16 feet = ? meters ?

Answer:

A is the answer

Step-by-step explanation:

The work done to empty the tank by pumping the water out of the top of the tank is 3.4 * 10^6 .

Given :

a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank .

Formula :

\(W=\int_a^bpA(y)D(y)dy\)

Using the base radius of 4, I found the equation of the line which was y = 5x / 2 and by solving for x gives us x = 2y / 5 .

Work = \(9.8*1000\int_0^{8} (\pi(\frac{2y} 5)^2)(10-y)dy\)

= 3.4 * 10^6

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Answer: (c)

Step-by-step explanation:

Given

The inequality is \(7y+1<8y-9\\\)

Solving the above inequality

\(\Rightarrow 7y+1<8y-9\\\\\Rightarrow 1+9<8y-7y\\\\\Rightarrow 10<y\ \text{or}\\\\\Rightarrow y>10\)

Thus, option (c) is correct.

Answer:

x: {-3, 5}

Step-by-step explanation:

Step 1. Find least common denominator

Step 2. Multiply missing factors on top AND bottom

Step 3. Combine like terms

Step 4. Simplify (get rid of denominator)

Step 5. Solve for x

\(\frac{x}{x-5} +\frac{3}{x+2} =\frac{7x}{x^2-3x-10}\)            LCD = \(x^2-3x-10\)   OR  \((x-5)(x+2)\)

\(\frac{x}{x-5}(\frac{x+2}{x+2}) +\frac{3}{x+2}(\frac{x-5}{x-5}) =\frac{7x}{x^2-3x-10}\)

\(\frac{x(x+2)}{(x-5)(x+2)} +\frac{3(x-5)}{(x+2)(x-5)} =\frac{7x}{(x-5)(x+2)}\)

\(\frac{x(x+2)+3(x-5)}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}\)

\(\frac{x^2+2x+3x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}\)

\(\frac{x^2+5x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}\)

\(x^2+5x-15=7x\)

\(x^2-2x-15\)

\((x-5)(x+3)\)

x = -3, 5

Answer:

\(x=-5\frac{1}{3}\)

Step-by-step explanation:

36 - 5x = 7x + 48

3x - 5x + 5x = 7x + 5x + 48

3x = 12x + 48

3x - 12x = 12x - 12x + 48

- 9x = 48

- 9x ÷ - 9 = 48 ÷ - 9

\(x=-5\frac{1}{3}\)

The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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The function h(x) = (12 - x)/(4x - 3) could be representative of the function h.

To determine if h(x) = (12 - x)/(4x - 3) could be representative of the function h with a non-existing limit as x approaches 3, we need to evaluate the left-hand and right-hand limits of h(x) at x = 3 separately. If the left-hand and right-hand limits are not equal or do not exist, then h(x) satisfies the given condition.

Let's evaluate the left-hand limit as x approaches 3: lim(x→3-) h(x)

h(x) = (12 - x)/(4x - 3) for x < 3

lim(x→3-) h(x) = lim(x→3-) (12 - x)/(4x - 3) = (-∞)

Now, let's evaluate the right-hand limit as x approaches 3: lim(x→3+) h(x)

h(x) = (12 - x)/(4x - 3) for x > 3

lim(x→3+) h(x) = lim(x→3+) (12 - x)/(4x - 3) = (+∞)

Since the left-hand and right-hand limits are not equal and approach different infinities, the limit of h(x) as x approaches 3 does not exist.

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If the left-hand and right-hand limits are not equal, the limit of h(x) as x approaches 3 does not exist.

The given piecewise function is h(x) = {12 - x for x < 3, 4x - 3 for x > 3}.

To determine whether the limit of h(x) as x approaches 3 exists, we need to evaluate the left-hand limit and right-hand limit separately.

Since the left-hand and right-hand limits are not equal, the limit of h(x) as x approaches 3 does not exist.

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Answer:

It’s either A or C. However I’m mostly going with C. For C tells us 2 hours and 23 minutes have passed. I hope this helps.

Step-by-step explanation:

Please correct me if I am wrong.

Answer:

Step-by-step explanation: 25÷ 12545.5 = 5,018.20

the breadth of the rectangle ,b = A/x

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

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

If the area is denoted as A, breadth by b and length by x

breadth , b = A/x

therefore the breadth of the rectangle is b = A/x

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-3/2

slope = rise/run

We can use the two points to calculate rise (y value change) and run (x value change)

slope = (-6)/4 = -3/2

The factors of the given polynomials are found using factorization methods.

Consider the polynomials given.

x⁴ - 8x² + 16 = (x²)² - 8x² + 16

Using the factorization method,

                   = (x² - 4)(x² - 4)

                   = (x² - 2²)(x² - 2²)

                   = (x - 2)(x + 2)(x - 2)(x + 2) [By difference of squares formula]

The factor is x - 2.

x⁴ - 16 = (x²)² - 4²

          = (x²- 4)(x² + 4)

          = (x² - 2²)(x² + 4)

          = (x - 2)(x + 2)(x² + 4)

The factors are x - 2 and x² + 4.

x⁶ - 8 = (x²)³ - 2³

        = (x² - 2) (x⁴ + 2x² + 4)

        = (x² - 2) ((x²)² + 2x² + 4)

Factor is x² - 2.

x⁴ + 2x² - 8 = (x²)² + 2x² - 8

                  = (x² + 4) (x² - 2)

The factors are x² - 2 and x² + 4

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A local area network (LAN) connects two or more devices in a limited geographical area.

A local area network (LAN) is a type of network that links computers and other devices within a certain geographic region, such as a house, a school computer lab, an office building, or a cluster of nearby structures.

The nodes, or individual computers or devices that make up a network, frequently share resources like printers, big hard drives, and software. Cables are frequently used to connect the nodes. A LAN without physical wires is known as a wireless LAN (WLAN). A cable LAN and a WLAN frequently communicate in order for a WLAN to access its resources.

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The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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\( 1.\frac{4}{5} \times 0.820 \\ = 4 \times 0.164 \\ = 0.656\)

\(2. \frac{3}{8} + 0.13 \\ = \frac{3 + 1.04}{8} \\ = \frac{4.04}{8} \\ = 0.505\)

\(3. \frac{7}{9} \times 0.230 \\ =0.178 \: (approximately)\)

ray4918 here

The change in equilibrium real GDP is B220.

To calculate the change in equilibrium real GDP resulting from an increase in autonomous investment, we need to use the expenditure-output model. In this model, equilibrium real GDP (Y) is determined by the aggregate expenditure (AE), which is the sum of consumption (C), investment (I), government spending (G), and net exports (NX). The equation is:

Y = AE = C + I + G + NX

Given the information provided, let's calculate the initial equilibrium real GDP (Y) using the given values:

C = 80 + (9/10)Y

DI = 1800

G = 1600

TR = 10

T = (1/3)Y

Substituting the values into the equation:

Y = (80 + (9/10)Y) + 1800 + 1600 + 10 - (1/3)Y

Simplifying the equation:

Y = 3490 + (5/6)Y

Multiplying through by 6 to remove the fraction:

6Y = 6(3490) + 5Y

6Y = 20940 + 5Y

Y = 20940

The initial equilibrium real GDP is 20940.

Now, let's calculate the equilibrium real GDP after the B220 increase in autonomous investment (ΔI):

Y' = Y + ΔI

Substituting the values:

Y' = 20940 + B220

Calculating the change in equilibrium real GDP:

Change in Y = Y' - Y

Change in Y = (20940 + B220) - 20940

Change in Y = B220

The change in equilibrium real GDP is B220.

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The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.

Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:

P = (√2 + 1) / (√2 - 1)

P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]

P = (√2 + 1)² / (2 - 1)

P = (√2 + 1)²

P = 2 + 2√2 + 1

P = 3 + 2√2

Q = (√2 - 1) / (√2 + 1)

Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]

Q = (√2 - 1)²

Q = 2 - 2√2 + 1

Q = 3 - 2√2

Then, the value of P² + Q² + P · Q is:

M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)

M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8

M = 9 + 8 + 9 - 8 + 3 - 8

M = 21 - 8

M = 13

The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.

The statement is poorly formatted and reports typing mistakes, correct form is presented below:

If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.

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Step-by-step explanation:

According to the lesson, three important purposes of faith are:

Finding meaning and purpose in life: Faith can provide a sense of purpose and meaning to life by offering a framework for understanding the world and our place in it.

Providing comfort and hope: Faith can be a source of comfort and hope during difficult times by providing a sense of support, guidance, and encouragement.

Promoting personal growth and transformation: Faith can promote personal growth and transformation by challenging individuals to become their best selves, to develop a greater sense of empathy and compassion, and to cultivate virtues like forgiveness and humility.

Answer:

$0.78

Step-by-step explanation:

You divide the $7.80 by 10 to get the cost of one tulip.

The first four nonzero terms of the Maclaurin series for the function g(x) = (1+x)e^(-x) are:

g(0) = 1

g'(0) = -1

g''(0) = 1

g'''(0) = -1/3

The Maclaurin series is a way of representing a function as an infinite sum of its derivatives evaluated at zero.

The first term in the series is the value of the function at zero, which is 1 in this case. The second term is the first derivative of the function evaluated at zero, which is -1. The third term is the second derivative evaluated at zero, which is 1. And the fourth term is the third derivative evaluated at zero, which is -1/3.

These terms continue on indefinitely to form the complete Maclaurin series for g(x) = (1+x)e^(-x).

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Answer:

The radius is 9.28 inches.

Step-by-step explanation:

Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)

2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.

45.1 × 6

= 270.6

The entire spinner has the area 270.6

The area of a circle is:

A = pi•r^2

We are looking for r. Thats the radius they asked for in the question.

270.6 = pi•r^2

pi is a number, I'm using the pi button on the calculator bc it is most exact.

270.6 = pi•r^2

Divide both sides by pi.

86.134655 = r^2

square root both sides.

9.28 = r

The radius is 9.28 inches.

Applying the triangle proportionality theorem, the length of line EC is: 7.2 units.

Since lines AC and DE are parallel to each other in the triangle, and DE intersects sides AB and AC, then we would have the following proportion based on the triangle proportionality theorem:

BD/DA = CE/EA

BD = 18 units

DA = 15 units

CE = ?

EA = 6 units

Plug in the values

18/15 = CE/6

(18)(6) = (CE)(15)

108 = CE(15)

Divide both sides by 15

108/15 = CE(15)/15

7.2 = CE

EC = 7.2 units

Therefore, applying the triangle proportionality theorem, the length of line EC is: 7.2 units.

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Answer:

y = 45x miles

Step-by-step explanation:

Speed is the rate of change of distance with time. Mathematically,

speed = distance/time

Given that Darla travels at a constant speed of 45 miles per hour and for y miles, it takes her x hours then

45 = y/x

multiply both sides by x

45x = y

then the number of miles (y) Darla can drive in x hours

y = 45x (in miles)

Answer:

x=-1/4

Step-by-step explanation:

this might be wrong

Answer:

C . 130 angle

This is the answer

Answer: The answer is C. A 130 angle

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

Ok, first we know that:

Tan(0) = 0

While in the graph, we can see that:

f(0) = -2

Then our function will be something like:

f(x) = tan( k*x) - 2

We also can see that the graph has asymptotes at x = π/2 and at x = -π/2

While the normal tangent equation has the asymptotes at x = pi

So here we have that:

k*(pi/2) = pi

k = pi*(2/pi) = 2

k = 2

then the function is something like:

f(x) = tan(2*x) - 2

If we look at the options, we can see one that is:

tan( 2*(x + π)) - 2

we can rewrite this as:

tan(2*x + 2π) - 2

And remember that the period of a trigonometric function is 2π

This means that:

tan(a + 2π) = tan(a)

Then:

tan(2*x + 2π) - 2 =  tan(2*x) - 2

Which is the function that we found.

Then the correct option is C

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)