounds

Weight is described as the product of mass and the acceleration due to gravity

Thus, 25 = 10 * mass

mass = 2.5 unit

Weight of the object on the Moon: 4 pounds

4 = 2.5 * acceleration due to gravity on the moon

Acceleration due to gravity on the moon = 1.6 m/s²

Weight of astronaut with gear on earth = 500 pounds

500 = mass * 10

mass = 50 units

Weight of astronaut with gear on earth = 50 * 1.6

= 80 pounds

Learn more about Weight:

https://brainly.com/question/29555156

#SPJ1

We can say that the behavior of x − 3 as x → ± [infinity] is best estimated by the monomial expression x.

The monomial expression that best estimates the behavior of x − 3 as x → ± [infinity] is simply x.

As x approaches positive or negative infinity, the -3 term becomes insignificant compared to the large values of x, and the behavior of the expression is dominated by the linear term x.

Thus, we can say that the behavior of x − 3 as x → ± [infinity] is best estimated by the monomial expression x.

To know more about monomial refer here

https://brainly.com/question/9183135#

#SPJ11

Therefore, the least value of k for which the alternating series error bound guarantees that |s - pk| < 3100 is k = 7.

To determine the least value of k for which the alternating series error bound guarantees that |s - pk| < 3100, we need to use the alternating series error bound formula:

|s - pk| ≤ a_(k+1)

In this case, a_n represents the absolute value of the (n+1)-th term of the series.

Given that the series is s = ∑n=1[∞] (-1)^n * 12^n, we can see that each term is decreasing in magnitude as n increases.

To find the least value of k, we need to find the smallest value of n such that the absolute value of the (n+1)-th term is less than 3100.

|(-1)^(n+1) * 12^(n+1)| < 3100

12^(n+1) < 3100

Taking the natural logarithm of both sides:

(n+1) * ln(12) < ln(3100)

n+1 < ln(3100) / ln(12)

n < ln(3100) / ln(12) - 1

Using a calculator, we find that ln(3100) / ln(12) - 1 ≈ 6.685

To know more about alternating series,

https://brainly.com/question/31307236

#SPJ11

The smallest sample size that a microscope with NA = 0.6 can resolve at 480 nm is approximately 400 nm.

1. The formula for resolution using the Abbe criterion is given by:

Resolution = λ / (2 * NA)

Where λ represents the wavelength of light and NA represents the numerical aperture.

2. Given values:

λ = 480 nm (wavelength)

NA = 0.6 (numerical aperture)

3. Substitute the values into the formula:

Resolution = 480 nm / (2 * 0.6)

4. Simplify the expression:

Resolution = 480 nm / 1.2

Resolution ≈ 400 nm

Therefore, the smallest sample size that a microscope with a numerical aperture (NA) of 0.6 can resolve, according to the Abbe criterion at a wavelength of 480 nm, is approximately 400 nm.

To understand the calculation further, the numerical aperture (NA) of a microscope is a measure of its ability to gather light and resolve fine details. The wavelength (λ) represents the size of the light waves used in the microscope.

According to the Abbe criterion, the resolution of a microscope is inversely proportional to the numerical aperture. A larger numerical aperture allows for higher resolution and the ability to resolve smaller details.

By plugging the values of wavelength (480 nm) and numerical aperture (0.6) into the formula, we find that the smallest resolvable sample size is approximately 400 nm. This means that the microscope with a numerical aperture of 0.6 can distinguish objects or features that are at least 400 nm apart. Smaller features closer than 400 nm may not be discernible with this microscope setup.

Know more about the sample size click here:

https://brainly.com/question/31734526

#SPJ11

It is true that in regression analysis, the variable being predicted (dependent variable) is commonly denoted by "y" and the predictor variable(s) (independent variable(s)) is denoted by "x".

Regression analysis is a statistical method used to investigate and model the relationship between a dependent variable and one or more independent variables. The dependent variable is the variable of interest, whose behavior we want to explain or predict. This variable is commonly denoted by "y" and is also known as the response variable or outcome variable.

On the other hand, independent variables are those that are hypothesized to influence the behavior of the dependent variable. They are commonly denoted by "x" and are also known as predictor variables, explanatory variables, or covariates. The relationship between the independent and dependent variables is typically modeled using a linear or non-linear function, which is estimated using regression analysis.

To know more about regression analysis,

https://brainly.com/question/28202475

#SPJ11

The derivative of the given function using the Fundamental Theorem of Calculus, Part 1, is -2sinx * cosx.

In mathematics, the derivative of a function of a real variable measures the sensitivity to a change in the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

To find the derivative using the Fundamental Theorem of Calculus, Part 1, for the function [tex]d/dx(\int_{0}^{(sinx)} (1 - t^2) dt)[/tex], proceed as follows:

1. Identify the function within the integral:

f(t) = 1 - t²
2. Take the derivative of the function with respect to t:

f'(t) = -2t
3. Replace the t variable with the upper limit of the integral, which is sinx:

f'(sinx) = -2sinx
4. Multiply the result by the derivative of the upper limit with respect to x:

d/dx(sinx) = cosx
5. Multiply the results from steps 3 and 4:

-2sinx * cosx

Learn more about derivative:

https://brainly.com/question/23819325

#SPJ11

Pumber D charges the lowest hourly rate.

To find out which plumber charges the lowest hourly rate, we need to calculate the hourly rate charged by each plumber.

For plumber A, the hourly rate can be calculated as:

(Total cost of repairs for 2 hours - Total cost of repairs for 1 hour)/1 hour = ($65 - $35)/1 hour = $30/hour.

Similarly, for plumber B, the hourly rate is ($75 - $55)/1 hour = $20/hour.

For plumber C, the hourly rate is ($100 - $50)/2 hours = $25/hour.

And for plumber D, the hourly rate is ($70 - $50)/3 hours = $6.67/hour.

Therefore, plumber D charges the lowest hourly rate.

Learn more about hourly rate at https://brainly.com/question/28437761

#SPJ1

Answer: 4

Step-by-step explanation:

80-32-12-24=12

12/2.5=4.8

She can buy 4

Harriet earns the same amount of money each day. The expression that represents Harriet's gross pay each day is 5h 8.

To determine Harriet's gross pay each day, we need to divide the total gross pay at the end of 7 workdays (35h 56 dollars) by the number of workdays (7). This will give us the amount of money she earns per day.

Dividing 35h 56 dollars by 7, we get 5h 8 dollars. Therefore, the expression that represents Harriet's gross pay each day is 5h 8. This means that Harriet earns 5 dollars and 8 cents each day of work.

It's important to note that the other expressions mentioned (8h 5, 7h 11, and 2h 7) are not correct representations of Harriet's gross pay each day. The correct expression is 5h 8, which indicates a consistent daily earning amount for Harriet.

Learn more about expression here:

https://brainly.com/question/28170201

#SPJ11

For part (a), f: R \ {0} → R is a well-defined function. For part (b), g: R \ {5} → R is a well-defined function. For part (c), h: [42, ∞) → R is a well-defined function.

For part (a), the function f(a) = 1/a is not defined at a = 0, so to make it well-defined, we choose the subset A of R to be R \ {0}.

For part (b), the function g(a) = 1/(a - 5) is not defined at a = 5, so to make it well-defined, we choose the subset A of R to be R \ {5}.

For part (c), the function h(x) = √(x - 42) is not defined for x < 42, so to make it well-defined, we choose the subset A of R to be [42, ∞).

Learn more about well defined function

brainly.com/question/31465399

#SPJ11

Answer:

x = 31/3 or 10 1/3 or 10.33

Step-by-step explanation:

(6 + 8 + x + 2 + 10 + 2x - 1 + 2) / 6 = 9

(2x + x + 23) / 6 = 9

3x + 23 = 54

3x = 31

x = 31/3

To find the slope of the line representing the ramp, we can use the formula for slope:

slope = (change in vertical distance) / (change in horizontal distance)

In this case, the change in vertical distance is 4 feet (the height of the building entrance), and the change in horizontal distance is 20 feet (the distance from the base of the ramp to the building).

Therefore, the slope of the line representing the ramp is:

slope = 4 feet / 20 feet = 1/5

The slope of the ramp line is 1/5.

To know more about slope refer here:

https://brainly.com/question/3605446

#SPJ11

The number of workers needed for this study is approximately 2512.

To determine the number of workers needed to estimate the mean assembly time with a confidence interval of 10.1 minutes and 90% confidence, we can use the formula:

n = (Z * σ / E)^2

where:

n = sample size

Z = Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645)

σ = standard deviation of the assembly time

E = maximum allowable error (half of the confidence interval width)

In this case, the maximum allowable error is 10.1 minutes / 2 = 5.05 minutes.

Plugging in the values, we have:

n = (1.645 * 3.9 / 5.05)^2 ≈ 2512

Know more about confidence interval here;

https://brainly.com/question/24131141

#SPJ11

The triple integral for the volume of D in spherical coordinates is:

∫[0,π/4]∫[0,2π]∫[0,2cos(φ)]ρ^2 sin(φ) dρ dθ dφ + ∫[π/4,π/2]∫[0,2π]∫[0,6cos(φ)]ρ^2 sin(φ) dρ dθ dφ

To set up the triple integral for the volume of D in spherical coordinates, we need to express the bounds of integration in terms of spherical coordinates.

First, we note that the base of the cylinder lies in the xy-plane and has a radius of 2 cos(theta), which means that in spherical coordinates, the cylinder is defined by:

0 ≤ ρ ≤ 2cos(φ)

0 ≤ θ ≤ 2π

0 ≤ z ≤ 5 - ρ cos(φ) sin(θ) - ρ sin(φ) cos(θ)

Next, we consider the region bounded below by the cone phi = pi/4 and above by the sphere Q = 6. In spherical coordinates, the cone is defined by:

0 ≤ ρ ≤ 6 cos(φ)

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π/4

The sphere is defined by:

0 ≤ ρ ≤ 6

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π/2

To find the volume of D, we need to integrate over the region that is common to both the cylinder and the region bounded by the cone and sphere.

Know more about triple integral here:

https://brainly.com/question/31385814

#SPJ11

The discriminant of f is (3200x^4y^4 - 6400x^3y^3 + 2400x^2y^2) / (2x^2 + 8y^2)^6.

To find the discriminant of f, we need to find the second-order partial derivatives of f with respect to x and y, and then calculate their product:

f(x, y) = 10x^2y^2 / (2x^2 + 8y^2)

∂f/∂x = (40x^3y^2 - 20xy^2) / (2x^2 + 8y^2)^2

∂^2f/∂x^2 = (120x^2y^2 - 40y^2) / (2x^2 + 8y^2)^3

∂f/∂y = (20x^2y^3 - 80xy) / (2x^2 + 8y^2)^2

∂^2f/∂y^2 = (240x^2y - 80x^2) / (2x^2 + 8y^2)^3

∂^2f/∂x∂y = (40x^2y - 40xy^2) / (2x^2 + 8y^2)^2

Now, we can calculate the discriminant:

D = (∂^2f/∂x^2) * (∂^2f/∂y^2) - (∂^2f/∂x∂y)^2

D = [(120x^2y^2 - 40y^2) / (2x^2 + 8y^2)^3] * [(240x^2y - 80x^2) / (2x^2 + 8y^2)^3] - [(40x^2y - 40xy^2) / (2x^2 + 8y^2)^2]^2

Simplifying this expression, we get:

D = (3200x^4y^4 - 6400x^3y^3 + 2400x^2y^2) / (2x^2 + 8y^2)^6

So, the discriminant of f is (3200x^4y^4 - 6400x^3y^3 + 2400x^2y^2) / (2x^2 + 8y^2)^6.

To know more about discriminant refer here :

https://brainly.com/question/14124941#

#SPJ11

The radius of convergence of the power series is scaled down by a factor of 6, when raising the variable to the power of 6.

To find the radius of convergence of the power series ∑cnx6n, we can use the ratio test. Let an = cnx6n, then we have:

lim┬(n→∞)⁡|a_(n+1)/a_n| = lim┬(n→∞)⁡|c_(n+1)x^(6(n+1))/c_nx^(6n)|

= |x|^6 lim┬(n→∞)⁡|c_(n+1)/c_n|

Since the radius of convergence of the power series ∑cnxn is R, we know that the series converges absolutely for |x| < R and diverges for |x| > R. Therefore, the ratio test for ∑cnxn tells us that:

lim┬(n→∞)⁡|c_(n+1)/c_n| = L

exists, where L is a real number.

Thus, the radius of convergence of the power series ∑cnx6n is:

R' = (R)^(1/6)

This means that the series ∑cnx6n converges absolutely for |x| < (R)^(1/6) and diverges for |x| > (R)^(1/6).

In other words, the radius of convergence of the power series is scaled down by a factor of 6, when raising the variable to the power of 6.

Learn more about convergence here

https://brainly.com/question/30275628

#SPJ11

The area of rectangle PQRS is approximately 10.6 square units.

To find the area of the rectangle PQRS, we need to use the formula for the area of a rectangle, which is A = lw, where A represents the area, l represents the length of the rectangle, and w represents its width.

To find the length and width of the rectangle, we need to use the distance formula, which is [tex]d = √((x₂-x₁)² + (y₂-y₁)²[/tex][tex]).[/tex] Using this formula, we can find the length of the rectangle PQ and the width of the rectangle QR.

The length of PQ = √[tex]((5-0)² + (3-(-2))²) = √(5² + 5²) =[/tex]√50

The width of QR = √[tex]((2-5)² + (6-3)²) = √9 + 9 =[/tex] √18

Therefore, the area of the rectangle PQRS is[tex]A = lw = ([/tex]√50)(√18) ≈ 10.6 square units.

We can also verify our answer by drawing a graph of the rectangle on a coordinate plane and using the count-the-squares method. We can count the number of squares inside the rectangle and multiply by the area of each square (1 square unit). The result will be the same as the area calculated using the formula.

Overall, the area of rectangle PQRS is approximately 10.6 square units.

Learn more about distance formula

brainly.com/question/25841655

#SPJ11

If PQ = 18,  OP is equal to 72.

In a dilation, the ratio of corresponding lengths is equal to the scale factor. So, we have:

OP / PQ = scale factor

Substituting the given values, we have:

OP / 18 = 4

To find OP, we can multiply both sides of the equation by 18:

OP = 4 * 18

OP = 72

Know more about dilation here:

https://brainly.com/question/13176891

#SPJ11

The information that is not sufficient to prove that a parallelogram is a square is the measurement of its angles alone. Additional information about the lengths of its sides is needed to confirm if a parallelogram is indeed a square.

To determine whether a parallelogram is a square, we need to consider both the angles and the side lengths. A parallelogram has opposite sides that are parallel and equal in length, and opposite angles that are congruent. While a square is a special type of parallelogram with four equal sides and four right angles, simply knowing that the angles of a parallelogram are equal is not enough to establish it as a square.

To confirm that a parallelogram is a square, we must also ensure that all four sides are of equal length. In a square, all angles are right angles, and all sides are congruent. Therefore, if we have information about the side lengths of a parallelogram and can verify that they are equal, along with the knowledge that the angles are right angles, then we can conclude that the parallelogram is indeed a square.

To learn more about parallelogram click here: brainly.com/question/1563728

#SPJ11

The square root of x² - 8x + 16, where -4 ≤ x < 4, can be simplified to |x - 4|.

1. Start with the expression x² - 8x + 16.

2. Factor the expression inside the square root: (x - 4)².

3. Since we are given the condition -4 ≤ x < 4, we know that x - 4 will always be non-negative.

4. Take the square root of (x - 4)², resulting in |x - 4|.

5. Therefore, the simplified expression is |x - 4|.

Note: The absolute value ensures that the output is always positive, regardless of the value of x within the given range.

For more such questions on square root , click on:

https://brainly.com/question/428672

#SPJ8

The volume of the solid generated by revolving the region between y=2sin(x) and the x-axis for 6 ≤ x ≤ 5π/6 about the y-axis is 2π (6sin(6) - 5√3) cubic units.

To find the volume of the solid generated by revolving the region between y=2sin(x) and the x-axis for 6 ≤ x ≤ 5π/6 about the y-axis, we use the method of cylindrical shells.

The formula for the volume of the solid generated by revolving the region between y=f(x) and the x-axis for a ≤ x ≤ b about the y-axis is given by:

V = 2π ∫[a,b] x f(x) dx

In this case, f(x) = 2sin(x) and the interval is 6 ≤ x ≤ 5π/6, so we have:

V = 2π ∫[6,5π/6] x (2sin(x)) dx

Using integration by parts, we obtain:

V = -2π [x cos(x)]6^5π/6 + 2π ∫[6,5π/6] cos(x) dx

V = 2π [x sin(x)]6^5π/6 - 2π sin(5π/6) + 2π sin(6)

Simplifying the expression, we get:

V = 2π (6sin(6) - 5√3)

Therefore, the volume of the solid generated by revolving the region between y=2sin(x) and the x-axis for 6 ≤ x ≤ 5π/6 about the y-axis is 2π (6sin(6) - 5√3) cubic units.

Learn more about volume here

https://brainly.com/question/27710307

#SPJ11

To calculate the mass of the Earth, we can use the following formula:

M = (4π²rₑₘ³) / (Gtₘ²)

Where:

M is the mass of the Earth

rₑₘ is the distance from the center of the Earth to the center of the Moon (384 million meters)

G is the gravitational constant (approximately 6.67430 x 10^-11 m³/(kg·s²))

tₘ is the orbital period of the Moon around the Earth (27.3 days converted to seconds)

Let's plug in the values and calculate the mass of the Earth:

M = (4π² * (384 x 10^6)³) / (6.67430 x 10^-11 * (27.3 x 24 x 60 x 60)²)

Know more about mass here:

https://brainly.com/question/19694949

#SPJ11

Answer:

The mean weight of an adult is 66 kilograms with a variance of 144. If 123 adults are randomly selected, the sample mean would follow a normal distribution with a mean of 66 kilograms and a standard deviation of sqrt(144/123) = 3/sqrt(123) kilograms.

We can standardize the sample mean to find the probability that it would be greater than 66.7 kilograms. The standardized value for 66.7 is (66.7 - 66) / (3/sqrt(123)) = 2.3094.

Using a standard normal distribution table, we find that the probability of a standard normal variable being greater than 2.3094 is approximately 0.0104.

Therefore, the probability that the sample mean would be greater than 66.7 kilograms is approximately 0.0104, rounded to four decimal places.

Step-by-step explanation:

They requried a positive liner to describe the association on the given graph.

Based on the graph provided, it appears that the association is positively linear. As the value of x increases, the value of y also increases in a consistent and linear manner. Therefore, the answer is B: positive linear.

Thus, the requried positive liner describes the association on the given graph.

Learn more about graph here:

https://brainly.com/question/17267403

#SPJ1

The arc length of the indicated portion of the curve r(t) is :

√101 units.

To calculate the arc length of the indicated portion of the curve r(t), we first need to find the parametric equation for the curve.
r(t) = (1-9t)i + (5+2t)j + (6t-5)k

To find the arc length, we use the formula:
L = ∫a^b ||r'(t)|| dt
where ||r'(t)|| is the magnitude of the derivative of r(t), and a and b are the bounds of integration.

Taking the derivative of r(t), we get:
r'(t) = -9i + 2j + 6k

Taking the magnitude of r'(t), we get:
||r'(t)|| = √((-9)^2 + 2^2 + 6^2) = √101

So the arc length of the indicated portion of the curve r(t) is:
L = ∫a^b √101 dt

We need to find the bounds of integration for t. If we have no other information, we can assume that t goes from 0 to 1 (a=0, b=1).

L = ∫0^1 √101 dt

Integrating, we get:
L = [t√101]0^1
L = √101

Therefore, we can state that the arc length of the indicated portion of the curve r(t) is √101 units.

To learn more about arc length visit : https://brainly.com/question/2005046

#SPJ11

The differential equation that models the concentration of the drug in the bloodstream as a function of time is dc/dt = -k c(t).

where c(t) is the concentration of the drug in the bloodstream at time t and k is the constant of proportionality.

The side condition is:

c(0) = c0

which states that the initial concentration of the drug in the bloodstream is c0 g/mL.

Supporting answer: The differential equation dc/dt = -k c(t) is a first-order homogeneous linear ordinary differential equation, which means it can be solved using separation of variables:

dc/c(t) = -k dt

Integrating both sides gives:

ln|c(t)| = -k t + C

where C is the constant of integration. Exponentiating both sides of the equation yields:

c(t) = e^(C-k t)

To find the value of C, we use the initial condition c(0) = c0:

c(0) = e^C

C = ln(c0)

Therefore, the solution to the differential equation with the side condition is:

c(t) = c0 e^(-k t)

This is an exponential function that decays over time with a decay constant of k, which represents the rate of elimination of the drug from the bloodstream. The larger the value of k, the faster the drug is eliminated and the shorter its half-life. The concentration of the drug in the bloodstream at any time t is proportional to its initial concentration c0, but inversely proportional to the exponential decay factor e^(k t).

Learn more about differential equation here

https://brainly.com/question/28099315

#SPJ11

The terminal point on the unit circle determined by t = 11/6 is approximately:

p(-0.866, 0.5)

For the terminal point on the unit circle determined by t = 11/6, we use the fact that the angle t (in radians) measured counterclockwise from the positive x-axis to the terminal point is given by:

t = arctan(y/x)

where (x, y) is the point on the unit circle.

Since we know that the point lies on the unit circle, we have:

x^2 + y^2 = 1

Solving for y, we get:

y = ±sqrt(1 - x^2)

Substituting this into the equation for t, we get:

t = arctan(±sqrt(1 - x^2)/x)

To determine the correct sign, we note that t = 11/6 is in the second quadrant, where x is negative and y is positive.

Therefore, we need to take the positive square root:

t = arctan(sqrt(1 - x^2)/(-x))

Multiplying both sides by -x and taking the tangent of both sides, we get:

tan(t) = sqrt(1 - x^2)/x

Squaring both sides and using the identity tan^2(t) + 1 = sec^2(t), we get:

x^2 = 1/(1 + tan^2(t)) = 1/(1 + (tan(11/6))^2)

Solving for x, we get:

x = -sqrt(1/(1 + (tan(11/6))^2)) ≈ -0.866

Substituting this value of x into the equation for y, we get:

y = sqrt(1 - x^2) ≈ 0.5

Therefore, the terminal point on the unit circle determined by t = 11/6 is approximately:

p(-0.866, 0.5)

To know more about terminal points refer here :

https://brainly.com/question/20336387#

#SPJ11

The angle between the vectors a and b is approximately 48 degrees.

To find the angle between two vectors a and b, we can use the formula:

cos θ = (a · b) / (|a| |b|)

where a · b is the dot product of a and b, and |a| and |b| are the magnitudes of a and b, respectively.

First, let's find the dot product of a and b:

a · b = (i)(4) + (2j)(0) + (-2k)(-3) = 4 + 6 = 10

Next, let's find the magnitudes of a and b:

|a| = √(1^2 + 2^2 + (-2)^2) = √9 = 3

|b| = √(4^2 + 0^2 + (-3)^2) = √25 = 5

Substituting these values into the formula for cos θ, we get:

cos θ = 10 / (3 * 5) = 2/3

To find the angle θ, we can take the inverse cosine (cos^-1) of 2/3:

θ = cos^-1(2/3) = 48.19 degrees

Therefore, the angle between the vectors a and b is approximately 48 degrees.

To know more about vectors refer here:

https://brainly.com/question/29740341?#

SPJ11