The owner of Sandy’s Boat House advertises the cost to rent a canoe is $15 per hour for trips on the Red Cedar River. He is also willing to adjust the $15 per hour if a customer rents for only a part of an hour.

The manager suggests another deal for customers. She uses the equation cmanager = 0.15t + 2.50 to find the charge c in dollars for renting a canoe for t minutes.



Which option would you choose, the manager’s equation or the owner’s cost of $15 per hour? Explain.

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.

Answer:

Based on triangles of angles: 45-45-90:

chord/2=(radius√2)/2

chord/2=(10√2)/2

chord/2=5√2

chord=10√2

Step-by-step explanation:

Hope it helps ;)

Answer:

80 inches

Step-by-step explanation:

12 x 7=34

23 x 2=46

34+46=80 inches

The nail protrudes 5\(\frac{9}{15}\) inches from the other side of the board having a thickness of  2\(\frac{2}{5}\) inches

Given that A nail 6 \(\frac{1}{3}\) inches long is driven into a board 2 \(\frac{2}{5}\) inches thick and asked to find out how much the nail protrudes into the board.

To calculate the nail protrudes, need to subtract the length of the nail and the thickness of the board.

Length of nail protrudes= 6 \(\frac{1}{3}\) - 6 \(\frac{1}{3}\)

Length of nail protrudes=\(\frac{19}{3}\)-\(\frac{12}{5}\)

Length of nail protrudes=\(\frac{59}{15}\)

Length of nail protrudes= 5\(\frac{9}{15}\) .

Therefore,The nail protrudes 5\(\frac{9}{15}\) inches from the other side of the board having a thickness of  2\(\frac{2}{5}\) inches

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Alexa has 10/36, Gayle 16/36, and Mei 10/36 respectively. Due to Gayle's comparatively enhanced likelihood of claiming the post of captain, the overall system is unfair.

This approach of decision-making is adversely biased since the probabilities of each individual's choice as captain are not equivalent.

Through cogitating the potential outcomes for all three contestants--Alexa, Gayle and Mei--we can establish that due to the number of combinations augmenting each sum, their respective ranges possess different frequencies.

Whilst two dice have a total of 36 possible outcomes upon being thrown, enumerating their extent yields:

Alexa (sum of 2 through 5):

2: (1, 1) -> just one combination

3: (1, 2), (2, 1) -> two combinations

4: (1, 3), (2, 2), (3, 1) -> three combos

5: (1, 4), (2, 3), (3, 2), (4, 1) -> four combinations

Consequently, Alexa's total combinations amount to 10.

Contrastingly, Gayle (sum 6 through 8) obtains 5+6+5 = 16 combinations whereas Mei (sum 9 through 12) collects 4+3+2+1 = 10 combinations in total.

With this knowledge, deducing the affinities for each contestant comes with ease; Alexa has 10/36, Gayle 16/36, and Mei 10/36 respectively. Due to Gayle's comparatively enhanced likelihood of claiming the post of captain, the overall system is unfair.

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The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).

To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.

1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).

Therefore, 3 yards is equal to 3 * 36 = 108 inches.

Now, we can compare 108 inches to 3 yards 16 inches.

108 inches is equal to 3 yards, so it matches the given length.

To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.

Therefore, 3 yards 16 inches is equivalent to:

3 yards

108 inches

3 yards 0.44 yards (or approximately 3.44 yards)

108 inches 0.44 yards (or approximately 108.44 inches)

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Answer:

The surface area of the box increase by 0.2P (the perimeter of the base multiplied by 0.2)

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

If the height is increased by 0.2

then

The surface area of the box increase by 0.2P (the perimeter of the base multiplied by 0.2)

See attachment for the graph of  4 > |x + 1| + 2

The absolute value inequality is given as:

4 > |x + 1| + 2

Subtract 2 from both sides of the absolute value inequality.

So, we have

2 > |x + 1|

Rewrite as

|x + 1| < 2

So, we plot the graph of  |x + 1| < 2 to represent 4 > |x + 1| + 2

See attachment for the graph

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Answer:

A) (1 s, 2.3 s)

B) (-4 m/s², 3.8 m/s²)

Step-by-step explanation:

The car's position which is the distance is given by the equation;

s(t) = t³ - 5t² + 7t

A) Velocity is the first derivative of the distance. Thus;

v(t) = ds/dt = 3t² - 10t + 7

At v = 0, we have;

3t² - 10t + 7 = 0

Using quadratic formula, we have;

t = 1 and t = 2.3

Thus, time at velocity of 0 is t = (1 s, 2.3 s)

B) acceleration is the derivative of the velocity. Thus;

a(t) = dV/dt = 6t - 10

At velocity of 0, we got t = 1 and t = 2.3

Thus;

a(1) = 6(1) - 10 = -4 m/s²

a(2.3) = 6(2.3) - 10 = 3.8 m/s

Thus, a(t) at v = 0 gives; (-4 m/s², 3.8 m/s²)

Answer:

250÷50=3 because I have a great day and I will be in the 3 1 4 a few days ago a friend of ours was the only thing

Step-by-step explanation:

yes maybe no more options visit in the future please reply with your family

Answer:

ok buddy

Step-by-step explanation:

Answer:

y= 2x -6

Step-by-step explanation:

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

To find the equation of a line, two information are needed:

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

Additional:

For a similar question on slope-intercept form, do check out the following!

Step-by-step explanation:

(x-2)^2 + (y-9)^2   = r^2

this is of the form fora circle with center  h,k and radius r

(x-h)^2 + (y-k)^2 = r^2

for the equation given   center =   2, 9    and radius = r

Answer:

56

Step-by-step explanation:

Answer:

x = 2

AB = 14

DC = 14

Step-by-step explanation:

If opposite sides are congruent, then:

AB = DC

AB = 3x + 8

DC = x + 12

Thus:

3x + 8 = x + 12

Collect like terms

3x - x = -8 + 12

2x = 4

Divide both sides by 2

x = 2

AB = 3x + 8

Plug in the value of x

AB = 3(2) + 8 = 14

DC = x + 12

Plug in the value of x

DC = 2 + 12 = 14

Answer:

Step-by-step explanation:

Consider the angle of depression is same as the angle between horizontal line on the ground and the direct line from the plane to the airport (alternate interior angles).

Use tangent to find the missing length.

tan = opposite / adjacent

The distance is 4744  ft

Answer:

Money raised by Mr. Simmons class = $ 45.89

Answer:

Where is the picture?

Step-by-step explanation:

Have a great day

Answer: The square root of 283 lies between the square roots of 256 and 324, which are 16 and 18, respectively. Therefore, an estimate for the square root of 283 is between 16 and 18, and we can round to the nearest whole number, which is 16.

Step-by-step explanation:

Answer:

1 2/6 of pizza

Step-by-step explanation:

first lets make 1/2 equal to 5/6 so at the denomonator so lets times 1/2 by 3 to get 3/6 now lets add that together now we have 3/6 + 5/6 and the sum of that is 1 2/6 so 1 2/6 is your answer

Given:

Let B represent number of hours Brain travelled

Let A represent number of hours Annie travelled.

Since number of hours Annie travelled is 3 time and 2 that of Brain and they travelled for a total of 8 hours, we have:

Annie travelled = 3(B + 2)

Total number of hours travelled = 3(B + 2) + B = 12

Solve for B:

3(B + 2) + B = 12

3B + 6 + B = 12

4B + 6 = 12

4B = 12 - 6

4B = 6

Brain travelled for 1½ hours

LEt's find the number of hours annie travelled:

A = 3(B + 2)

Substitute B for 1½

A = 3(1½ + 2)

= 4.5 + 6 = 10.5 = 10½

Therefore Annie travelled for 10½ hours.

Brain ravelled for 1½ hours

Annie travelled for 10½ hours.

We have:

Where h represents number of hours Brain travelled

So,

Here we have the following points:

From the drawing above, you can notice that the translation from A to A' is clearly given by moving the point 1 unit to the left and 7 units up.

Answer: it should be 8

Answer:

11

Step-by-step explanation:

Substituting the values of x, y, and z into the expression, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.

Answer:

11

Step-by-step explanation:

if x = 2, y = 3, and z = 4.

2x²-y + 2(z-1)

Substituting the given values of x, y, and z, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.

BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).

Negative value has least value.

Answer:

Y=-2/-7(x) + 6

may I get branliest

Since DA is the diameter the formed angle equals 180

since DZC=2x

then

since x= 11

then the measure of the angle CZB is given by

measure of the angle CZB is 73°

Correct answer option D

73°

The unknown measures are from right angle triangle is

KM = 10.68

∠m = 35 and ∠k = 55

Given that

KL =6.2

LM =8.7

KM = x

The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

The triangle that is presented is a right angle triangle.

\(KM^{2}\) = \(LM^{2}\) + \(KL^{2}\)

KM = \(\sqrt{(8.7)^{2} + (6.2)^{2} }\)

KM = \(\sqrt{114.13}\)

KM = 10.68

Now figure out the angles.

∠m = sinm

     = P/H

     =6.2/10.2

∠m = 35

Again,

∠k = sink

     =P/H

    = 8.7/10.6

∠k = 55

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Answer:

3

Step-by-step explanation:

You solve the inner first, then move to the outer.

Let's look at g(3) first. It is stated in the problem that g(3) = 2.

We then use this value for f(x). It is stated in the problem that f(2) = 3.

The answer is 3.