WILL MARK BRAINLIEST 100 POINTS

Answer:

\(\boxed{\sf A)\: -16}\)

Step-by-step explanation:

\(\sf 5+\left(3\left(2-\sqrt{81}\right)\right)\)

\(\bigstar\) Calculate the square root of 81 = 9

\(\longrightarrow\) \(\sf 5+3(2-9)\)

\(\bigstar\) Subtract 9 from 2= -7

\(\longrightarrow\) \(\sf 5+3(-7)\)

\(\bigstar\) Multiply 3 and -7 = -21

\(\longrightarrow\) \(\sf 5-21\)

\(\bigstar\) Subtract 21 from 5 = -16

\(\longrightarrow\) \(\sf -16\)

______________________

Answer:

b => base  => 40 cm

h => altitude => 30 cm

A = h*b/2

h=b-10

600=(b-10)b/2

600 = (b^2-10b)/2

1200=b^2-10b

b^2-10b-1200=0

(b-40)(b+30)=0

b=40 cm

h=b-10 = 40-10=30

3.31 it will take her to complete the triathlon.

To find this, we can apply the equation distance = rate x time.

We are aware of the length and pace of each triathlon leg. Let's name them, respectively, d and r. We must locate the time, which we shall designate as t.

d = r x t    or

t = d/r

The distance is 0.93, or 93/100, and the rate is 1.2, or 12/10 when swimming. As a result of our formula, we have:

12/10 divided by 93/100 yields the same result as

93/100 * 10/12

time to swim = 93/120 = 31/40

We have a distance of 24.8 miles, or 248/10, and a speed of 18.8 miles, or 188/10, for biking. Using the same formula, we obtain:

248/10 divided by 188/10 or

248/10 * 10/188 = 248/188 = 62/47 = time to bike

Finally, for the run, the distance is 6.2 = 62/10 and the rate is 5.1 or 51/10. Plugging this into the formula gives:

62/10 divided by 51/10 or

62/10 * 10/51 = 62/51 = time to run

= 31/40 + 62/47 + 62/51

=3.31

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The trigonometric formula 2 tan (x/2) can be made simpler by using the half-angle identities. Where x is the angle in radians, the half-angle identity for a tangent is tan(x/2) = sin(x)/(1 + cos(x)).

We obtain 2 sin(x)/(1 + cos(x)) by substituting this identity into the expression. By multiplying the numerator and denominator by the conjugate of the denominator, which is 1 - cos(x), we can further reduce the complexity of the equation. As a result, we get 2 sin(x)(1 - cos(x))/(1 - cos2(x)). The expression can be rewritten as 2 sin(x)(1 - cos(x))/(sin(x)), which is based on the Pythagorean identity sin(2x) + cos(2x) = 1. Finally, we arrive at the abbreviated equation 2(1 - cos(x))/sin(x) by eliminating sin(x) from the numerator and denominator.

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Approximately 4680 minutes are required for 10.0% of a sample of cyclopropane to isomerize to propene at 700 K, based on the given rate constant of 6.2 × 10^(-4) min^(-1).

The isomerization of cyclopropane to propene follows first-order kinetics, which means that the rate of the reaction is directly proportional to the concentration of cyclopropane. The rate constant (k) is a proportionality constant that relates the rate of the reaction to the concentration of the reactant.

In this case, the rate constant for the reaction is given as 6.2 × 10^(-4) min^(-1), and we want to determine the time required for 10.0% of the cyclopropane to isomerize to propene. To solve this, we use the first-order kinetics equation:

ln(A/A₀) = -kt

Where ln is the natural logarithm, A₀ is the initial concentration of cyclopropane, A is the final concentration (10% of A₀), k is the rate constant, and t is the time.

By substituting the given values into the equation, we can isolate t and solve for it. The calculation yields approximately 4680 minutes as the time required for 10.0% of the cyclopropane sample to isomerize to propene at 700 K.

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Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

9.3 ft

Step-by-step explanation:

The average rate of change between year 1 and year 4 is $500-$100/(4-1) years = $400/3 years = $133.33 per year. This statement accurately calculates the average rate of change in cost.

To determine the correctness of the observations based on the graph, we need to carefully analyze the information presented.

Observation 1 states that the cost of maintaining the machine is constantly rising. However, this statement is incorrect as there is a flat spot and a downward trend from 4 to 6 years, indicating a decrease in maintenance costs during that period.

Observation 2 claims that the cost of maintenance is $300 for the first 3 years. This statement is also incorrect since the graph shows a rising trend in the cost during the first 3 years, and it is only in the third year that the cost reaches $300. The cost is not constant for the entire period.

Observation 3 states that the average rate of change between year 1 and year 4 is $400/400 = $100/year. This statement is incorrect because the change in time from year 1 to year 4 is actually 3 years, not 4. Therefore, the correct calculation would be $400/3 years, which is approximately $133.33 per year.

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Answer:

x = 32, y = 51

Step-by-step explanation:

You know the longest side of ΔTUS is 13m and the longest side of ΔMNP is (2x-y). Thus:

2x - y = 13 --- Equation 1

You know the sum of angles in a triangle is 360°. Two of the angles are given in ΔMNP (142° & 24°) and the remaining angle is (2x-50)°. Thus:

142 + 24 + 2x - 50 = 180

2x + 116 = 180

2x = 180 - 116

2x = 64

x = 64 ÷ 2

x = 32 --- Equation 2

Substitute x = 32 into Equation 1:

2(32) - y = 13

64 - y = 13

-y = 13 - 64

   = -51

y = 51 --- Equation 3

Answer:

x = 32, y = 51

Step-by-step explanation:

Since the triangles are congruent then corresponding angles and sides are congruent, then

∠ U = ∠ N and NP = US

Require to find ∠ N

∠ N = 180° - (24 + 142)° ← sum of angles in triangle

      = 180° - 166°

      = 14°

Thus

2x - 50 = 14 ( add 50 to both sides )

2x = 64 ( divide both sides by 2 )

x = 32

and

NP = US

2x - y = 13 ← substitute x = 32

2(32) - y = 13

64 - y = 13 ( subtract 64 from both sides )

- y = - 51 ( multiply both sides by - 1 )

y = 51

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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Given the diagram below

Introducing 'a', as shown above, it can be observed that

It can also be observed that

It can also be observed that

Substitute for y to get z

Hence, the value of y is 34°, while z is 119°.

Answer:

The figure should be 56 units squared.

Step-by-step explanation:

The long side is 14 units long (6+6+2) and the short side is 4 units long, so 14 multiplied by 4 is 56.

Answer:

b

Step-by-step explanation:

used a calucator

Answer:

a = 3

Step-by-step explanation:

The point (- 5, 7a ) satisfies the equation

Substitute the coordinate points into the equation and solve for a

7a = 7(- 5) + 56 = - 35 + 56 = 21 ( divide both sides by 7 )

a = 3

Answer:

The system has no solution because if 0=8, this means this is an empty set. If you get 2 numbers that don't equal each other for an answer then you know there's no solution

Step-by-step explanation:

the requried length and width of the pool can be given by the expression l = 38.5 - w.

Let's use algebra to solve this problem. Let's call the length of the pool "l" and the width of the pool "w". We know that the perimeter of a rectangle is given by:

Perimeter = 2l + 2w

2l + 2w = 77

l + w = 38.5

l = 38.5 - w

Thus, the requried length and width of the pool can be given by the expression l = 38.5 - w.

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Answer: Kaye is 4 years old

Step-by-step explanation:

Paula is 10 less than thrice of Kaye's age. two years from now, Paula's age is twice Kaye's present age. how old is Kaye now?  Let Kaye's age now be x years Paula is 10 less than thrice of Kaye's age =3x-10   TWO YEARS LATER  Paula,s age = (3x-10)+2 = 3x-8 3x-8 =x 2x=8 x=4  Kaya,s age = 4 years

Answer: The velocity of the ball is 108.8 ft/s downwards.

Step-by-step explanation:

When the ball is dropped, the only force acting on the ball will be the gravitational force. Then the acceleration of the ball will be the gravitational acceleration, that is something like:

g = 32 ft/s^2

To get the velocity equation we need to integrate over time, to get:

v(t) = (32ft/s^2)*t + v0

where v0 is the initial velocity of the ball. (t = 0s is when the ball is dropped)

Because it is dropped, the initial velocity is equal to zero, then we get:

v(t) = (32ft/s^2)*t

Which is the same equation that we can see in the hint.

Now we want to find the velocity 3.4 seconds after the ball is dropped, then we just replace t by 3.4s, then we get:

v(3.4s) = (32ft/s^2)*3.4s = 108.8 ft/s

The velocity of the ball is 108.8 ft/s downwards.

To find the side lengths of a triangle using angles, you can employ trigonometric ratios like sine, cosine, and tangent

To find the side lengths of a triangle using angles, you can follow these steps:

Identify the given information: Determine which angles are known and which angles are unknown. Let's assume you have the measures of angles A, B, and C.

Apply the angle sum property: In a triangle, the sum of the interior angles is always 180 degrees. So, if you have the measures of two angles, you can find the measure of the third angle by subtracting the sum of the known angles from 180 degrees.

Determine the relationship between angles and side lengths: In a triangle, the lengths of the sides are related to the angles through the trigonometric ratios. The most common ratios are sine (sin), cosine (cos), and tangent (tan).

Use the trigonometric ratios: Depending on the given information, you can use the appropriate trigonometric ratio to find the side lengths. For example:

If you know an angle and the length of the side opposite to that angle, you can use the sine ratio: sin(A) = opposite/hypotenuse.

If you know an angle and the length of the adjacent side, you can use the cosine ratio: cos(A) = adjacent/hypotenuse.

If you know an angle and the lengths of the two sides that form that angle, you can use the tangent ratio: tan(A) = opposite/adjacent.

Solve for the unknown side lengths: Once you have the trigonometric equation involving an angle and side lengths, you can solve for the unknown side length using algebraic manipulations or a calculator.

Repeat these steps for the other angles to find the lengths of the remaining sides. Remember to consider the units of measurement (degrees or radians) and apply the appropriate trigonometric functions based on the given information.

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Answer:

y = 12

Step-by-step explanation:

y = x^2 + 8

y = (-2)^2 + 8

y = 4 + 8

y = 12

Answer:

x + 7

Step-by-step explanation:

1+7=8

2+7+9

so on

To find the subtransient current in per unit for a three-phase fault on bus 4, we need to calculate the fault current using the bus impedance matrix.

Given bus impedance matrix Zbus:

| j0.15 j0.08 j0.04 j0.07 |

| j0.08 j0.15 j0.06 j0.09 |

| j0.04 j0.06 j0.13 j0.05 |

| j0.07 j0.09 j0.05 j0.12 |

To find the fault current on bus 4, we need to find the inverse of the Zbus matrix and multiply it by the pre-fault voltage vector.

The pre-fault voltage vector V_pre-fault is given as:

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Let's calculate the inverse of the Zbus matrix:

Zbus_inverse = inv(Zbus)

Now, we can calculate the fault current using the formula:

I_fault = Zbus_inverse * V_pre-fault

Calculating the fault current, we have:

I_fault = Zbus_inverse * V_pre-fault

Substituting the values and calculating the product, we get:

I_fault = Zbus_inverse * V_pre-fault

= Zbus_inverse * | 1.0/0° |

| 1.0/0° |

| 1.0/0° |

| 1.0/0° |

Please provide the values of the Zbus matrix and the pre-fault voltage vector to obtain the specific values for the fault current and the per-unit current from generator 2.

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Answer:

Interval Notation:

( − ∞ , ∞ )

Step-by-step explanation:

h = 0.75m + 49.5 equation models Jeremy’s growth spurt, where h represents his height in inches, and m represents time in months.

Finding the product of two or more integers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

Jeremy was 49.5 inches tall when this picture was taken, and every month after then, his height has risen 0.75 inches.

h = 0.75m + 49.5, simulates Jeremy's growth spurt, where h represents his height in inches and m indicates time in months.

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Answer:

\(r=\sqrt{\frac{3V}{\pi h} }\)

Step-by-step explanation:

\(V=\frac{1}{3} \pi r^2h\)

Lets solve for \(r\).

Multiply both sides of the equation by 3.

\(3V=\pi r^2h\)

Divide both sides of the equation by \(\pi h\).

\(\frac{3V}{\pi h} =r^2\)

Take the square root of both sides.

\(\sqrt{\frac{3V}{\pi h} } =r\)

Answer:

A)5 is the answer because she already has 75 + 25=100 and she needs 150 more so 150÷25=5

ᴇʏᴏᴀᴘᴜᴀ8ᴡ8ᴇɪᴇᴜᴇᴜɪᴇ8ᴡ8ᴡ8ǫ

Answer:

3g=x-2

Step-by-step explanation:

3g+2=x then, move 2 to the other side(nb*change to negative) then it will be 3g=x-2 finally divide both sides by 3 then it will be g=x-2

3

The linear approximation for the change in the predicted probability per degree increase in temperature is approximately 0.003.

Linear approximation is an estimation method that approximates a function by a linear function. Linear approximation is also known as the tangent line approximation method.

This method is useful for finding out the approximate value of the function at a point near the given point. The linear approximation of the change in predicted probability per degree increase in temperature can be found using the formula given below: Linear Approximation Formula: Linear approximation formula is given by the following equation: f(x) ≈ f(a) + f′(a)(x − a)Where f(x) is the function, f(a) is the value of the function at the point x=a, f′(a) is the first derivative of the function at x=a, and x is the point near the point a that we want to find the approximation.

Let us apply the linear approximation formula to find the linear approximation for the change in the predicted probability per degree increase in temperature.

Let f(t) be the function that gives the predicted probability of a particular event at a temperature t. Suppose that at a temperature of 100 °F, the predicted probability is 0.8. Let f′(t) be the first derivative of the function f(t).

We need to find the linear approximation of the change in predicted probability per degree increase in temperature when the temperature is 100 °F. We can use the following steps to find the linear approximation.

Step 1: Find the value of f(100)f(100) = 0.8This means that when the temperature is 100 °F, the predicted probability is 0.8.

Step 2: Find the value of f′(100)f′(100) = df/dt = 0.003 This means that the rate of change of predicted probability with respect to temperature at 100 °F is 0.003 per degree.

Step 3: Use the linear approximation formula to find the linear approximation of the change in predicted probability per degree increase in temperature. The linear approximation formula is given by: f(x) ≈ f(a) + f′(a)(x − a)Substitute a=100, f(100)=0.8, f′(100)=0.003, and x=101 into the formula. f(101) ≈ f(100) + f′(100)(101 − 100)f(101) ≈ 0.8 + 0.003(1)f(101) ≈ 0.803

This means that the predicted probability of the particular event when the temperature is 101 °F is approximately 0.803.

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both countries can benefit from trade by specializing in the goods and services that they are relatively more efficient at producing and exchanging them with each other.

China is using the comparative advantage perspective in regards to not trading silk with Germany in exchange for automobiles. According to the theory of comparative advantage, a country should specialize in producing and exporting the goods or services that they can produce more efficiently or at a lower opportunity cost compared to other goods and services.

In this case, China has a comparative advantage in producing silk and a comparative disadvantage in producing automobiles compared to Germany, which has a comparative advantage in producing automobiles and a comparative disadvantage in producing silk.

Hence, both countries can benefit from trade by specializing in the goods and services that they are relatively more efficient at producing and exchanging them with each other.

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