A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet. 12f 3 ft 31 (a) if water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.2 feet deep? X ft/min (b) if the water is rising at a rate of 3/8 inch per minute when h - 2.3, determine the rate at which water is being pumped into the trough fo/min

The side length RQ of the triangle QRT that is 'x' will be 4 units.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

In triangle ΔRST, the side RT is given by the sine of angle 60°. Then we have

sin 60° = (2√3) / RT

(√3)/(2) = (2√3) / RT

RT = 2 x 2(√3) / (√3)

RT = 4

In triangle ΔQRT, the side QR is given by the tangent of angle 45°. Then we have

tan 45° = RQ / RT

1 = x / 4

x = 4

The side length RQ of the triangle QRT that is 'x' will be 4 units.

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The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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Answer:

2 \(\frac{2}{9}\) days

Step-by-step explanation:

Let d = the number of days.

\(\frac{1}{4}\) d = \(\frac{1}{5}\)d = 1

\(\frac{5}{20}\) d + \(\frac{4}{20}\) d = 1

\(\frac{9}{20}\) d = 1  Multiply both sides by \(\frac{20}{9}\)

(\(\frac{20}{9}\))(\(\frac{9}{20}\)) d = 1(\(\frac{20}{9}\))

d = \(\frac{20}{9}\)   I can break 20 into 9 + 9 + 2

d = \(\frac{9}{9}\) + \(\frac{9}{9}\) + \(\frac{2}{9}\)           \(\frac{9}{9}\) = 1

d = 1 + 1 + \(\frac{2}{9}\)

d = 2 \(\frac{2}{9}\)

Answer:

7

6

3

6

7 x 6 = 42

3 x 6 = 18

Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Answer:

25 over 4

Step-by-step explanation:

Improper fraction for the given mixed fraction is

\(\frac{25}{4}\)

Given :

We are given with mixed fraction .

Convert the mixed fraction into an improper fraction

Given mixed fraction is \(6 \frac{1}{4}\)

To convert it in to improper fraction , multiply the whole number 6 by the denominator 4  and then add the numerator .

\(6 \frac{1}{4} \\ \frac{6 \cdot 4 +1}{4} \\ \frac{25}{4} \\\)

The improper fraction for the given mixed fraction is

\(\frac{25}{4}\)

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Answer:

the perimeter is 130, the area is 640

Step-by-step explanation:

area = (40×13)+(12×10)

= 520+120

= 640

perimeter = 25+40+13+30+12+10

= 130

hope that helped!

Answer:

43a + c = 13.25

Step-by-step explanation:

A = 9

C = 81

The get Exam Range method must be used to an array of students in order to provide the student with the highest exam range. I must also construct a get Most Improved Student.

As part of my assignment, I'm supposed to write a method called get Exam Range that takes the lowest and highest scores from an array containing the exam results of various students, subtracts the minimum exam score from the maximum exam score, and then looks at the array again. The get Exam Range method must be used to an array of students in order to provide the student with the highest exam range. I must also construct a get Most Improved Student. When the code is run, I'm having difficulties receiving the right results.

You must complete the methods get Most Improved Student and get Exam Range using the Student and Classroom example from previously. The student with the widest variety of exam scores is the one who has progressed the most.

You must deduct the minimum and maximum exam scores in order to get the exam score range.

For instance, the range would be 90 - 75 = 15 if the exam scores were 90, 75, and 84.

Therefore,

The get Exam Range method must be used to an array of students in order to provide the student with the highest exam range. I must also construct a get Most Improved Student.

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Ok, so:

Let me draw something here below:

So, this is an equilateral triangle.

a. An equilateral triangle has the same lenght for its three sides.

For this reason, the measure of all its angles is 60°.

b. Let me draw the situation below:

We can fit 6 equilateral triangles together at one vertex, as you can see in the figure.

c. As we can see in the upper figure, these 6 triangles form a hexagon as an outside shape.

Answer:

b and d

Step-by-step explanation:

edge 2021

If the first term (a) is 4 and the common ratio (r) is 0.9, then the sequence diverges. Then the correct option is D.

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

a, ar, ar², ar³, ...

The sequence is given below.

\(\rm a_n = 4 (0.9)^n\)

Then the sum of the sequence will be given as

The first term (a) is 4. And the common ratio (r) is 0.9.

Then we get

\(\rm S_n = \dfrac{a (1 - r ^n)}{ (1 - r)}\\\\\rm S_n = \dfrac{4 (1 - 0.9 ^n)}{ (1 - 0.9)}\\\\\rm S_n = \dfrac{4 (1 - 0.9 ^n)}{0.1}\\\\\rm S_n = 40 (1 - 0.9^n)\)

For n = 1, we have

S₁ = 40 (1 - 0.9)

S₁ = 40 x 0.1

S₁ = 4

For n = 2, we have

S₂ = 40 (1 - 0.9²)

S₂ = 40 x 0.19

S₂ = 7.6

For n = 3, we have

S₃ = 40 (1 - 0.9³)

S₃ = 40 x 0.271

S₃ = 10.84

If the common ratio is less than one then the sequence will diverge.

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The probability that the basketball player makes 0 shots out of 3 is 0.343, or 34.3%. This can be calculated by using the binomial probability formula.

To calculate the probability of any outcome of a binomial experiment, use the formula: P(x) = nCx * px * (1-p)n-x, where n is the number of trials, x is the number of successes, and p is the probability of success in any one trial.

The Binomial Probability formula is

In this case, n = 3, x = 0, p = 0.39, and (1-p) = 0.61. Plugging these values into the formula, we get

P(x) = 3C0 * \(0.39^0\) * 0.61³

= 0.343.

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Step-by-step explanation:

y = mx + b

m = 3

b = 2

y = 3x + 2

______________________

y = mx + b

m = 1/2

b = -1

y = 1/2x + (-1)

y = 1/2x -1

The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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According to the information we can infer that the change between 11 and 12 is 1.3 m/hr

To establish the value of the change in height between 11 and 12 we must look at the values of the y axis. According to this information we can establish that 11 o'clock coincides with 5.2 and 12 o'clock coincides with 3.9. So we must subtract these two values:

According to the above, we can infer that the change between these two hours is 1.3 m/hr.

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Answer:

your answer for this question will be the 3rd answer choice

Answer:

52

Step-by-step explanation:

20 + 30 + 15+ 10+ 100= 175

30% of 175 is 52.5  but there can't be 52.5 students so 52

The salary for a given period depends on the salary unit rate and the

duration of the period under consideration.

Responses:

1. A) $903.85

2. G) $25,680

3. H) $48,450

4. C) $29.54

5. D) $26,822.40

1. The weekly salary = Annual salary ÷ 52

Which gives;

Sally's weekly salary = $47,000 ÷ 52 ≈ $903.85

2. Annual salary = Weekly salary × 12

Which gives;

Justin's annual salary = $2,140 × 12 = $25,680

3. Annual salary = Number of credit hours × Salary per credit hour

Which gives;

Annual salary = $950 × 51 = $48,450

4. Hourly rate = Annual income ÷ Number of hours worked

Number of hours worked = 205 days × 8 hours/day = 1,640 hours

Marc's annual income = $48,445.60

Which gives;

Hourly rate = $48,445.60 annually ÷ 1,640 hours/annum = $29.54

Marc's hourly rate = $29.54

5. Annual salary = Hourly rate × Number of hours worked per year

Number of hours worked per year = 254 × 8 = 2032

Which gives;

David's annual salary = $13.20/hour × 2032 hours = $26,822.4

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The interval of convergence of the Maclaurin series of (A)-1 is x≈P(x)=x

The concept of Maclaurin series states that the function is just the part of Taylor series of the function if in the Taylor series the center is taken as c = 0 then the Taylor series is called Maclaurin series.

Here we need to find the the interval of convergence of the Maclaurin series.

Let us consider  x up to n=3. and the function is x.

Then the Maclaurin series is given by

Find the 1st derivative: f(1)(x)=(f(0)(x))′=(x)′=1

valuate the 1st derivative at the given point: (f(0))′=1

Find the 2nd derivative: f(2)(x)=(f(1)(x))′=(1)′=0

Evaluate the 2nd derivative at the given point: (f(0))′′=0

Find the 3rd derivative: f(3)(x)=(f(2)(x))′=(0)′=0 (steps can be seen here).

Evaluate the 3rd derivative at the given point: (f(0))′′′=0

Now, use the calculated values to get a polynomial:

f(x)≈0/0! x⁰ + 1/1! x¹ + 0/2! x² + 0/3! x³

Finally, after simplifying we get the final answer:

=> f(x)≈P(x)=x

Therefore the Taylor (Maclaurin) series of x up to n=3 is x≈P(x)=x

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Answer:

he will give 4 pencils to the teacher he will give each classmate 5 pencils

Answer:

 0 5  

 1 5 ⟌ 7 9  

     - 0    

       7 9  

     - 7 5  

         4  

Step-by-step explanation:

The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2

How to solve a function?

If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:

g(x) = a(4) raise to the power x-k/2

where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:

f(x) = g(x)/2

Substituting the expression for g(x) into this equation and simplifying, we get:

4raise to the power x - 6 = a(4)raise to the power x-k/2

To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:

f(0) = 4 - 6 = -5

f(1) = 4- 6 = -2

Using the equation g(x)/2 = f(x), we can write:

g(0)/2 = -5

g(1)/2 = -2

Substituting the expression for g(x) into these equations, we get:

a(4) raise to the power -k/2 = -10

a(4) raise to the power 1-k/2 = -4

Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":

(4)raise to the power -k/2 / (4)  raise to the power 1-k/2 = -10 / -4

Simplifying this equation, we get:

4.raise to the power(1-k/2) = 5

Taking the logarithm of both sides (with base 4), we get:

1-k/2 = log4(5)

Solving for "k", we get:

k = 2 - 2 log4(5)

Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":

a = -10 / (4)   raise to the power  -k/2

Substituting the numerical value of "k", we get:

k = 2 - 2 log4(5) ≈ 0.872

a = -10 / (4) raise ti the power  -k/2 ≈ 2.323

Therefore, the equation for the transformed function g(x) is:

g(x) = 2.323 (4)raise to the power x-0.872/2

or equivalently:

g(x) = 1.1615 (4) raise to the power -x0.872

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Answer:

g(x) = 1/2 (4)^x - 3

Step-by-step explanation:

A vertical compression by a factor of 1/2

means that the entire function f is multiplied by 1/2:

1/2 f (x) = 1/2 (4^x - 6)

= 1/2 (4)^x - 3

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer:

7 times 4 which is 28 at each fair.

Choe saki earn $258  in commission on tuesday. This problem is simple algebra problem where you have to form equation to answer the question.

From the question it is evident that Cho Saaki had a commission based job. we will simply solve it as any other equation in algebra

Given :

Cho Saaki makes $9 for 12 demonstrations. so total money she makes for 12 demonstrations is $108.

then she makes $15 for each demonstration over 12.

On Tuesday she makes 22 demonstrations. it means that she makes 10 more demonstration over 12. therefore she makes  $150  with those 10 more demonstrations.

so total money she earns in commission according to the equation is

12 × $9 + 10 × $15 = $108 + $150 = $158.

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Transform the variable x² into u

Use the quadratic formula to solve for solutions in u, with a = -3, b = 27, c = 1200.

Revert u back into x²

Equate to zero all the factors, and solve for x

The real zeroes to the given equation is x = -5, and x = 5.

Answer:

An isosceles triangle has 2 equal sides. If the perimeter is 110 inches, and your base is 34 inches, subtract the base from the total perimeter. 110-34= 76. If 2 sides have to be equal, the total length of the 2 sides is 76 inches, divide the 2 lengths by 2 to get the measure of each side individually. 76÷2=38.

Hence, your answer is each of the equal sides of the plate equals 38 inches.

Hope this helps!

Answer:

The equation that will represent the number of grams present after n hours is \(A(n) = 150(0.85)^n\)

3.035 grams will be left one day from now.

Step-by-step explanation:

Exponential equation for the amount of a substance:

The exponential equation for the amount of a substance is given by:

\(A(t) = A(0)(1-r)^t\)

In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time period.

A radioactive isotope is decaying at a rate of 15% every hour.

This means that \(r = 0.15\)

Currently there are 150 grams of the substance.

This means that \(A(0) = 150\)

Write an equation that will represent the number of grams present after n hours.

\(A(n) = A(0)(1-r)^n\)

\(A(n) = 150(1-0.15)^n\)

\(A(n) = 150(0.85)^n\)

How much will be left one day from now?

One day is 24 hours, so this is A(24).

\(A(24) = 150(0.85)^{24} = 3.035\)

3.035 grams will be left one day from now.

Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

Answer:

Jemma: 22x + 5

Debra: 20x

Step-by-step explanation: