6 Find the value of x from the following figures.
1)

The rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3 is 0.3 m²/s.

If the lengths a and b for two sides of the triangle, as well as the included angle θ, are known, the area of a triangle can be calculated using the sine formula.

\(\text { Area }=\frac{1}{2} a b \sin \theta\)

Now, according to the question;

The two sides of the triangle are given;

Let a = 4m and b = 5m.

Let θ = π/3. be the angle between the two sides;

Then,

Differentiate the area with respect to time (as rate of change of area)

\(\begin{aligned}\frac{\mathrm{d} A}{\mathrm{~d} t}=\frac{\mathrm{d}}{\mathrm{d} t} \frac{1}{2} a b \sin \theta &=\frac{1}{2} * 4 * 5 * \frac{\mathrm{d}(\sin \theta)}{\mathrm{d} \theta} \cdot \frac{\mathrm{d} \theta}{\mathrm{d} t} \\&=10 *(\cos \theta) * 0.06 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.6 \cos (\pi / 3) \frac{\mathrm{m}^{2}}{\mathrm{~s}} \\&=0.6 * 0.5 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.3 \frac{\mathrm{m}^{2}}{\mathrm{~s}}\end{aligned}\)

Therefore, the area of the triangle as a function of angle is 0.3 m²/s.

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The complete question is-

Two sides of a triangle are 4m and 5 m in length and the angle between them is increasing at a rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3.

The account that will give Grady at least a 5% annual yield is Account C

We can use the formula for compound interest to compare the three investment accounts and find the one that will give Grady at least a 5% annual yield:

FV = PV × (1 + r/n)^(n*t)

where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

For Account A:

APR = 4.95%, compounded monthly

r = 0.0495

n = 12

t = 1

FV = PV × (1 + r/n)^(nt)

FV = PV × (1 + 0.0495/12)^(121)

FV = PV × 1.050452

To get at least a 5% annual yield, we need FV/PV ≥ 1.05

1.050452/PV ≥ 1.05

PV ≤ 1.000497

Therefore, Account A will not give Grady at least a 5% annual yield.

For Account B:

APR = 4.85%, compounded quarterly

r = 0.0485

n = 4

t = 1

FV = PV × (1 + r/n)^(nt)

FV = PV × (1 + 0.0485/4)^(41)

FV = PV × 1.049375

To get at least a 5% annual yield, we need FV/PV ≥ 1.05

1.049375/PV ≥ 1.05

PV ≤ 1.000351

Therefore, Account B will not give Grady at least a 5% annual yield.

For Account C:

APR = 4.75%, compounded daily

r = 0.0475

n = 365

t = 1

FV = PV × (1 + r/n)^(nt)

FV = PV × (1 + 0.0475/365)^(3651)

FV = PV × 1.049038

To get at least a 5% annual yield, we need FV/PV ≥ 1.05

1.049038/PV ≥ 1.05

PV ≤ 1.000525

Therefore, Account C will give Grady at least a 5% annual yield.

Therefore, the account that will give Grady at least a 5% annual yield is Account C.

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The percentage of pupils that miss class each day is the most appropriate indicator to track with a p chart. P charts are a specific kind of control chart used to track the percentage of nonconforming products produced over time in a process.

It is frequently applied to attribute data, where the data can be categorised as conforming or nonconforming depending on particular standards.The percentage of pupils that skip class daily in the given alternatives can be categorised as either a conforming (present) or nonconforming (missing) feature. We can track the variation in absenteeism and see any patterns or trends that might need attention or intervention by using a p chart to track the percentage of pupils who are missing over time.

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The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.

The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.

Let's analyze the behavior of the parent absolute value function:

For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.

For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.

At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.

Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).

In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.

On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.

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The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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Answer:

The answer is -34

Step-by-step explanation:

3-33-4=-34

Answer:

115

Step-by-step explanation:

20% is one fifth. If Mary has one fifth fewer than Susan, then she has 4 fifths of what Susan has. So 92 is 4 fifths of some number.

To find out what one fifth is, you can divide 92 by 4 because it is four fifths.

92/4 = 23

So one fifth of the number of blouses Susan has is 23. Now you can multiply 23 by 5 to get the total number of blouses Susan has.

23 * 5 = 115

Answer:

9 ÷ 7 + d.

Step-by-step explanation:

Answer:

d × (5d + 11)

Step-by-step explanation:

5d² + 11d

Factor out d from the expression

When d is factored out;

5d² becomes 5d

11d becomes 11

And d multiplies it all;

d × (5d + 11)

To maximize the manufacturer's total weekly profit, we need to find the critical point of the profit function P(x,y).

(a) To find the critical point, we need to find where the partial derivatives of P(x,y) are equal to zero.

Taking the partial derivative of P(x,y) with respect to x and y, we get:
P_x = 560 + 20y - 40x
P_y = 20x - 12y

Setting P_x = 0 and P_y = 0, we get:
560 + 20y - 40x = 0  and  20x - 12y = 0
Solving these equations simultaneously, we get:
x = 7 and y = 35

(b) To classify the critical point, we need to use the D-Test. The D value is:
D = P_xx * P_yy - (P_xy)^2
Substituting the values of P_xx, P_yy, and P_xy, we get:
D = -9600
Since D is negative, we have a saddle point at the critical point.

(c) To maximize the manufacturer's total weekly profit, we need to produce and sell 7,000 units of Product A and 35,000 units of Product B per week.

(d) Plugging x = 7 and y = 35 into the profit function P(x,y), we get:
P(7,35) = 560(7) + 20(7)(35) - 20(7)^2 - 6(35)^2
P(7,35) = $8,050
Therefore, the maximum weekly profit is $8,050.

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Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

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The measure of angle A remains as (4x + 20) degrees until we have more information or the specific value of x.

The measure of angle A is given by the expression (4x + 20) degrees. To find the specific measure of angle A, we need to determine the value of x or be provided with additional information.

The given information provides the measure of angle D as (5x - 65) degrees, but it does not directly give us the measure of angle A.

Without knowing the value of x or having any additional information, we cannot determine the specific measure of angle A.

The expression (4x + 20) represents the general form of the measure of angle A, but we need more information or the value of x to evaluate it.

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Answer:

12

Step-by-step explanation:

1 -----> 3

?------>36

By make Cross

36*1/3 =12

Answer:

9^y

Step-by-step explanation:

the way u write nine to the yth power, if y is something meet me in the comments!!

hope this helps, brailiest plzz!

Answer:

\(9^{y}\)

Step-by-step explanation:

It literally means 9 to the power of whatever value y represents,...

Chow,...!

The number of teams and matches in the soccer league illustrates permutation and combination

There are 12 teams in the soccer league in the first season

The number of teams in the soccer league is given as n.

So, the total number of matches played in a season is:

Matches = n(n-1)/2

When the number of teams increases by 2, we have:

Matches = (n + 2)(n + 2 -1)/2

Also, the number of matches increases by 27.5%.

So, we have:

Matches = n(n-1)/2 * (1 + 27.5%)

Equate both equations

\(\frac{(n + 2)(n + 2 -1)}{2} = \frac{n(n-1)}{2} * (1 + 27.5\%)\)

Simplify

\(\frac{(n + 2)(n + 1)}{2} = \frac{n(n-1)}{2} * (1.275)\)

Multiply through by 2

\((n + 2)(n + 1) = n(n-1) * (1.275)\)

Expand

\(n^2 + 3n + 2 = 1.275n^2 - 1.275\)

Collect like terms

\(n^2 -1.275n^2+ 3n + 2 +1.275 = 0\)

Evaluate the like terms

\(-0.275n^2+ 3n + 3.275 = 0\)

Using a graphing calculator, we have:

n = -1 or n = 11.909

n cannot be negative.

So, we have:

n = 11.909

Approximate

n = 12

Hence, there are 12 teams in the soccer league in the first season

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The measure of acute angle x is approximately 63.9 degrees.

If cos 32 degrees = sin x, we can use the trigonometric identity \(sin^2x +\)\(cos^2x = 1\) to find the value of sin x. First, we need to convert the given angle from degrees to radians, which is done by multiplying it by\(\pi /180\\\). Thus, \(cos 32° = cos(32π/180) = cos(0.56 radians)\).

\(cos^2x + sin^2x = 1sin^2x = 1 - cos^2xsin^2x = 1 - cos^2(32°)sin^2x = 1 - cos^2(0.56)sin^2x = 0.804\\\)

Taking square root:

\(sin x = \sqrt{0.804}\)

sin x = 0.896

Therefore, the acute angle x measures\(arcsin(0.896)\)in radians or degrees, which is approximately 63.9°.

In conclusion, if cos 32° = sin x, the measure of acute angle x is approximately 63.9 degrees.

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Answer:

hope this helps!!

Step-by-step explanation:

Answer:

y=-4, x=-3

Step-by-step explanation:

1. Find x in terms of y

x-6y=21

x=21+6y

2. Substitute the x value for the y equivalent of x times the coefficient (6)

6(21+6y)+2y=-26

3. Distribute and simplify

126+36y+2y=-26

126+38y=-26

-152=38y

y=-4

3. Find x using the y value. Substitute y with -4

x-6(-4)=21

x+24=21

x=-3

10 and 13 are the measure of the values of x and y respectively

The given diagram is a parallelogram with unknown values x an y.

Since the measure of sum of angles in a triangle is 180 degrees, hence we will take the measure of the angles in the triangle EFY to have:

70 + 7x - 5 + 45 = 180

110 + 7x = 180

7x = 180 - 110

7x = 70

x = 10

Similarly for the triangle EDY;

45 + 70 + 5y = 180

115 + 5y = 180

5y = 180 - 115

5y = 65

y = 13

Hence the measure of the values of x and y are 10 and 13 respectively

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Answer:

if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price

Step-by-step explanation:

Answer:

The answer would be 140 = 36

The simplified form of the expression log(10⁸) - log(10⁴) ÷ log(10⁴) - log(10²) is 5.

Given the expression in the question;

log(10⁸) - log(10⁴) ÷ log(10⁴) - log(10²)

To simplify, first we find the common denominator.​

log(10⁸) - log(10⁴) ÷ log(10⁴) - log(10²)

(log(10⁸)log(10⁴))/log(10⁴) - log(10⁴) ÷ log(10⁴)  + ( - log(10²)log(10⁴))/log(10⁴)

Now, combine the numerators over the common denominator.

( (log(10⁸)log(10⁴) - log(10⁴) - log(10²)log(10⁴) ) / log(10⁴)

Simplify each terms

( 32 - 4 - 8 ) / log(10⁴)

( 20 ) / log(10⁴)

( 20 ) / 4log(10)

5 / log(10)

5/1

5

Therefore, 5 is the simplified form of the expression.

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Answer:

X-7

Step-by-step explanation:

Because I did algebra 1

Answer:

X-17

Step-by-step explanation:Its X-17 because it said 17 less than a number X. So its X-17 and variable comes first.

Sophie's favorite number is 83

We have that;

A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.

To get Sophie's favorite number, we need to assume the case as;

Let,

⇒10x + y = 10y + x + 45

   x + y = 11

   y = 11-x

⇒10x + 11 - x = 10(11 - x) + x + 45

  10x + 11 - x = 110 - 10x + x + 45

  9x + 11 = 155 - 9x

  18x + 11 = 155

  18x = 144

  x = 8

Therefore, y = 11 - 8

                  y = 3

Sum = x + y = 8 + 3 = 11

Hence, the given condition is satisfied.

Sophie's favorite number is 83.

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The Arizona Department of Real Estate takes its rules and regulations from three basic sources: The Arizona State Constitution, Arizona Revised Statutes, and the Arizona Administrative Code.

The Arizona Department of Real Estate derives its rules and regulations from three primary sources. Firstly, the Arizona State Constitution serves as a fundamental legal document that outlines the framework and principles upon which the state operates.

Secondly, the Arizona Revised Statutes (ARS) provide the statutory laws enacted by the Arizona State Legislature. These statutes specifically address real estate matters and govern the activities and conduct of individuals and organizations involved in the real estate industry.

Lastly, the Arizona Administrative Code (AAC) contains the administrative rules and regulations established by various state agencies, including the Arizona Department of Real Estate. The AAC provides detailed guidelines and procedures for implementing and enforcing the laws set forth in the Arizona Revised Statutes, ensuring compliance and facilitating the proper functioning of the real estate sector within the state.

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Answer:

Its A. Just had this question

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

DIscount = 121/2 % 0ff

Answer:

1.What is the theoretical probability that a coin toss results in two heads showing?

33%

2.What is the experimental probability that a coin toss results in two heads showing?

25%

3.What is the theoretical probability that a coin toss results in two tails showing?

33%

4.What is the experimental probability that a coin toss results in two tails showing?

21%

5.What is the theoretical probability that a coin toss results in one head and one tail showing?

33%

6.What is the experimental probability that a coin toss results in one head and one tail showing?

54%

Step-by-step explanation:

Hope this helps, I just finished my assingmnet like this tonight :))