A cylindrical tank has a diameter of 30m and height 20m.
a) Find its volume in m³, correct to two decimal places.
b) What is the capacity of the tank in litres?​

now, this is implicit differentiation, so it comes with the assumption that "y" is a function in "x terms", as opposed to a plain vanilla variable, whilst "x" is just that, so

[tex]\cfrac{d}{dx}[x^2+y^4=20]\implies 2x+\stackrel{chain~rule}{4y^3\cdot \cfrac{dy}{dx}}=0\hspace{5em}\cfrac{d}{dx}\left[ 2x+4y^3\cdot \cfrac{dy}{dx}=0 \right] \\\\\\ 2+\stackrel{product~rule}{\left( 12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2} \right)}=0\implies 2+12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2}=0 \\\\\\ 2+12y^2\cdot \cfrac{dy}{dx}=-4y^3\cdot \cfrac{d^2y}{dx^2}\implies {\Large \begin{array}{llll} \cfrac{2+12y^2\cdot \frac{dy}{dx}}{-4y^3}=\cfrac{d^2y}{dx^2} \end{array}}[/tex]

Answer: The question is asking for the number of households that have between 3.67 and 4.35 people, which corresponds to the number of households whose number of people per household falls within one standard deviation of the mean.

A normal distribution is symmetric, so approximately 68% of the data falls within one standard deviation of the mean. So, we can estimate that approximately 68% of the 1,500 households have between 3.67 and 4.35 people.

The calculation is:

1,500 households x 68% = 1,020 households

So, approximately 1,020 households have between 3.67 and 4.35 people.

This is a rough estimate and the actual number may be slightly different, but it can be considered as a good approximation. From the given options, The answer closest to 1,020 is 945 households.

Step-by-step explanation:

Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

when we have to solve an equation, it does not has an equal sign and inequalities.

When we have to solve an inequality equations usually are exact answers.

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

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Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.

Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.

And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.

I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.

Step-by-step explanation:

The line that parallels y = 1/2 x + 8 and goes through the point (-2, 2) is represented by the equation y = 1/2 x + 3.

The entire time, the x-coordinate -2 is shown. A function is NOT what this is. A number is multiplied three times by itself to form a cube. The symbol for the cube of a number is x. 3.

To increase an integer to the third power is to cube it. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

A function, in general, is a relationship between two variables. In other words, the relationship x = y2 is not a function.

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Answer:

  -6

Step-by-step explanation:

You seem to want the value of q₃ in the matrix Q⁻¹.

The inverse matrix, Q⁻¹, is the transpose of the cofactor matrix, divided by the determinant. That makes q₃ = -q₂₁/det(Q):

  q₃ = -(-2/3)/((-1(-1/9) -(-2/3)(-1/3))

  q₃ = (2/3)/(1/9 -2/9) = (6/9)/(-1/9)

  q₃ = -6

__

Additional comment

The transpose of the cofactor matrix of a 2×2 matrix is the original with the diagonal terms swapped, and the off-diagonal terms negated. Basically, the only math involved in computing the inverse is finding the determinant, and dividing by it.

Answer:

-----------------------------------

Given lines:

Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.

See attached.

The solution is (-1, 0).

The value of u is given by the equation u = 37°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the sum of total internal angles of a triangle be = 180°

Now , the triangle be ΔABC

The measure of ∠A = u + 4°

The measure of ∠B = u

The measure of ∠C = ( 180° - ( u + 41° ) ) ( angles on a straight line = 180° )

From the triangle theorem ,

u + 4° + u + ( 180° - ( u + 41° ) ) = 180°   be equation (1)

On simplifying the equation , we get

2u + 184° - u - 41° = 180°

u + 143° = 180°

Subtracting 143° on both sides of the equation , we get

u = 37°

Therefore , the value of u is 37°

Hence , the value of u in the triangle is 37°

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Answer: y = 17x - 19

Step-by-step explanation:

17x + y = -19

Subtract 17 on both sides

Y= -19 - 17x

Then put it in y= mx + b

Y= -17x - 19

Answer:

y = -17x -19

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

17x+y = -19

Solve for y

y = -17x -19

Answer:

Below

Step-by-step explanation:

"Lynn is making a snack. The recipes call for 3/8 cup of water for oats and 1/4 cup"

(I changed the numbers to fractions ....)

she needs   3/8 + 1/4 cup ....add them together by finding a common denominator

1/4 = 2/8    

then   3/8 + 2/8 = (3+2)/8 = 5/8 cup

  if she has one cup of water she has enough....she only needs 5/8 cup

The value of y is 16 when x = 32 for equation y = (1/4)x divided by 2.

Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It displays how the expressions on the left and right sides are equally related. We have LHS = RHS in any mathematical equation. Equations can be solved to get the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation.

The given equation is

y = 1/4 x divided by 2

So,

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

y = (2/4) × x

Put x = 32

y = 2/4 ×32

y = 2 × 8

y = 16

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Maria’s vegetable garden measures 5⅔ feet by 6⅚ feet. 38.72 feet² is the area of the garden. This can be solved using the concept of the area of rectangle.

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Each and every square is a rectangle since it is a quadrilateral with right angles on all four sides. But not all rectangles are squares; for a shape to be a square, all of its sides must have the same length.

So a square is also a rectangle and a rhombus. There is no square shape in the rectangle or rhombus. The trapezium shape is a parallelogram.

Maria’s vegetable garden measures 5⅔ feet by 6⅚ feet.

So, it is a rectangular garden.

Now, area = 5⅔ feet × 6⅚ feet

or, area = 17/3 feet × 41/6 feet

or, area = 697 /18 feet²

or, area = 38.72 feet²

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On solving the provided question, we can say that - the value of the function is = x-5/x + 2 => x= 2  => -3/4

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

x-5/x + 2

x= 2

-3/4

ans also  4x² = 4 *2*2 = 16

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Answer:

See below

Step-by-step explanation:

I guess if you look at the zeroes/x-intercepts, we got (3,0) and (-7,0) as zeroes.

Additionally, we can calculate the minimum by expanding the function:

[tex](x-3)(x+7)=x^2+4x-21[/tex]

[tex]\displaystyle x=-\frac{b}{2a}=-\frac{4}{2(1)}=-2\\\\f(-2)=(-2)^2+4(2)-21=4+8-21=12-21=-9[/tex]

So the minimum of the function is (-2,-9)

Also, our y-intercept is (0,-21)

Answer:

x + 23 = 65

x = 42

She had 42 buttons to begin with.

3 x 3 x 3 x 3 x 3 x 3 x 2 x 3 x 3 x 434 = 5,694,948

It's difficult to determine exactly how much interest Timothy will pay over 30 years without more information about the terms of his mortgage. However, we can use the following formula to calculate his monthly mortgage payment, which includes both the principal and the interest:

Monthly payment = P * (r/12) / (1 - (1 + r/12)^(-n))

Where:

P is the principal amount (the total cost of the house minus the down payment)

r is the monthly interest rate (we need to convert the annual interest rate to a monthly rate by dividing it by 12)

n is the number of payments (in this case, the number of months over which Timothy will pay off the mortgage, which is 30 years * 12 months/year = 360 months)

We can plug in the given values to find Timothy's monthly payment:

Monthly payment = $360,000 * (0.04/12) / (1 - (1 + 0.04/12)^(-360)) = $1,375.69

To find the total amount of interest Timothy will pay over 30 years, we would need to know the interest rate on his mortgage and the length of the loan in months. With this information, we could calculate the total amount of interest Timothy will pay by multiplying his monthly payment by the number of payments he makes (360 payments in this case) and subtracting the principal amount ($360,000).

Answer:

1/12

Step-by-step explanation:

3/4 - 2/3 = 9/12 - 8/12 = 1/12

Answer:

The answer is 1/12 good luck with the rest

Answer:

C, neither.

I've attached a picture of what it looks like when you plot it on a graph. As you can see, it is neither. So the answer is C

Hope this helped :)

Answer:

105.72 meters

Step-by-step explanation:

We can set up a system of equations to represent the information given in the problem, and then use algebra to solve for the length of the blue rope. Let x be the length of the red rope.

According to the problem statement:

blue rope = 3 * red rope = 3x

green rope = 4 * blue rope = 4 * 3x = 12x

we know that:

red rope + blue rope + green rope = 563.84

x + 3x + 12x = 563.84

then we can solve for x:

16x = 563.84

x = 35.24

So the length of the red rope is 35.24 meters.

The length of the blue rope is 3x = 3 * 35.24 = 105.72 meters.

The distance of the ship from lighthouse found using sine law at both locations are 14.12 miles and 4.8 miles.

What is sine law?

The sine law asserts that the ratio of a triangle's side length to the sine of its opposing angle, which is constant for all three sides.

From the given figure we can find θ = 30 - 10 = 20°

According to sine law, we can write the following equation,

[tex]\frac{9.6}{sin \theta} = \frac{x}{sin \angle ABL} = \frac{y}{sin \angle LAB} \\[/tex]

From the figure, we get that ∠LAB= 10° (alternate angles)

∠LBC = 30°

∠ABL = 180 - 30 = 150°

θ = 20°

Substituting above values in the equation we get ,

[tex]\frac{9.6}{sin 20} = \frac{x}{sin 150} = \frac{y}{sin 10} \\\\\frac{9.6}{0.34} = \frac{x}{0.5} = \frac{y}{0.17}[/tex]

Solving the above we get,

x = 14.12

y = 4.8

Therefore the ship began 14.12 miles from the lighthouse and after travelling 9.6 miles south it is at 4.8 miles from the lighthouse.

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Answer:

Refer to step-by-step

Step-by-step explanation:

Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]

Plug in the value of 2 into the limit.

[tex](2)^{2}=4[/tex]

Thus we proved the limit.

Answer:

81

Step-by-step explanation:

9x9 = 81

After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.

so the equation of the image is y = 2x + 1.

A reflection over a line is a transformation in which each point of the initial figure (the pre-image) has an image that is on the opposite side of the reflection line from the original point and is situated at the same distance from the reflection line. The pre-size image's and shape are replicated in a reflection.

The line of reflection is typically expressed as y = m x + b y=mx+by, equals, m, x, plus, b. What need I do to draw the line of reflection? The starting points in the figure are all perpendicularly separated from the line of reflection by the same amount as the starting points in the image.

To reflect a line in the y-axis, we need to negate the slope of the line.

The line y = -2x +1 has a slope of -2 and y-intercept of 1.

After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.

so the equation of the image is y = 2x + 1.

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Answer:

To solve this problem, we can set up the following equation:

2L + 2W = 64

We are told that the length of the rectangle is two more than double the width, so we can write the following equation:

L = 2W + 2

Substituting this equation into the first equation, we get:

2(2W + 2) + 2W = 64

Simplifying this equation, we get:

6W + 4 = 64

Subtracting 4 from both sides, we get:

6W = 60

Dividing both sides by 6, we get:

W = 10

The width of the rectangle is 10 feet.

To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:

L = 2(10) + 2

= 20 + 2

= 22

The length of the rectangle is 22 feet.

Therefore, the dimensions of the rectangle are 10 feet by 22 feet.

Step-by-step explanation:

Step-by-step explanation:

Why can't I plus x² to each side of the inequality x²+4x > -x² ?

(Note: one adds things; one does not plus them.)

You can easily add x² to both sides here:

(x² + 4x) + x² > (-x²) + x², or

2x² + 4x > 0, or

x² + 2x > 0, or

x(x + 2) > 0.

For this to be true, x > 0 and x+2 > 0; or else x < 0 and x+2 < 0.

Case 1: x > 0 and x+2 > 0.

Rewrite this as x > 0 and x > -2.

This is true for all x > 0.

Case 2: x < 0 and x+2 < 0.

Rewrite this as x < 0 and x < -2.

This is true for all x < -2.

The solution set for the inequality, in interval notation, is then (-∞,-2) ∪ (0,∞).

done its a good question btw ....

Answer:

2x^3+5x^2−28x−15

Step-by-step explanation:

Answer:

Bike: 10 miles per hour
Car: 30 miles per hour

Step-by-step explanation:

He spent: 2h/(1+3) = 0,5h by car and 0,5h x 3 = 1,5h by bike
The car is: 15 miles/ 0,5h = 30 miles/h
The bike is: 15 miles/ 1,5h = 10 miles/h