How many feet did Mike descend (go down) in the last three hours of his hike?

The instantaneous rate of change of the area A  is A) 120π m. To find the instantaneous rate of change of the area A of the circular oil spill with respect to its radius r, we need to use the formula for the area of a circle and differentiate it with respect to r.

1. The formula for the area of a circle is A = πr^2.
2. Differentiate the formula with respect to r: dA/dr = 2πr.
3. Now, plug in r = 60 m to find the instantaneous rate of change of the area: dA/dr = 2π(60) = 120π m.

The answer is A) 120π m. This represents the rate at which the area of the circular oil spill is increasing when its radius is 60 meters.

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Answer:

381 in^3

Step-by-step explanation:

The volume of the green block is V1 = length(width)(height), or

                                                         V1 = (16 in)(7 in)(3 in) = 336 in^3, and

the volume of the red triangular prism is V2 = (1/2)(3 in)(5 in)(6 in) =

                                                           V2 = 45 in^3

So the total volume is the sum of these two results:  381 in^3

Step-by-step explanation:

2.5 hours = 150 min

1/3 of 150 is 50 min, which means she spent 50 min on her history project = 100 min leftover

3/5 of 100 min is 60 min (1 hour) = 40 min leftover

She spent 40 min writing her essay

hope this helps <3

Answer: 40 min or 2/3 an hour

Step-by-step explanation: :)

The equation which represents 3 x 3/4 as a unit fraction is; 3 × 3/4 = 9 × 1/4.

A unit fraction by definition is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

On this note, the given expression when expressed as a unit fraction is;

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The value of the angle ∠ECF=37

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: Two triangles DCE and ACB with C as the common vertex

Now in triangle ACB we have

∠A=53 and ∠B=45

Thus ∠A=180-53-45

              =82°

Now in triangle GCB we have ∠G=90

Thus ∠GCB=180-90-45

                   =45

And in triangle GCA we have

∠GCA= 180-90-53

          =37

But ∠ECF=∠GCA as they are vertically opposite angles.

Hence, ∠ECF=37

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A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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The explicit equation for the function is: f(x) = 8(1.5)^(x - 1)

Given that we have the table of values

x f(x)

0 8

1 12

2 18

3 27

We can see that the function is a geometric function

So, the common ratio is

r = 12/8

r = 1.5

The explicit equation for the function is then calculated as

f(x) = ar^(x - 1)

So, we have

f(x) = 8(1.5)^(x - 1)

Hence, the explicit function is f(x) = 8(1.5)^(x - 1)

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The length of the park not counting the path is 98 yards

The formula for determining the area of a rectangle is expressed as;

Area = lw

Where;

From the information given, we have that;

The dimensions of the path having a width of 1 yard path around it are

(L+2) x (W+2)

We have to add 2 to the length and width because there will be a 1 yard path on all 4 sides of the rectangle

Given that the area is 4200 square yards; the original width is 40 yards

Now, substitute the values into the formula, we have;

Since Area = LW

4200 = (L+2)(W+2)

4200 = (L+2)(40+2)

Add the values

4200 = (L+2)(42)

expand the bracket

4200 = 42L + 84

collect like terms

4116 = 42L

Make 'L' the subject of formula

L = 98 yards

Hence, the length is 98 yards

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Answer:

98 yards

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

expand the brackets

2x² - x + 10x -5 = 3x + 15

combine like terms

2x² + 9x  - 5 = 3x + 15

2x² + 6x - 20 = 0

divide through by 2

x² + 3x - 10 = 0

factorise

determine factors of -10x² that would add up to 3x

they are 5x - 2x

(x² -2x) (5x - 10)

x(x - 2) +5(x-2)

x + 5 = 0

x = -5

x - 2 = 0

x = 2

Answer:

simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

Step-by-step explanation:

derivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

limit(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

taylor_series_expansion(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

antiderivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

integral(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

equation_solver(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4))=0)

simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

Answer:

B.

Step-by-step explanation:

Exponential Functions

Answer:

7 jarras costarán 14 $

Step-by-step explanation:

Si 3 cubiertos cuestan  7.20 $

1 cubierto cuesta     7.20/3  =  2.40 $

y 5 cubiertos cuestan    5* 2.40   =  12 $

que también cuestan 6 jarras  =  12 $

Luego 1 jarra cuesta  12/6  =  2  $

Por lo que 7 jarras costarán:  7 * 2  =  14 $

Answer: 51

Step-by-step explanation:

We will use the Order of Operations, sometimes known as PEMDAS.

    Given:

5x² - x + 9

    Plug in the value of 3:

5(3)² - (3) + 9

    To the power of 2:

5(9) - 3 + 9

    Multiply:

45 - 3 + 9

   Subtract:

42 + 9

    Add:

51

Answer:

Option (2)

Step-by-step explanation:

Given inequality is,

\(-\frac{1}{2}x\geq 4\)

⇒ \(\frac{1}{2}x\leq -4\)

⇒ x ≤ -8

When we plot this inequality on a number line,

An arrow starting with a solid point from x = -8 and arrow directing towards negative numbers will represent the given inequality.

Option (2) will be the answer.

Answer:

\( - \frac{1}{2} x \geqslant 4 \\ - x \geqslant 2 \times 4 \\ - x \geqslant 8 \\ \boxed{\ x \leqslant - 8}\)

x→{-∞,-8]

Number line :---

Arrow which represents solid sphere directed from (-8) moving towards left (-∞) will be the answer

1. Converting 8-bit binary expansion to a decimal expansion: The binary number 1100 0110 can be broken down into 2 binary numbers: 1100 and 0110. Then, each of these binary numbers can be converted to decimal separately, and combined to get the decimal expansion. 1100 = 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 0 × 2^0 = 12, 0110 = 0 × 2^3 + 1 × 2^2 + 1 × 2^1 + 0 × 2^0 = 6.

Therefore, 1100 0110 in binary is equal to 12 + 6 = 18 in decimal. 2. Converting decimal expansion to 8-bit binary expansion: We can use the division-by-2 method to convert decimal to binary. Dividing 109 by 2, we get: 109 ÷ 2 = 54 remainder 1 Then, we divide 54 by 2: 54 ÷ 2 = 27 remainder 0 Continuing with this process, we get the binary number as follows: 109 = 0110 1101.

We need to add 3 leading zeros to make it 8-bit binary number: 0001 1011 Therefore, 109 in decimal is equal to 0001 1011 in 8-bit binary.3. Converting hexadecimal expansion to octal expansion: To convert hexadecimal to octal, we need to convert hexadecimal to binary first, and then binary to octal.

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Answer:

x = 1

y = 1

Step-by-step explanation:

Given:

Add up the two equations side-by-side, this will cancel y/b and 1/b:

Subtract the  two equations side-by-side, this will cancel x/a and 1/a:

Answer:

x = 1, y = 1

Step-by-step explanation:

\( \frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b} .....(1) \\ \frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b} .....(2) \\ \\ let \: \: \frac{1}{a} = m, \:\:\&\: \: \frac{1}{b} = n \\ so \: equatin \: (1) \: reduces \: to: \: \\ \\ so \: equatin \: (1) \: reduces \: to: \: \\ mx + ny = m + n....(3)\\ and \: equatin \: (2) \: reduces \: to: \: \\ mx - ny = m - n....(4) \\ adding \: equations \: (3) \: (4) \\ mx + ny = m + n \\ mx - ny = m - n \\ - - - - - - - - - - \\ 2mx = 2m \\ x = \frac{2m}{2m} \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m \times 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = \frac{n}{n} \\ \huge \purple{ \boxed{y = 1}}\)

Answer:

he equation given in the exercise  is:

Observe that highest exponent of the variable "x" is 2. Therefore, it is a Quadratic equation.

Therefore, making an exponent 1 instead of the exponent 2 would turn the given equation into a Linear function.

Step-by-step explanation:

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The equation of the tangent plane to f(x, y) = x^2 - 2xy + 3y^2, with slopes 2 in the positive x direction and 2 in the positive y direction, is 2x + 4y - 8 = 0.

To locate the equation of the tangent airplane to the floor described with the aid of the feature f(x, y) = \(x^2 - 2xy + 3y^2\), we need to decide the gradient vector and consider it at a given point.

The gradient vector will grant the ordinary vector to the tangent plane, and by way of the use of the slope information, we can discover the equation of the plane.

Calculate the partial derivatives of the feature with recognize to x and y:

f_x = 2x - 2y

f_y = -2x + 6y

Set up a device of equations the use of the given slope information:

f_x = 2

f_y = 2

Solve the machine of equations to discover the factor where the slopes are satisfied:

2x - 2y = 2 --> x - y = 1 --> x = y + 1

-2x + 6y = 2 --> -x + 3y = 1 --> -x = 1 - 3y --> x = 3y - 1

Setting the two expressions for x equal to every other:

y + 1 = 3y - 1

2 = 2y

y = 1

Substitute y = 1 into both expression for x:

x = 1 + 1

x = 2

Therefore, the factor the place the slopes are comfy is (2, 1).

Evaluate the gradient vector at the factor (2, 1):

grad(f) = (f_x, f_y) = (2x - 2y, -2x + 6y)

= (2(2) - 2(1), -2(2) + 6(1))

= (2, 4)

The ordinary vector to the tangent airplane is the gradient vector (2, 4).

Using the point-normal structure of the equation for a plane, the equation of the tangent airplane is:

2(x - 2) + 4(y - 1) + d = 0

To decide the price of d, alternative the coordinates of the factor (2, 1):

2(2 - 2) + 4(1 - 1) + d = 0

0 + 0 + d = 0

d = 0

The equation of the tangent airplane is:

2(x - 2) + 4(y - 1) = 0

Simplifying the equation, we have:

2x - 4 + 4y - 4 = 0

2x + 4y - 8 = 8

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Answer: it would be 6

Step-by-step explanation:

The length DL of the rhombus is 24 units

The figure that completes the question is added as an attachment

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

DA = 4x

AL = 5x - 3

This means that

DA = A:

So, we have

5x - 3 = 4x

Evaluate the like terms

x = 3

So, we have

DL = 2 * DA

This gives

DL = 2 * 4 * 3

Evaluate

DL = 24

Hence, the length is 24 units

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Special angles in geometry are specific angle measures that have unique properties and are often encountered in geometric problems:

(1) Right angle      (2) Acute angle        (3)  Obtuse angle         (4)Straight angle              (5)Reflex angle

(6) Complementary angles          (7)Complementary angles

In geometry, special angles refer to specific angles that have special properties or characteristics. These angles include right angles, acute angles, and obtuse angles. A right angle is an angle that measures exactly 90 degrees, while an acute angle is an angle that measures less than 90 degrees. An obtuse angle, on the other hand, measures more than 90 degrees but less than 180 degrees. These angles are important in geometry as they form the foundation for many geometric shapes and concepts. Understanding the properties and characteristics of these special angles is crucial for solving geometry problems and constructing geometric figures accurately.

Special angles in geometry are specific angle measures that have unique properties and are often encountered in geometric problems. These angles include:

1. Right angle: A right angle is an angle that measures exactly 90 degrees. It is formed when two lines intersect perpendicularly.

2. Acute angle: An acute angle is an angle that measures between 0 and 90 degrees. It is smaller than a right angle.

3. Obtuse angle: An obtuse angle is an angle that measures between 90 and 180 degrees. It is larger than a right angle.

4. Straight angle: A straight angle is an angle that measures exactly 180 degrees. It is formed when two lines intersect in a straight line.

5. Reflex angle: A reflex angle is an angle that measures between 180 and 360 degrees. It is larger than a straight angle.

6. Complementary angles: Two angles are complementary if their sum is equal to 90 degrees.

7. Supplementary angles: Two angles are supplementary if their sum is equal to 180 degrees.

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Your midpoint is (6,4). Hope this helps! Please mark brainliest:) Have a great day.

Answer:

4/50 = 8%

Step-by-step explanation:

The bus is 4 blocks east of the hotel.

For given question

A sightseeing bus picks up a group of tourists at a hotel. It then travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south, to determine where the bus is in relation to the hotel, the following calculation must be carried out:

North and South are antagonistic, the same as East and West  

2 N + 2 E - 1S + 2E - 1S

2 N - 2S = 0

2E + 2 E = 4E

Therefore, the bus is 4 blocks east of the hotel.

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The probability that the coin is a one-sided coin after one flip that outcomes in tails is around 10.9%.

Bayes' theorem is a mathematical formula that assists us with refreshing our convictions about the probability of an occasion happening in view of new information or proof. It includes the earlier probability, which is our underlying conviction about the probability of an occasion, and the probability of the proof given that the occasion has happened. By consolidating these two snippets of information, Bayes' theorem permits us to work out the refreshed or back probability of the occasion happening.

After one flip that outcomes in tails, the probability that the coin is a one-sided coin can be tracked down utilizing Bayes' theorem:

P(biased coin | tails) = P(tails | one-sided coin) * P(biased coin)/P(tails)

P(tails | one-sided coin) = 3/5 (given)

P(biased coin) = 0.1 (given)

P(tails) = P(tails | fair coin) * P(fair coin) + P(tails | one-sided coin) * P(biased coin)

= 1/2 * 0.9 + 3/5 * 0.1

= 0.55

Along these lines,

P(biased coin | tails) = (3/5 * 0.1)/0.55

= 0.109 (around)

Consequently, the probability that the coin is a one-sided coin after one flip that outcomes in tails is around 10.9%.

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