Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: f(0) = -3 \)

\(\qquad \tt \rightarrow \: f(2) = 1\)

\(\qquad \tt \rightarrow \: f(4) = 1 \)

____________________________________

\( \large \tt Solution \: : \)

F(x) represents the value of y on curve for given value of x

\( \textsf{\large First -} \)

\(\qquad \tt \rightarrow \: f(0) =( 0) {}^{2} - 3\)

[ since 0 < 2 ]

\(\qquad \tt \rightarrow \: f(0) = 0 {}^{} - 3\)

\(\qquad \tt \rightarrow \: f(0) = - 3\)

\( \textsf{\large Second} \)

\(\qquad \tt \rightarrow \: f(2) = (2) {}^{2} - 3\)

[ since 2 = 2 ]

\(\qquad \tt \rightarrow \: f(2) = 4{}^{} - 3\)

\(\qquad \tt \rightarrow \: f(2) = 1\)

\( \textsf{\large Third -} \)

\(\qquad \tt \rightarrow \: f(4) = - 4 + 5\)

[ since 4 > 2 ]

\(\qquad \tt \rightarrow \: f(4) = 1\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The steady-state solution of the heat conduction equation refers to the temperature distribution that remains constant over time. This occurs when the heat flow into a system is balanced by the heat flow out of the system.

To find the steady-state solution of the heat conduction equation, follow these steps:

1. Set up the heat conduction equation: The heat conduction equation describes how heat flows through a medium and is typically given by the formula:

  q = -k * A * dT/dx,

  where q represents the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area through which heat flows, and dT/dx is the temperature gradient in the direction of heat flow.

2. Assume steady-state conditions: In the steady-state, the temperature does not change with time, which means dT/dt = 0.

3. Simplify the heat conduction equation: Since dT/dt = 0, the equation becomes:

  q = -k * A * dT/dx = 0.

4. Apply boundary conditions: Boundary conditions specify the temperature at certain points or surfaces. These conditions are essential to solve the equation. For example, you might be given the temperature at two ends of a rod or the temperature at the surface of an object.

5. Solve for the steady-state temperature distribution: Depending on the specific problem, you may need to solve the heat conduction equation analytically or numerically. Analytical solutions involve techniques like separation of variables or Fourier series expansion. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution.

It's important to note that the exact method for solving the heat conduction equation depends on the specific problem and the boundary conditions given. However, the general approach is to set up the heat conduction equation, assume steady-state conditions, simplify the equation, apply the boundary conditions, and solve for the steady-state temperature distribution.

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Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of phones produced abroad and y represent the number of phones produced locally.

The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:

30x + 20y = 6000            (1)

Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:

20x + 60y = 12000           (2)

Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:

70x = 6000

x = 600/7 ≈ 86

Put x = 86 in equation 1:

30(86) + 20 y = 6000

20y = 3420

y = 171

86 phones should be produced abroad and 171 phones locally

The given function is \(`f(x) = -2x³ - 6x² + 48x + 3`\). Here, we will find out the local maximum and minimum values of the function `f(x)` using the second derivative test.

First derivative test To find the critical values, let's find the first derivative of the given function. `\(f(x) = -2x³ - 6x² + 48x +\)3`Differentiating both sides with respect.

\(`x`, we get,`f'(x) = -6x² - 12x + 48`\)

Simplifying it further.

\(`f'(x) = -6(x² + 2x - 8)``f'(x) = -6(x + 4)(x - 2)`\)

The critical points of the function\(`f(x)`\)are\(`x = -4\)` and \(`x = 2`.\)

Second derivative test To determine the local maximum and minimum points, let's use the second derivative test.\(`f'(x) = -6(x + 4)(x - 2)`\)Differentiating `f'(x)` with respect to `x`, we get \(,`f''(x) = -12x - 12`\) At the critical point.

\(`x = -4`,`f''(-4) = -12(-4) - 12``f''(-4) = 36 > 0\)

Hence, the point is a local minimum point. At the critical point .

\(`x = 2`,`f''(2) = -12(2) - 12``f''(2) = -36 < 0`\)

Hence, the point \(`(2, f(2))`\) is a local maximum point.

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the exact values of sin 2 a and tan 2 will be: tan 2a = (2 tan a)/(1 - tan^2 a) and tan 2a = (2(-(sin a)/(√(1 - sin^2 a))))/(1 - (-(sin a)/(√(1 - sin^2 a)))^2)

If sin a = (blank) and 90º < a < 180°, we know that a is in the second quadrant. To find sin 2a, we can use the double-angle formula:

sin 2a = 2 sin a cos a

We know sin a, but we need to find cos a. To do this, we can use the fact that sin^2 a + cos^2 a = 1. Since we know sin a, we can solve for cos a:

cos^2 a = 1 - sin^2 a
cos a = ±√(1 - sin^2 a)

Since a is in the second quadrant (where cosine is negative), we take the negative square root:

cos a = -√(1 - sin^2 a)

Now we can use the double angle formula:

sin 2a = 2 sin a cos a
sin 2a = 2 sin a (-√(1 - sin^2 a))

To find tan 2a, we can use the tangent double-angle formula:

tan 2a = (2 tan a)/(1 - tan^2 a)

We know sin a and cos a, so we can find tan a:

tan a = sin a/cos a
tan a = (blank)/(-√(1 - sin^2 a))

To find the exact value of tan a, we can use the fact that sin a is positive and cos a is negative in the second quadrant:

tan a = -(sin a)/(√(1 - sin^2 a))

Now we can substitute into the tangent double angle formula:

tan 2a = (2 tan a)/(1 - tan^2 a)
tan 2a = (2(-(sin a)/(√(1 - sin^2 a))))/(1 - (-(sin a)/(√(1 - sin^2 a)))^2)

Simplifying this expression requires some algebraic manipulation.

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Answer:hope it helped

Step-by-step explanation:

A function is always a relation

Answer:

9

Step-by-step explanation:

jayfeather friend me

Answer:

2 19/56 is the answer.

Step-by-step explanation:

10 5/8 - 8 2/7

or, 85/8 - 58/7

or, (595-464)/56

or, 131/56

= 2 19/56

Answer:

ummm well that hard let me solve it real quick

Step-by-step explanation:

:/

The correct answer is not listed among the given options. None of the listed options is a CSS3 2D transformation function that resizes an object by a factor of x horizontally.

Here are brief explanations of the given options:

a. scaleY(y) - This function scales an object vertically by a factor of y.

b. rotate(angleY) - This function rotates an object around the y-axis by the specified angle.

c. translateY(offY) - This function translates an object vertically by the specified offset.

d. skewY(angleY) - This function skews an object along the y-axis by the specified angle.

To resize an object horizontally by a factor of x, you can use the scaleX(x) function. This function scales an object horizontally by a factor of x.

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The value of X is 4/7.

Addition, subtraction, multiplication, and division are the four fundamental operations of mathematics. There is an order of operations used while performing arithmetic. One or more operands are subject to an action by an operator.

Given expression 6 - 2/3(x+5) = 4x.

Simplifying this

6- 2/3 (x + 5) = 4x

multiplying  by 3 on both sides and Using PEMDAS

18 - 2x -10  = 12x

8 = 14x

x = 4/7

Therefore the exact value of x for the given equation is 4/7.

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Step-by-step explanation:

4/7÷21/3

=4/7*3/21

=12/147

Answer:

\(\frac{12}{49}\)

Step-by-step explanation:

Given

\(\frac{4}{7}\) ÷ 2 \(\frac{1}{3}\) ← change mixed number to improper fraction

= \(\frac{4}{7}\) ÷ \(\frac{7}{3}\)

To perform the division

Leave the first fraction. change division to multiplication and turn the second fraction upside down.

= \(\frac{4}{7}\) × \(\frac{3}{7}\) ← multiply numerators/ denominators together

= \(\frac{4(3)}{7(7)}\)

= \(\frac{12}{49}\)

We have: P(brown then yellow) = 2/11 and P(green then green) = 2/132.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

let's calculate the probability of selecting a brown marble followed by a yellow marble without replacement:

P(brown then yellow) = (4/12) * (6/11) = 24/132 = 2/11

We multiply 4/12 (the probability of selecting a brown marble on the first draw) by 6/11 (the probability of selecting a yellow marble on the second draw, after one brown marble has already been removed). Note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

Now let's calculate the probability of selecting two green marbles without replacement:

P(green then green) = (2/12) * (1/11) = 2/132

We multiply 2/12 (the probability of selecting a green marble on the first draw) by 1/11 (the probability of selecting another green marble on the second draw, after one green marble has already been removed). Again, note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

So, we have:

P(brown then yellow) = 2/11

P(green then green) = 2/132

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Answer:

<a=32

<b=40

<c=40

Step-by-step explanation:

to find angle a you have to subtract the 50 minus 180 to find the angle close to the 50 because angles in a straight line add up to 180. the answer will be

180-50=130

after finding the angle in that triangle you must add it to the other angle present which is 18° then subtract by 180 because angles in a straight line add up to 180

130+18+a=180

a=180-148

a=32 and that's how you find a

to find b you must know that the angle at the center is twice the angle at the circumference meaning the large angle C is 90°,now if it's 90° inorder to find the big angle B you must add the 18+90 then subtract 180

18+90+B=180

B=180-108

=72

since the combination of angle a and b will give you 72 you can find angle c by subtracting a from 72

c=72-32

=40

then if you look at angle c and angle b you can tell that they are alternating meaning angle b is also 40

I hope this helps

Answer:

28 in² = 28

Step-by-step explanation:

\(a = \frac{a + b}{2}h\)

\(a = 6\)

\(b = 8\)

\(h = 4\)

\(a = \frac{6 + 8}{2}4\)

\( \frac{14}{2} 4\)

\(7 \times 4\)

\( = 28\)

Answer = 28 _

The dimensions of the crate with minimum possible surface area are 4 meters by 4 meters by 2 meters.

We are given that we want to design a rectangular crate with a square bottom, open top, and volume 32 cubic meters. Let's call the length of one side of the square bottom x and the height of the crate y. Then the volume of the crate is,

V = x²y = 32

We want to minimize the total surface area of the crate. This consists of the area of the square bottom, which is x², and the area of the four sides, which are all identical rectangles with dimensions y by x. Therefore, the total surface area of the crate is,

A = x² + 4xy

We can use the volume constraint to solve for y in terms of x,

x²y = 32

y = 32/x²

Substituting this expression for y into the equation for A, we get,

A = x² + 4x(32/x²) = x² + 128/x

To minimize A, we can take the derivative with respect to x and set it equal to zero,

dA/dx = 2x - 128/x² = 0

Solving for x, we get,

2x = 128/x²

x³ = 64

x = 4

Therefore, one side of the square bottom is 4 meters. Using the volume constraint, we can solve for y,

x²y = 32

4²y = 32

y = 32/16 = 2

So, the height of the crate is 2 meters. Thus, the dimensions of the crate with minimum surface area are 4 meters by 4 meters by 2 meters.

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If an independent event has four uncertain outcomes, their probabilities are 20%, 45%, 15%, and C: 20%.

In probability, the sum of the probabilities of all possible outcomes must equal 100%. In this case, the probabilities of the four uncertain outcomes are given as 20%, 45%, 15%, and 20%. This means that each of these outcomes has a chance of occurring equal to the given percentage, and the total probability of all four outcomes is 20% + 45% + 15% + 20% = 100%.

It is important to note that when calculating probabilities, the percentages must add up to 100% to ensure that the total chance of all possible outcomes occurring is equal to 1 or 100%.

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Answer:

it's 300=8 hours per hour

Step-by-step explanation:

533=9=5=8 you have to jump two times till u get 8

Answer:

Sergio will buy the kayak first in 33.33 weeks.

Step-by-step explanation:

Sergio's per week savings = $24

Let the period of the savings = x

Then total savings of Sergio in x weeks = $24x

If y represents the total amount,

y = 24x ------(1)

Table given in the picture represents the savings of Lia.

If the points given in the table are plotted on graph, a straight line is formed.

Let the equation of the line is,

y = mx + b

m = Slope of line

b = y-intercept

Slope of the line = Savings per week

                            = \(\frac{y_2-y_1}{x_2-x_1}\)

For two points (4, 72) and (8, 144) lying on the straight line,

Slope 'm' = \(\frac{144-72}{8-4}\)

               = \(\frac{72}{4}\)

               = 18

Equation of the line will be,

y = 18x + b

Since, (12, 216) also lies on the line,

216 = 18(12) + b  

b = 216 - 216

b = 0

Therefore, equation of the line will be,

y = 18x -----(2)

Cost of kayak = $800

For Lia's savings,

800 = 18x

18x = 800

x = 44.44 weeks

For Sergio,

800 = 24x

x = 33.33 weeks

Therefore, Sergio will be able to buy the kayak first and it will take 33.33 weeks to purchase.

Answer:

The rate of change is -0.75

Step-by-step explanation:

For each unit of t the volume of water is decreasing by 0.75.

At t=13.333 the volume of water is 0. at t=0 the volume of water is 10

Hope this helps

Answer:

204 ft²

Step-by-step explanation:

Let's split the room to make it look like there are two squares.

We can make it to where one square is 14 ft long and 10 ft wide.

The other square can be 16 ft long and 4 ft wide

Find the areas of those two squares by multiplying width and length

14 x 10 = 140

16 x 4 = 64

Add those two together

140 + 64 = 204

Answer:

a

Step-by-step explanation:

The bisection method will converge to a root of f(x) = cos(x) on the interval [0, 65].

The bisection method is a numerical algorithm that finds a root of a function f(x) within a given interval [a, b] by repeatedly dividing the interval in half and determining which half contains a root. The method converges to a root if the function is continuous and changes sign across the interval [a, b].

In this case, the function f(x) = cos(x) is continuous on the interval [0, 65], and it changes sign multiple times, indicating the presence of multiple roots. Specifically,

so there are roots at x = π/2 and x = 3π/2, as well as additional roots between 0 and π/2, and between π/2 and 3π/2.

Since there are 21 roots of the function on the interval [0, 65], it is not possible to determine which root the bisection method will converge to without further information about the behavior of the function within the interval.

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Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

An illustration of data or mathematical functions is a graph. It is a method for presenting numerical data in a way that is simple to comprehend and interpret. A set of axes, one for each variable being represented, and one or more plots or lines that reflect the data or function being graphed are the main components of a graph. There are many distinct graph kinds, each of which is appropriate for displaying various sorts of data, including line graphs, bar graphs, scatter plots, and pie charts.

given

The axes cannot be identified because they are not specified in the query.

The blue ABC bar graph is as follows:

Using the equation (x, y) (y, -x), rotate AABC 90 degrees clockwise by applying the following transformation to each point:

A(-3, 0) → A' (0, 3) (0, 3)

B(-2, 4) → B' (-4, -2) (-4, -2)

C(1, -1) → C' (1, -1) (1, -1)

The red A'B'C' coordinates are as follows: A' (0, 3), B' (-4, -2), and C' (1, -1).

We take the y-coordinate of each point and subtract 3 to translate AA'B'C' three units down:

A' (0, 3) → A" (0, 0) (0, 0)

B' (-4, -2) → B" (-4, -5) (-4, -5)

C' (1, -1) → C" (1, -4) (1, -4)

Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

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The complete question is:-  

1. Label the axes.

2. Graph: A(-3, 0) B(-2, 4) C(1,-1) Draw ABC in blue.

3. Rotate AABC 90° clockwise to

create ▲A'B'C' in red. List the coordinates below:

Formula: (x, y) → (y, -x)

A(-3, 0) A' ()

B(-2, 4)→ B' ()

C(1, -1) C' ()

4. Translate AA'B'C' three units down to create ▲A"B"C" in green. What are the coordinates of AA"B"C"?

Answer:

tiiiuhhhghhjpjjhhjhgghhuuhh

Answer:

yes

(1,2)

(2,1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of months is x, and number of pairs of shoes after each month is y.

7 new pairs of shoes every 2 months means that after each month:

y = 7/2 x

We need to add the 15 pairs from start.

y = 3.5x + 15

The probability of a student spending time reading given that the student spends time watching TV is  \(P(Reading|Watching\:\:TV)=0.12\)

If any two occurrences in sample space S, A and B, are specified, then the conditional probability of event A given B is:

\(P(A|B)=\frac{P(A\:and\:B)}{P(B)}\)

Probability theory is an important branch of mathematics that is used to model and analyze uncertain events in various fields, including science, engineering, finance, and social sciences. The concept of probability is based on the idea of random experiments, where the outcomes are uncertain and can vary each time the experiment is performed.

The probability of an event can be determined by analyzing the possible outcomes of the experiment and assigning a probability to each outcome based on the assumptions of the model. The theory of probability has several applications in real life, such as predicting the outcomes of games of chance, evaluating risks in insurance and finance, and making decisions in scientific research.

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