Water is flowing into a tank at a rate of R(t) where t is measured in seconds. Is there ever a time where the R'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem. t R(t) 0 70 1 72 2 78 3 80 4 83 5 78 6 82

The solutions to the equation word problems are as follows;

1) Amount jane will have is 50 + 2d

2) Amount Elis will have = 24 + 6d

3) The equation is; 50 + 2d = 24 + 6d

4) Amount each has saved = $63

We are given that;

Amount Jane has = $50

Amount Elis has = $24

Amount saved by Jane each day = $2

Amount saved by Elis each day = $6

1) After d days of saving, amount jane will have is;

A = 50 + 2d

2) After d days of saving, amount Elis will have is;

A = 24 + 6d

3) The equation that will be used to show when Joan and Elis would have saved same amount is;

50 + 2d = 24 + 6d

4) 50 + 2d = 24 + 6d

26 = 4d

d = 26/4

d = 6.5 days

Amount each has saved = 50 + 2(6.5) = $63

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Answer:

To graph the relationship between the pool's water level and time, we can start by creating a table of values for the water level at different times. Here is an example of such a table:

Time (minutes) Water Level (centimeters)

0 0

1 6

2 12

3 18

4 24

5 30

6 36

7 42

8 48

9 54

10 60

11 66

12 72

13 78

14 84

15 90

16 96

17 102

18 108

19 114

20 120

We can then plot these values on a graph, with the time on the x-axis and the water level on the y-axis. The resulting graph would be a straight line that slopes upwards, starting at the origin (0, 0) and ending at (20, 120).

The graph shows that the water level in the pool increases linearly with time. The slope of the line represents the rate at which the water level is increasing, which in this case is 6 centimeters per minute.

Step-by-step explanation:

If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.

To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:

y = -x + 4

f(x) = x^2 - 5x + a

Then, we can substitute the equation for the function into the equation for the line:

-x + 4 = x^2 - 5x + a

We can then solve this equation for a by moving all the terms to one side:

-x + 4 - x^2 + 5x = a

-x^2 + 6x - 4 = a

We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.

The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:

2x - 5 = -1

2x = -6

x = -3

Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:

f(-3) = (-3)^2 - 5(-3) + a

f(-3) = 9 + 15 + a

f(-3) = 24 + a

Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:

y = -(-3) + 4

y = 3 + 4

y = 7

Substituting this back into the equation for the function, we get:

f(-3) = 24 + a = 7

a = 7 - 24

a = -17

Therefore, the value of a is -17.

what do you mean by tangent?

A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.

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An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.

What is Parallel lines?

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Parallel lines will have the same slope but different y-intercepts  so again we can  use the coordinates to determine the y intercept of the new equation.

So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.

12 = 4(9) + b

12 = 36 + b

b = -24

The equation will be y= 4x -24.

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The equation of the line is (b) y = 2.25x - 6.25

From the question, we have the following parameters that can be used in our computation:

Points = (3, 1/2) and (5, 5)

A linear equation can be represented as

y = mx + c

Substitute the known values in the above equation, so, we have the following representation

1/2 = 3m + c

5 = 5m + c

Subtract the equations

2m = 4.5

Divide by 2

m = 2.25

Substitute m = 2.25 in 5 = 5m + c

5 = 5 * 2.25 + c

So, we have

c = 5 - 5 * 2.25

Evaluate

c = -6.25

Recall that

y = mx + c

So, we have

y = 2.25x - 6.25

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Complete question

Select the equation for the line crossing the points (3,1/2) and (5,5).​

(a) y = 5x + 2

(b) y = 2.25x - 6.25

(c) y = 2.25x + 6.25

(d) y = -5x - 2

The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.

Let M = speed of the motorcycle.

Hence, speed of the car = 2M - 30.

Distance covered = Time taken x Speed.

Hence in 2 hours,

Distance covered by motorcycle = 2M

Distance covered by car = 2(2M-30).

Given, the car is 20 miles ahead of the motorcycle.

Hence,

2(2M-30) = 2M + 20

4M-60 = 2M + 20

2M = 80

M = 40

2M-30 = 2(40)-30 = 80-30 = 50

Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.

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A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours

Given,

Chance Product is designed to function for 10,000 hours

of failure is 3%

To find,

Average number of failures per hour

MTTF

Solution,

Average number of failures per hour = Chance of failure/Total hours of function

= 3%/10000

= 0.03/10000

= 0.000003

MTTF = 1/Average number of failures per hour

= 1/0.000003

= 333,333 hours

The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.

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The simplest form of  [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is found to be  8.66025403784 .

A fraction is  in  its  simplest form   when   the    numerator   and   the denominator have  no common factors besides one.

Reducing equation is a method of rewriting the equation in a simpler form. Certain equations in mathematics are not in the form of linear equations but they can be put in the form of linear equations by performing some mathematical operations on them. After reduction of these equations in linear form they can be solved and the value of unknown can be calculated easily.

Given the equation is;

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

Now solving it ,

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

By adding this we get,

[tex]5\sqrt{3}[/tex]  (∵ [tex]\sqrt{3}[/tex] is common in both )

= 8.66025403784

The decimal (or) simplified value of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is  8.66025403784.

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Answer:

(A) 19 times, 16 people.

Step-by-step explanation:

There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.

The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.

Since the Caterpillar cannot run a fraction of a time, it must run 19 times.

There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.

Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.

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The Ancient Egyptians were the first to invent a dish close to what we know as a pie today. They had a honey filling covered in a crusty cake made from oats,

And cost of one pumpkin pie = $8

Let the cost of one apple pie be $x

And cost of one pumpkin pie be $ y.

According to given problem,

For Lisa :  sold 8 apple pies and 4 pumpkin pies for a total of $80

8x + 4y = 80   ------------(1)

For Shreya :  sold 8 apple pies and 3 pumpkin pies for a total of $72

8x + 3y = 72    ---------------(2)

Solving equation (1) and (2), to get x and y.

Subtract equation (2) from equation (1)

i.e 8x + 4y - (8x +3y) = 80 - 72

or 8x - 8x + 4y - 3y = 8

or  y = 8

And x = 6   { 8x + 4×8 = 80   or x = (80 - 32)/8  = 48/8 = 6 }

Hence, the cost of one apple pie = x = $6

And cost of one pumpkin pie = y =$8

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Answer:

its d I did the test hope its helps

Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Step-by-step explanation:

First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".

We can set up the following equation: 3V + 4T = 85

Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.

We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42

Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.

We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.

For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.

If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15

Since V + T = 25, this means that T = 25 - 15 = 10

Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.

The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.

Hence, The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.

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The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5

From the question, we have the following parameters that can be used in our computation:

x^4 – 3x^3 – 7x + 1 ÷ x + 2

Rewrite as

x⁴ – 3x³ – 7x + 1 ÷ x + 2

This means that

Divisor = x + 2

Dividend = x⁴ – 3x³ – 7x + 1

Using the synthetic division, we have the following setup

-2 |    1     -3    -7     1

Bring down the first factor

-2 |    1     -3    -7     1

        1

Multiply by -2

-2 |    1     -3    -7     1

              -2

        1

Repeat the above steps as follows

So, we have

-2 |    1     -3    -7     1

              -2    10    -6

        1      -5    3    5

The last number represents the remainder of the division

This means that

Remainder = 5

Quotient = x³ - 5x² + 3x

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An isosceles triangular prism, its surface area becomes: 568 feet²

The faces of a polyhedron called an isosceles triangular prism are made up of polygons. It has six edges, five faces, and five vertices. Isosceles triangles make up the two portions at the base that face each other and rectangles make up the vertical faces of the five faces.

where the isosceles triangle's base has equal sides measured in "a" units, each triangle's base measured in "b" units, the triangle's height measured in "h" units, and the length of the congruent rectangles measured in "l" units.

The surface area of an isosceles triangular prism is:

Surface area = (b × h) + (2× l × a) + (l × b)

here, b = the base of each of the triangle = 16 feet

h = the height of the triangle = 18 feet

l = length of the congruent rectangles = 10 feet

a = isosceles triangle in the base have the equal sides be "a" units = 6 feet

Now, Surface area = (16 × 18) + (2 × 10 × 6) + (10 × 16)

or, Surface area = 568 feet²

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The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth

Multiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product

Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures

4 1/10 * -4 * 5/10

solving the equation

= 4 1/10 * -4 * 5/10

= 41/10 * -4 * 5/10

= -41/5

= -8 1/5

The product of the multiplication is negative 8 and one fifth

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The angle of the elevation comes to be 41.94 degrees.

The angle of elevation is the angle that is to be formed between the horizontal line and the given line of sight. If the line of sight is upward from the given horizontal line, then the angle formed is an angle of the elevation.

The most crucial area of mathematics is trigonometry. Combining the Greek "Trigonon" and "Metron," which respectively mean "triangle" and "measure," creates the word "trigonometry." It is the examination of the relationship between a right-angled triangle's sides and angles. By employing formulas and identities based on this relationship, it is thus possible to determine the measure of a right-angled triangle's unknown dimensions.

As in the case of right angled Triangle

From Trigonometry,

tan (α) =  [tex]\frac{124}{138}[/tex]

α = arctan(  [tex]\frac{124}{138}[/tex] )

α = 41.94 degrees

and in radians = 0.732

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If Tommy is flying his kite one afternoon and notices that he has let out

the entire 130 ft of string.  The height , to the nearest foot, is his kite at this time is : 144 ft.

Given data:

String = 130 ft

Angle =  48°

Let h represent the height

Hence,

Tan48° = h/130

h= 130 tan48°

h = 130 (1.11061251483)

h = 144 ft

Therefore we can conclude that the height is 144ft.

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Answer:The Flemish giant rabbit weighs 32 pounds.

Step-by-step explanation:

Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:

P' = P ← 6 ↓ 2

Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.

With the Application of Arithmetic operators the value of given equation is 492.

what is Arithmetic operators?

an operator that works with groups and numbers in arithmetic. The prefix and the binary plus (+) and minus (-) symbols are the only arithmetic operators in AHDL that are supported for Boolean expressions.

solution:

sub  k =8,j=2 in equation k^3-4j = 12

Therefore, (8)^3 - 4 (2) = 12

                  512 - 8 - 12 = 0

492 is the value.

Therefore the value of given equation is 492

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Complete Question:
What Is The Answer
k3 - 4j +12, when k=8, j=2​

Answer: pls show list of equations

Step-by-step explanation:

The exponent [tex]3^{21}[/tex] is 9 times greater than the exponent [tex]3^{19}[/tex]

What are Exponents?

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.

Solution:

To solve this type of question all we need to know are the Rules of Exponents with their help any question of this type can be solved

Since we are required to find the number of times the value os greater so we will divide the numbers

3^21 / 3^19

By rule of exponents if a^b/a^c then we can write it as a^(b-c)

Similarly 3^21 / 3^19 = 3^(21 - 19) = 3^2 = 9

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Answer:

Step-by-step explanation:

Answer:

-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.

Step-by-step explanation:

Using slope-intercept form, the slope and y-intercept of the equation are 1 and - 7 respectively

The slope-intercept formula is often used to calculate or identify the slope, the y-intercept, the x-intercept, or the equation of a straight line in the equation.

The slope of the line is defined as the rate of change of the y - axis to the change in the x - axis.

The formula is represented as;

m = Δy / Δx

where Δ represent the change

The y-intercept of a line is the point at which the line touches the y-axis of the graph.

With these information, we can write a slope-intercept form of a straight line which is given as;

y = mx + c

In the given question;

x - 3 = 4

Let's collect like terms

x - 3 - 4 = x - 7

The equation can be rewritten as y = x - 7

In this case, the slope is 1 and the y-intercept is - 7

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The measure of the angle x would be 30.26°.

What are inverse trigonometric functions?

Inverse trigonometric functions are functions that "undo" the action of the trigonometric functions. They allow us to find the angles of a right triangle given the values of the sides, or to find the values of the sides given the angles.

In the given triangle, by using sine ratio we can write

        sin(x°) = BC/AC

       [tex]sin(x^o)=39/74\\\\x^o=sin^{-1} \frac{39}{74}\\\\x^o=sin^{-1}{0.5270}\\\\x^o=30.26^o[/tex]

Hence, the measure of the angle x would be 30.26°.

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y = 2.115 + 0.842

= 2.957

no explanation

Answer:

Step-by-step explanation:

Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.

Answer:

Step-by-step explanation:

Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.