find the area of the surface. the part of the plane 3x 13y z = 39 that lies in the first octant

To find the equation of the tangent line to the curve y = sec(x) at the point (π/3, 2), we need to take the derivative of y with respect to x.

The derivative of sec(x) is sec(x)tan(x), so at x = π/3, we have: y' = sec(π/3)tan(π/3) = 2√3/3, Now we can use the point-slope form of a line to find the equation of the tangent line: y - y1 = m(x - x1)

where (x1, y1) is the point we're given (in this case, (π/3, 2)) and m is the slope of the tangent line (in this case, 2√3/3).

Plugging in the values, we get:

y - 2 = (2√3/3)(x - π/3)

Simplifying, we get:

y = (2√3/3)x + 2 - 2√3

So the equation of the tangent line to the curve y = sec(x) at the point (π/3, 2) is y = (2√3/3)x + 2 - 2√3.
To find the equation of the tangent line to the curve y = sec(x) at the point (π/3, 2), we need to follow these steps:

Step 1: Find the derivative of the function
The derivative of y = sec(x) is:
y' = sec(x)tan(x)

Step 2: Evaluate the derivative at the given point
At the point (π/3, 2), we can find the value of the derivative:
y'(π/3) = sec(π/3)tan(π/3) = 2*(√3/2) = √3

Step 3: Use the point-slope form of a linear equation
The point-slope form of a linear equation is:
y - y1 = m(x - x1)

Plug in the given point (π/3, 2) and the slope from Step 2 (√3):
y - 2 = √3(x - π/3)

Step 4: Simplify the equation
y - 2 = √3x - π√3/3
y = √3x - π√3/3 + 2

The equation of the tangent line to the curve y = sec(x) at the point (π/3, 2) is y = √3x - π√3/3 + 2.

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Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

Given:

At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.

y varies directly as x :

y = kx

k = constant of proportionality

y = 2.56 and x = 32

y = kx

k = y/x

= 2.56/32

k = 0.08

substitute k we get

y = 0.08x.

so x and y are directly proportional.

Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

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Answer:

9.09 years

Step-by-step explanation:

Use the simple interest formula

A=P(1+rt)

18000=9000(1+.11*t), solve for t

t = 9.0909

The rejection region for the test is z > 2.33, which corresponds to option C) z > 2.33.

For the given hypothesis test where H0: µ = 9 and Ha: µ > 9 with a significance level (α) of 0.01, you want to find the rejection region in terms of the z-statistic. Since Ha states that µ > 9, it is a right-tailed test. You can use the standard normal distribution table or a calculator to find the critical z-value corresponding to α = 0.01.

For a right-tailed test with α = 0.01, the critical z-value is approximately 2.33.

The rejection region for the test is z > 2.33, which corresponds to option C) z > 2.33.

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Answer:

12/5

Step-by-step explanation:

Remember SOH CAH TOA

Answer:

2.4

Step-by-step explanation:

tan= opposite/adjacent

so tan=12/5

The theatre sold 178 adult tickets and 261 children tickets for the play.

It is given that the total number of seats is 439 seats.

There are two types of tickets available- children and adults.

The price for adult tickets is $48 and that for children is $28.

Let the number of adult tickets sold be x

Let the number of children's tickets sold be y.

The show was a sold-out

Hence,

x + y = 439                                 [1]

48x + 28y = 15852                    [2]

From equation [1] we get

x = 439 - y

putting this result in equation [2] gives us

48(439 - y) + 28y = 15852

or, 21072 - 48y + 28y = 15852

or, -20y = - 5220

or, y = -5220/ -20

or, y = 261

Therefore,

x + 261 = 439

or, x = 439 - 261

or, x = 178

Hence, 178 adult tickets were sold and 261 children's tickets were sold.

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Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

Answer:

D=5g/ml

Step-by-step explanation:

D=M/V

D=55/11

The amount of water in the tank can be calculated by multiplying 3/4 to the volume of the tank: 3/4 x V = (3/4)L x W x H.

To calculate the amount of water in the aquarium's fish tank in the shape of a prism,

you would need to know the dimensions of the tank and then multiply the volume of the tank by 3/4.

Let's assume that the aquarium has a rectangular prism shape,

the amount of water in the tank would depend on the dimensions of the tank.

Let's assume the tank has a length of L, a width of W, and a height of H.

The volume of the tank can be calculated by multiplying the length, width, and height together: V = L x W x H.

If the tank is 3/4 full of water, the volume of water in the tank would be 3/4 of the total volume of the tank.

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The quotient of the division problem is (x + 1)/(x +2). The result is obtained by determining the factors of the two quadratic equations.

The quadratic equation can be expressed as

ax² + bx + c = 0

Where c is a constant.

To find the factors of a quadratic equation, follow these steps!

Find the quotient of (x² + 2x + 1)/(x² + 3x + 2) = 0!

For quadratic equation x² + 2x + 1:

The common factors: (x + 1)(x + 1)

For quadratic equation x² + 3x + 2:

The common factors: (x + 2)(x + 1)

The quotient of the quadratic equations is

(x² + 2x + 1)/(x² + 3x + 2) = 0

(x + 1)(x + 1)/(x + 2)(x + 1) = 0

(x + 1)/(x + 2) = 0

Hence, the quotient of the quadratic equations is (x + 1)/(x + 2) = 0.

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Answer:

Six.

Step-by-step explanation :

Each seamstress can sew one seam in twenty minutes, or 3 in an hour, or 6 in two hours. 150

make brainliest pls

Answer:

six each seamstresses can sew one seam in tewenty min

Answer:

Step-by-step explanation:

Answer is 65 simple

a. θ in degrees: 20°

b. Coterminal angle: 19π/9 radians or 380°

c. Complement of θ: 70°

a. To convert θ from radians to degrees, we can use the formula:

θ_degrees = θ * (180/π)

Substituting the given value θ = π/9 into the formula:

θ_degrees = (π/9) * (180/π) = 20°

Therefore, θ is equal to 20 degrees.

b. Coterminal angles are angles that have the same initial and terminal sides. To find one angle that is coterminal with θ, we can add or subtract any multiple of 2π (360 degrees) to/from θ.

One coterminal angle with θ can be obtained by adding 2π (360 degrees) to θ:

θ_coterminal = θ + 2π = π/9 + 2π = 19π/9 (radians) or 380° (degrees)

c. The complement of an angle is the angle that, when added to the given angle, forms a right angle (90 degrees or π/2 radians). The complement of θ can be found by subtracting θ from 90 degrees:

θ_complement = 90° - 20° = 70°

Therefore, the complement of θ is 70 degrees.

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The Onslow Company incurred a loss of $28,000 on the disposal of the machine.

The cost of the machine is $178,000, and the total cost of wiring and securing the machine is $2,840 + $1,160 = $4,000. The total cost of the machine is therefore $178,000 + $4,000 = $182,000.

The annual depreciation expense using straight-line method is calculated by subtracting the salvage value from the cost of the asset, and dividing the result by the useful life of the asset. In this case, the annual depreciation expense is:

($182,000 - $14,000) / 6 = $28,000

The accumulated depreciation for the machine at the end of its fifth year is 5 x $28,000 = $140,000.

The book value of the machine at the end of its fifth year is the cost of the machine minus the accumulated depreciation, which is $182,000 - $140,000 = $42,000.

Since the machine has been disposed of, we need to calculate the gain or loss on disposal. If the machine is sold for more than its book value, there will be a gain, and if it is sold for less than its book value, there will be a loss.

Since the salvage value of the machine is $14,000, we can assume that it was sold for this amount. Therefore, the loss on disposal is:

$42,000 (book value) - $14,000 (sale price) = $28,000

Therefore, the Onslow Company incurred a loss of $28,000 on the disposal of the machine.

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Answer:

8/25

Step-by-step explanation:

Since there are only three possible outcomes on the spinner (1, 2, or 3), we can find the probability of spinning a 2 by subtracting the probabilities of spinning a 1 or a 3 from 1

P(2) = 1 - P(1) - P(3)

P(2) = 1 - 7/25 - 2/5

P(2) = 1 - 35/125 - 50/125

P(2) = 1 - 85/125

P(2) = 40/125

P(2) = 8/25

Therefore, the experimental probability of spinning a 2 is 8/25 or 0.32.

Answer:

1/7

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

Answer:

The bakery sold 340 that day

Step-by-step explanation:

119 is 35 percent of 340

The inequality is represented as;

x/2 - 4 ≤  10

x  ≤ 28

Inequalities are described as the relation such that make an uneven comparison between two numbers, expressions or even variables.

The different signs of inequality are;

From the information given, we have that;

four less than the quotient of a number and two is no more than ten what is the number

Let the number be x

This can then be represented as;

x/2 - 4 ≤  10

x/2 ≤  10 + 4

x/2  ≤  14

x  ≤ 28

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A parametrization for the line segment with endpoints (-4,5) and (-9,-10) is given by x = -4 - 5t and y = 5 - 15t, where 0 ≤ t ≤ 1.

To find a parametrization for the given line segment with endpoints (-4,5) and (-9,-10), we can use the parametric form of the equation of a straight line, which is given by x = x1 + t(x2 - x1) and y = y1 + t(y2 - y1), where (x1,y1) and (x2,y2) are the endpoints of the line segment and t is a parameter that varies from 0 to 1.

Taking (x1,y1) = (-4,5) and (x2,y2) = (-9,-10), we get the following parametric equations for the line segment:

x = -4 + t(-9 - (-4)) = -4 - 5t

y = 5 + t(-10 - 5) = 5 - 15t

The parameter t varies from 0 to 1, so as t ranges from 0 to 1, the point (x,y) traces out the line segment joining the points (-4,5) and (-9,-10).

Therefore, a parametrization for the line segment with endpoints (-4,5) and (-9,-10) is given by x = -4 - 5t and y = 5 - 15t, where 0 ≤ t ≤ 1.

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Answer:

68

Step-by-step explanation:

Answer:

ok this question contains many operations we have addition sign subtraction sign and multiplication sign so in this case we use bodmas and in the bodmas we see multiplication coming fast so the first two letters that have the multiplication sign between them should be multiplied so in this case put a bracket between those two numbers so that you have it like this oneplus (2 x 3)-(4*5) + 6 - 7 plus (8 * 9 )+ 10 so we multiply the numbers in the brackets so that our equation comes to 1 + 6 - 20 + 6 - 7 + 72 + 10 then we rearrange so that you have 1 + 6 plus 6 + 72 + 10 - 20 - 7 1 + 6 + 6 + 72 + 10 is 95 - 20 -7 and your final answer is 68

(a) The y-intercept is when x=0, so the answer is (0,3).

(b) Perpendicular lines have gradients that multiply to -1, so the gradient of B is 1/4.

So, the equation is y = ¼x + 3.

Answer:

13

Step-by-step explanation:

If ABC is equilaterteral then all the angles must be equal and 60°

8x - 44 = 60 add 44 to both sides

8x = 104 divide both sides by 8

x = 13

The one function that satisfies f '(x) = 3x² + 6x + 5 is f(x) = x³ + 3x²÷2 + 5x + C. where C is the constant of integration.

The given function's derivative is f'(x) = 3x² + 6x + 5.

To find the original function f(x), we need to integrate the derivative.

We can integrate the given function f'(x) term by term, using the power rule of integration:

∫f'(x) dx = ∫(3x² + 6x + 5) dx

f(x) = x^3 + 3x²÷2 + 5x + C

Any constant value of C can be added to the above function, resulting in an infinite number of functions that satisfy

f '(x) = 3x² + 6x + 5.

f(x) = x^3 + 3x²÷2 + 5x + 2 and f(x) = x³ + 3x²÷2 + 5x - 7 are both valid solutions to f '(x) = 3x² + 6x + 5, with different constant values of C.

This is because the constant of integration represents an arbitrary constant, and when we take the derivative, the constant term becomes zero. Hence, any function that differs from the original function by a constant value will also have the same derivative.

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Answer:

x≤5p

Step-by-step explanation:

40/8=5 Kaitlin can buy UP TO 5 pounds of candy at $8/pound. So she will buy less than or equal to 5 pounds

Answer:

D) 0.2 repeating

Step-by-step explanation:

2÷9=0.2 repeating

Answer:

D

Step-by-step explanation:

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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Answer:

-8x-9y

Step-by-step explanation:

Hey There!

So basically this problem is asking you to simplify this expression using distributive property

The first step would be to distribute 7 into what is inside the parenthesis (2x and -3y)

2x*7=14x

-3y*7=-21y

so now we have 14x-21y + 4(3y-5x)

the next step would be to distribute 4 to what is inside the parenthesis (3y and -5x)

4*3y=12y

4*-5x=-20x

so now we have 12x-21y-20x+12y

the final step is to combine like terms

12x-20x=-8x

-21y+12y=-9y

so the simplified version of 7(2x - 3y) + 4(3y - 5x) is -8x-9y

Answer:

14x-21y+12y-20x. 14x-20x+12y-21y. -6x-9y

Answer: 33

Step-by-step explanation:

Answer:

Step-by-step explanation:

33