The top of a rectangular table has an area of 21 square feet. The width of the table is
3 feet. What is the length of the table?

Answer:

\(\frac{dA}{A} = -\frac{1}{70} dt\)

A(t) = \(40 e^{-\frac{t}{70}}\)

Step-by-step explanation:

Given - A tank contains 350 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t.

To find - Find the rate at which the number of grams of salt in the tank is changing at time t.

Find the number A(t) of grams of salt in the tank at time t.

Proof -

Given that,

Total fluid in the tank = 350 litres

Total salt = 40 grams

Rate in flow = 5 L/min

Rate out flow = 5 L/min

Concentration in = 0

Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)

Now,

Total solution in the tank at time t = Total fluid in the tank + (Rate in flow - Rate out flow )t

                                                        = 350 + (5 - 5)t

                                                        = 350

⇒Solution in the tank at time t = 350

⇒Concentration out = \(\frac{A(t)}{350}\)

Now,

Rate of change in the tank at time t = \(\frac{dA}{dt}\)

                                                           =  (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)

                                                           = 5(0) - 5(\(\frac{A(t)}{350}\))

                                                           = 0 - \(\frac{A(t)}{70}\)

                                                           = \(-\frac{A(t)}{70}\)

⇒\(\frac{dA}{dt}\) = \(-\frac{A(t)}{70}\)

⇒\(\frac{dA}{A} = -\frac{1}{70} dt\)

Integrate both sides , we get

ln(A) = \(-\frac{1}{70}t + C\)

⇒A(t) = \(e^{-\frac{t}{70}+ C}\)

         = \(e^{-\frac{t}{70}}*e^{C}\)

         = \(C_{1} e^{-\frac{t}{70}}\)

⇒A(t) = \(C_{1} e^{-\frac{t}{70}}\)

Now,

Given that,

Initially, the tank has 40 grams of salt

⇒A(0) = 40

⇒C₁ = 40

⇒A(t) = \(40 e^{-\frac{t}{70}}\)

Answer:

The equation is \(x^{2} +2\cdot x + 2 = 0\)-

Step-by-step explanation:

According to the statement, we have a second order polynomial of the form \(A\cdot x^{2}+ B\cdot x + C = 0\), whose solutions can be found by Quadratic Formula:

\(x_{1,2} = \frac{-B\pm \sqrt{B^{2}-4\cdot A\cdot C}}{2\cdot A}\) (1)

Where \(A\), \(B\) and \(C\) are the coefficients of the polynomial.

If roots are conjugated complex numbers, then:

\(B^{2}-4\cdot A\cdot C < 0\) (2)

\(B^{2} < 4\cdot A \cdot C\)

If we know that \(A = 1\), \(C = 2\) and \(x_{1,2} = -1\pm i\), then we find that:

\(-1\pm i = -\frac{B}{2}\pm \frac{\sqrt{B^{2}-8}}{2}\)

\(-2 \pm i\,2 = -B \pm \sqrt{B^{2}-8}\)

By comparing each side, we have the following system of equations:

\(-B = -2\) (3)

\(\sqrt{B^{2}-8} = 2\) (4)

Whose solution is \(B = 2\).

In a nutshell, the equation is \(x^{2} +2\cdot x + 2 = 0\)-

Answer:

10.5 mph

Step-by-step explanation:

To find the constant of proportionality in miles per hour, we need to divide the distance (in miles) by the time (in hours) for each of the two runs, and then take the average of the two rates.

For Monday's run:

Rate = Distance / Time = 21 miles / 3 hours = 7 miles per hourFor Wednesday's run:Rate = Distance / Time = 10 1/2 miles / 1 1/2 hours = (21/2) miles / (3/2) hours = 14 miles per hour

To find the average rate, we add the two rates and divide by 2:Average rate = (7 miles per hour + 14 miles per hour) / 2 = 10.5 miles per hour

Therefore, the constant of proportionality in miles per hour is 10.5. This means that Ashley runs at an average rate of 10.5 miles per hour during her training.

Answer:

Its B

Step-by-step explanation:

Answer: C

Step-by-step explanation: it is c trust me

Answer:

g(x) = (x - 4)^2 - 5, and the vertex is (4, -5)

Step-by-step explanation:

Please, use " ^ " to indicate exponentiation:  g(x) = (x - 4)^2 – 5.  Comparing this to y = a(x - h)^2 + k, we see that h must be 4 and k must be -5.  Thus, the vertex is (4, -5).

Make a table showing several x-values and the corresponding y-values:

x       g(x) = (x - 4)^2 - 5                     (x, y)

0                    (-4)^2 - 5 = 11               (0, 11)

4                (4 - 4)^2 - 5 = -5               (4, -5)

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

yshannmm

Step-by-step explanation:

yes

ANSWER

EXPLANATION

To complete the table, we have to see what is the ratio between the given pairs,

This means that b is 5 times a, so the value of b when a = 1 is 5. And, the value of a when b = 80 is 16,

If the pairs of numbers are equivalent ratios, it means that the division between the numbers, for example, b/a, is constant - i.e. it always gives the same result. In this case, the ratio is always 5.

The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

To know more about Percentage check:

https://brainly.com/question/29306119

#SPJ1

Step-by-step explanation:

For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.

For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.

For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.

Because 2×3=6

9514 1404 393

Answer:

  The principal was right. The numbers don't add up.

Step-by-step explanation:

Based on the categorization, the total number of students polled is ...

  290 +300 +270 -80 -70 -60 -2(50) = 550

The number reportedly polled is 500, so the numbers given are inconsistent.

____

Here's how we understand the categorization.

  N(laptop) = N(all three) +N(laptop & tablet) +N(laptop & desktop) +N(laptop only)

  N(tablet) = N(all three) +N(laptop & tablet) +N(desktop & tablet) +N(tablet only)

  N(desktop) = N(all three) +N(laptop & desktop) +N(desktop & tablet) +N(desktop only)

Then the sum N(laptop) +N(tablet) +N(desktop) is ...

  N(L) +N(T) +N(D) = 3N(ltd) +2N(lt) +2N(ld) +2N(td) +N(l) +N(t) +N(d)

where N(L) = number owning a laptop, and N(l) = number owning a laptop only.

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

for more search question point  

https://brainly.com/question/28162977

#SPJ8

Step-by-step explanation:

No, having only the y intercept gives us the c value in the quadratic equation.

The answer is :

Step-by-step explanation:

To write the equation of a parabola, you need the equation \(\bf{y=ax^2+bx+c}\). You need to know the values of a, b, and c in order to write the equation. So knowing only the y-intercept (0, 5) will not suffice. He knows where the parabola intersects the y-axis yet he isn't aware of the appearance of the parabola and how to draw it.

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

More can be learned about the mean of a data-set at brainly.com/question/1156334

#SPJ1

The value of the algebraic expression is:

a^2*b = -15 + 20i

Here we have the following expression:

a^2*b

And we want to use the values:

a = -1 + 2i

b = 5

Replacing these values in the expression we will get:

(-1 + 2i)^2*5

Expanding the  first part we get:

(-1 + 2i)*(-1 + 2i) = (-1)*(-1) + (-1)*(2i) + (2i)*(-1) + (2i)*(2i)

                        = 1 - 2i - 2i - 4

                        = -3 + 4i

Replacing that in the expression we get:

(-1 + 2i)^2*5 = (-3 + 4i)*5 = -3*5 + 4i*5 = -15 + 20i

Learn more about algebraic expressions:

https://brainly.com/question/4344214

#SPJ1

Hope this help!!!

Have a nice day!!!

The true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

From the given options, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

Let's analyze each statement:

Its leading coefficient is positive:

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.

It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.

If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.

None of the zeroes have even multiplicity:

The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.

In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.

The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.

Therefore, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

For similar question on polynomial function.  

https://brainly.com/question/31528136

#SPJ8

Answer:

Answer:

y = 1, I hope this helps, because I could barely find the answer myself

Step-by-step explanation:

N/A

The expected values of the raffle ticket for you are given as follows:

For the PTO, the expected values are given as follows:

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For you, the distribution is given as follows:

Hence the expected value for one ticket is given as follows:

E(X) = 62/280 - 4 x 279/280

E(X) = -$3.76.

For twelve tickets, the expected value is given as follows:

12 x -3.76 = -$45.12.

For the PTO, we use the inverse signals, as the distribution is the inverse, that is:

More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440

#SPJ1

From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.

A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.

The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.

A line is a collection of points that extends in two opposing directions and is endlessly long and thin.

From the given figure we observe that,

1. Two line segments are LA and EP.

2. Two rays are EC and AH.

3. Two lines are b and AP.

Learn more about ray here:

brainly.com/question/17491571

#SPJ1

Answer:  D.) The second difference is constant.

Step-by-step explanation:

The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.

Answer:

D.

Step-by-step explanation:

Answer:

- 1

Step-by-step explanation:

Mathematically, slope = (y2 - y1)/(x2 - x1)

Here,

(x1, y1) = (-3, 4) ; (x2, y2) = (2, - 1) or vice versa

Slope = (-1 - 4)/(2 - (-3))

= -5/5

= - 1

The value of the missing part of the triangle such as PR and ST = 8 and 5 respectively

Triangle PQS is congruent with triangle PRS

Therefore, PQ = PR

That is;

PQ = 8

PR = 2x

8 = 2x

X = 8/2 = 4

PR = 2(4) = 8

For ST;

Triangle VST = VUT

That is, TU = ST

ST = 5z

TU = 2z+3

5z = 2z+3

5z+2z = 3

z= 3/3 = 1

ST = 5(1) = 5

Learn more about triangles here:

https://brainly.com/question/28470545

#SPJ1

The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

Answer:

B.

Step-by-step explanation: