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The rate is the water level decreasing when the radius of the water's surface is r = 2cm is 0.08 cm/sec or dh/dt = - 0.08 cm/sec.

We have given that,

Water is dripping from an inverted cone.

height , h = 12 cm

diameter , d = 12 cm

so, radius, r = 6 cm

rate , dV/dt = - 1 cm³/sec

At any point, the portion of the cone that is filled will have the ratio of radius/height = 6/12 = 1/2. Put another way, h = 2r.

we have to calculate the rate is the water level decreasing , dh/dt when radius of the water's surface is r = 2 cm .

Volume of cone , V = 1/3 π (r)²h = 1/3π (h/2)²h

plugging all known values,

V = 1/3 ( h³/4)π

differentiating with respect to h we get,

dV/dh = 1/3(3h²)π/4 , h = 12

= 1/12(3× 4r²)π ( from r = 2 cm)

= 4π cm²

but we have required, dh/dt = dV/dt × dh/dV

= - 1 cm³/sec × 1/4π cm²

= - 1/4π cm/sec

= - 0.0792 ~ 0.08 cm/sec

Hence, the required value is - 0.08 cm/sec.

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Complete question:

Water is dripping from an inverted cone with a diameter of 12 cm and a height of 12 cm at a rate of 1 cm3 /sec. At what rate is the water level decreasing when the radius of the water's surface is r = 2 cm?"

The measure of one angle is 1.56° and another angle is 88.64°.

Complementary angles are two angles whose combined angle is 90 degrees.

Let's consider the smaller angle as A and the larger angle as B.

Given that the two angles are complementary, then their sum is A+B = 90°.

The angle B is 20° more than and 44 times angle A. Then B = 44A+20°. Substituting this equation in the A+B = 90° equation, we get,

A+44A+20° = 90°

45A = 90°-20°

A = 70°/45

A = 1.56°

Substitute A = 1.56°in B = 44A+20°, we get,

B = 44(1.56°)+20°

B = 88.64°

The answers are 1.56° and 88.64°. The sum of these two angles gives 90.2°. By rounding off, we will get 90°.

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Both conditions must be met in order to ride: being at least five years old and being at least 36 inches tall. expression evaluates to true if a person can ride - (Age >= 5) && (Height > 36)

In order for a person to ride, two conditions must be true: they must be at least 5 years old and taller than 36 inches. In order to evaluate whether a person can ride, we can use the expression (Age >= 5) && (Height > 36). This expression evaluates to true if both conditions are true; if either one is false, then the expression will evaluate to false. For example, if a person is 4 years old and 40 inches tall, then the expression will evaluate to false because the first condition is false. On the other hand, if a person is 5 years old and 40 inches tall, then the expression will evaluate to true because both conditions are true.

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Answer:

Step-by-step explanation:

210x550=115500

115,500 divide 10,000=11.55?

Answer:

12/3=4

Step-by-step explanation:

You have 12 blocks in total, and 3 sections each. It is asking you how many blocks per section.

12 blocks in total/ 3 sections each = 4 blocks per section

When jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters , the collection of nickels and quarters totaled $2.60 then he find eight quarters.

Given that:

Let N be the number of nickels.

     Q be the number of quarters.

The value of one nickels N is 0.05N

The value of quarters Q = 0.25Q

Sum of total quarters is $ 2.60

  Total number of coins

N + Q = 20   , N = 20 - Q

0.05 N + 0.25 Q = 2.60

substitute n = 20 - Q , we get

0.05 (20 - Q) + 0.25 Q = 2.60

    1 - 0.05 Q + 0.25 Q = 2.60

                       1 + 0.2Q = 2.60

                           0.2 Q = 1.6

                                  Q = 1.6 / 0.2

                                  Q = 8

Therefore , Jim finds 8 quarters

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The probability that they all have different birthdays is 0.903 or 90.3%.

1. Calculate the number of days in a year.

There are 365 days in a year.

2. Calculate the number of possible combinations for 3 people.

There are 365 x 365 x 365 = 4,738,625 possible combinations for 3 people.

3. Calculate the number of combinations where all 3 people have different birthdays.

There are 365 x 364 x 363 = 4,324,320 combinations where all 3 people have different birthdays.

4. Calculate the probability.

The probability that they all have different birthdays is 4,324,320 / 4,738,625 = 0.903 or 90.3%.

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y=x/2 is equation for a tangent to the graph of y=arcsin(x/2) at the origin.

In order to fing the equation of tangent of any graph we need 2 things

 i . A point on the graph

 ii . Slope a line on that point

Given y=[tex]sin^-^1(\frac{x}{2} )[/tex]

put x=0

y = [tex]sin^-^1[/tex] (0)

=> y =0

so the graph passes through point (0,0)

now we have to find slope of the graph

slope = [tex]y^'[/tex] = [tex]\frac{d(y)}{dx}[/tex]

=> [tex]\frac{1}{\sqrt{4-x^2} }[/tex]

slope of line at point (0,0) is 1/2

so equation of line is y-0=1/2(x-0)

so the equation of tangent to the given graph is y=x/2

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Answer:

b = - [tex]\frac{a}{a-1}[/tex]

Step-by-step explanation:

a = [tex]\frac{b}{1+b}[/tex] ( multiply both sides by 1 + b to clear the fraction )

a(1 + b) = b ← distribute parenthesis on left side

a + ab = b ( subtract b from both sides )

a + ab - b = 0 ( subtract a from both sides )

ab - b = - a ← factor out b from each term on left side

b(a - 1) = - a ( divide both sides by a - 1 )

b = - [tex]\frac{a}{a-1}[/tex]

Answer:

10

Step-by-step explanation:

[tex]x + 5 = 15 \\ x + 5 - 5 = 15 - 5 \\ x = 10 [/tex]

Answer:

0.65

Step-by-step explanation:

The probability that we would get tails is 0.35

so the probability we will get heads is

1 – 0.35 = 0.65

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Answer:1

Step-by-step explanation: 6x2= 12. 12/4=3. 3/3 is 1.

Answer:

1

Step-by-step explanation:

We can see only multiply and divide here so we go from left to right

6x2/4/3

= 12/4/3

= 3/3

= 1

The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.

Here, we note the following

Let the person walking away from the elevator be X

Let the other person going up in the elevator be Y

Therefore after 15 seconds, their positions will be;

For X,  2 ft/sec × 15 s = 30 ft away from the elevator

For Y,  7 ft/sec × 15 s = 105 ft up in the elevator

At that instant, the distance between them is given as

d² = x² + y²

d=√ 30² +105² = 11925 ft²

d = √11925 ft²  = 109.202 ft

The rate of change of the distance between the two people, X and Y is given as

[tex]\frac{dd^2}{dt} =\frac{dx^2}{dt} +\frac{dy^2}{dt} \\Therefore,2d\frac{dd}{ydt} =2x\frac{dx}{dt} +2y\frac{dy}{dt} \\[/tex]

                (or)

[tex]d\frac{dd}{dt} =x\frac{dx}{dt} +y\frac{dy}{dt} \\[/tex]

Since dx/dt is given as 2ft/sec and dy/dt is 7ft/sec

Then [tex]d\frac{dd}{dt} =30*2+105*7=975\\\frac{dd}{dt} =\frac{795}{105*202} =7.28ft/sec[/tex]

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Answer:

Below

Step-by-step explanation:

27 = 3^3        and 9 = 3^2

3^3  * (3^2)^3x

3^3 * 3^6x

3^(3+6x)     so k = 3+6x

1. The total amount (future value) Marcus had at the end of the second year of investing $5,000 at 2.5% compounded annually was $5,253.13.

2. The minimum number of years Marcus must leave the $5,253.13 to be more than $10,000 is 11.3 years.

The future value is the compounded present value at an interest rate.

The future value can be derived from an online finance calculator as follows:

With the future value so determined, we can then compute the minimum time in years required for it to reach more than $10,000 at the simple interest rate.

Initial investment = $5,000

Interest rate = 2.5% compounded annually

Investment period = 2 years

N (# of periods) = 2

I/Y (Interest per year) = 2.5%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

FV = $5,253.13

Total Interest = $253.13

Principal = $5,253.13

Interest rate = 8% per annum

Future amount = $10,000

Time to reach the future amount = (Future Value/Principal - 1) ÷ Interest rate

= ($10,000/$5,253.13 - 1) ÷ 0.08

= 11.3 years

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Answer:

Below

Step-by-step explanation:

= sqt (45*10) = sqrt (450) = 15 sqrt 2

The expression √45 × √10 is simplified using the property of square roots to give an equivalent choice of 15√2

The product √45 × √10 can be simplified by using the property of square roots that states √(a × b) = √a × √b.

By application of this property, we have that:

√45 × √10 = √(45 × 10).

To simplify further, we find that 45 and 10 have a common factor of 5, and thus,

45 × 10 = 5 × (9 × 10)

45 × 10 = 5 × 90.

Now, we can rewrite √(45 × 10) as √(5 × 90).

Using the same property again, we obtain √5 × √90. Finally, we recognize that 90 can be factored into 9 × 10.

Thus;

√45 × √10 = √(2 × 9 × 25)

√45 × √10 = √2 × √225

√45 × √10 = √2 × 15

√45 × √10 = 15√2

Therefore, the expression√45 × √10 have an equivalent of 15√2

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The correct option for given situation is,

⇒ To demonstrate your professionalism, you should arrive for the appointment ''Right on time''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

You have a meeting with a potential client for your printing business.

And, To demonstrate your professionalism, you should arrive for the appointment.

Now, We know that;

The rule of business is,

To demonstrate your professionalism, you should arrive for the appointment on the right time.

Therefore, The correct option for given situation is,

⇒ Right on time

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The graph has a horizontal intercept at (1, 0)

The line x = 0 (the y-axis) is a vertical asymptote; as x→0+,y→∞

The graph is decreasing if 0 < b < 1.

The domain of the function is x > 0, or (0, ∞)

The range of the function is all real numbers, or (−∞,∞)

What is function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The set of all positive real numbers serves as the function's domain. Assume that base 10 is written when no base is specified for the log. The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally. The graph would be moved upward if k>0.

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Answer:

y = 2x + 7.

Step-by-step explanation:

An equation that passes through the point (-4,-1) and is parallel to the line y = 2x + 14 is of the form y = 2x + b, where b is the y-intercept of the line. Since the line passes through the point (-4,-1), we can use this point to solve for b:

-1 = 2 * (-4) + b

-1 = -8 + b

b = 7

Therefore, an equation that passes through (-4,-1) and is parallel to y = 2x + 14 is y = 2x + 7.

Answer:

y = 2x + 7

Step-by-step explanation:

parallel = same slope

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

y+1 = 2(x+4)

y+1 = 2x + 8

y = 2x + 8 - 1

y = 2x + 7

Answer:

Functions

Step-by-step explanation:

ok so you gotta substitute x into the original then expand simplify collect like terms then your done

To establish the given identity, we need to first multiply the left side of the equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+1)(csc0-1)

We can then apply the difference of squares formula to this expression to get:

(csc0+1)(csc0-1) = (csc0+1)(csc0-1)

Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.

Therefore, the given identity is established using the Pythagorean Identity. This means that the correct answer is C. Pythagorean Identity.

Answer:

y= 4x + 0

Step-by-step explanation:

The perimeter y of a square with side length x can be described by the equation y = 4x + 0.

The perimeter of a square is equal to four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. We can use this information to write an equation in point-slope form to describe the relationship between the side length of a square and its perimeter.

Point-slope form is a way of writing the equation of a line when we know the slope of the line and the coordinates of a point on the line. In this case, the slope of the line is 4, since the perimeter of a square is four times the length of one side. The coordinates of a point on the line are (1, 4), since the side length of a square is 1 centimeter and the perimeter of the square is 4 centimeters.

We can use this information to write the equation of the line in point-slope form. The equation of a line in point-slope form is given by the following equation:

y - y1 = m(x - x1)

where y is the y-coordinate of a point on the line, y1 is the y-coordinate of a known point on the line, m is the slope of the line, and x is the x-coordinate of a point on the line.

In this case, we can substitute the values we know into the equation above to get:

y - 4 = 4(x - 1)

This simplifies to:

y = 4x + 0

Therefore, the equation in point-slope form that describes the relationship between the side length x of a square and its perimeter y is y = 4x + 0.

This equation tells us that for any square, the perimeter is four times the side length plus zero. For example, if the side length of a square is 5 centimeters, then the perimeter is 4 x 5 + 0 = 20 centimeters. If the side length of a square is 10 centimeters, then the perimeter is 4 x 10 + 0 = 40 centimeters.

In summary, the perimeter y of a square with side length x can be described by the equation y = 4x + 0.

The area of the rectangle shown on the coordinate plane is 12 square units.

What is the area of the rectangle shown on the coordinate plane?

To calculate the area of a rectangle, multiply the length by the width of the rectangle.

To find the area of the rectangle shown on the coordinate plane, first, we need to calculate the distance between the points that conforms two of the sides of the rectangle (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4, 1)

2 - (-1,-2)

3 - (-3,-4)

4 - (-6, -1)

Then, calculating the length of the sides,

Consider rectangle ABCD  with vertices A(-4, 1), B(-1, -2), C(-3, -4) and D(-6, -1). The area of the rectangle is

A = length * Width

Find the length and the width:

AB = √(-1 - (-4))² + (-2 - 1)² = √9 + 9 = √18

BC = √(-3 - (-1))² + (-4 - (-2))²  = √4 + 4 = √8

Then the area of the rectangle ABCD is

A = √18 * √8

A = 12 unit²

Hence, the area of the rectangle shown on the coordinate plane is 12 square units.

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Answer:

The answer is 3 3/4

Step-by-step explanation:

2 7/4 = 15/4 = 3 3/4

Answer:

x = 6

Step-by-step explanation:

We have a 30°-60°-90° right triangle here, so the length of the hypotenuse (12) is twice the length of the shorter leg (6). So x = 6.

Answer:

612.3 in.²

Step-by-step explanation:

Inner circle diameter = 34 in.

Inner circle radius = r = 17 in.

Outer circle diameter = 34 in. + 5 in. + 5 in. = 44 in.

Outer circle radius = R = 22 in.

The are of the ring is the area of the outer circle minus the area of the inner circle.

A = πR² - πr²

A = π(R² - r²)

A = 3.14[(22 in.)² - (17 in.)²]

A = 612.3 in.²

Answer:

03

Step-by-step explanation:

it is 03. in a polynomial the hightest power of varibale shows the degree of it.

Answer:

7 hours

every hour she makes $21

Step-by-step explanation:

378÷18=21

147÷21=7

7 hours

378÷18=21$/h in ONE hour Salma makes 21$ so you have to do 147÷21=7h