Find the parabola of the form y = ax2 + b which best fits the points (1, 0), (3, 2), (4, 4) by minimizing the sum of squares, s, given by

The solution to the given-equation represented by "3(4x + 6) = 9x + 12" is : (b) x = -2.

To find the solution to the equation 3(4x + 6) = 9x + 12, we simplify and solve for x,

First, we distribute the 3 to both terms,

12x + 18 = 9x + 12

Next, we separate variable-term by subtracting 9x from both sides:

12x - 9x + 18 = 9x - 9x + 12,

Simplifying further:

We get,

3x + 18 = 12,

Next, we separate "x" by subtracting 18 from both sides,

3x + 18 - 18 = 12 - 18,

3x = -6,

(3x) / 3 = (-6) / 3,

x = -2

Therefore, the correct answer is (b) x = -2.

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The given question is incomplete, the complete question is

What is the solution to the equation 3(4x + 6) = 9x + 12?

(a) x = 2,

(b) x = -2,

(c) x = 10,

(d) x = -10.

To estimate the error in the hypotenuse length of a right triangle using differentials, we use the trigonometric identity sin(θ) = opposite/hypotenuse, finding the derivative, and then apply the angle error to get an error estimate of
±0.31 cm in the hypotenuse length.

The question asks to use differentials to estimate the error in computing the length of the hypotenuse of a right triangle when one side is 9 cm and the opposite angle is 30° with a possible error of ±1°. To calculate the hypotenuse (c) when dealing with problems involving right triangles, you can use the trigonometric identity sin(θ) = opposite/hypotenuse, which can be rearranged to c = opposite/sin(θ). The differential of c with respect to θ is dc/dθ = -opposite * cos(θ)/sin2(θ). Given that the opposite side is 9 cm and the angle θ is 30°, we can find dc/dθ and then multiply by the possible angle error of ±1° to estimate the error in the hypotenuse length.

Plugging in the given values and converting the angle to radians (since the derivative is taken with respect to radians), we find

dc/dθ ≈ -9 cm × cos(30°)/sin2(30°) ≈ -18 cm.

The possible change in angle is ±1°, which in radians is approximately ±0.0175 radians, thus

Estimated error in hypotenuse ≈ -18 cm × ±0.0175 ≈ ±0.315 cm.

Therefore, the estimated error in the length of the hypotenuse, rounded to two decimal places, is ±0.31 cm.

The unit price of Starbucks Coffee, when 0.5 lb costs $6.48, is calculated by dividing the total cost by the pounds, resulting in $12.96 per pound.

If 0.5 lb of Starbucks Coffee costs $6.48, to find the unit price for Starbucks Coffee, we perform a simple division. You want to know how much 1 lb would cost, given that 0.5 lb costs $6.48. To do this, you divide the total cost by the number of pounds.

$6.48 ÷ 0.5 = $12.96 per pound

This means that the unit price of Starbucks Coffee, when given a price of $6.48 for a half-pound, is $12.96 per pound. This calculation is crucial in understanding how to break down costs into more manageable, standard units, making price comparisons easier and more straightforward.

To calculate the volume of a solid bounded by two functions, set up an integral in polar coordinates. The volume is found by integrating the difference of the two volumes described by the functions (50 - sqrt(x²+y²) - sqrt(x²+y²)) over r, θ, and z within their appropriate limits.

The subject of the question is mathematics, more specifically, integral calculus in spherical or polar coordinates. Calculating the volume of a solid bounded by two functions can be done by taking the difference of the two function volumes.

The integrals, using polar coordinates (r and θ), are set up as follows:

Volume = ∫∫∫(50 - sqrt(x²+y²) - sqrt(x²+y²)) r dr dθ dz,

where the limits for r are [0, sqrt(50)], for θ are [0, 2π], and for z are [0, 50]. Also, note that 'x²+y²' is replaced with 'r²' because in polar coordinates, 'r' represents the square root of x^2 plus y^2.

This integral, when solved, gives the volume of the ice cream cone-shaped solid.

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The volume of the ice cream shaped solid can be found by converting the limits of the cone to polar coordinates and performing a double integral. The limits of the cone are represented by the expressions z = r and z = sqrt(50 - r^2). The volume integral will be ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ.

To evaluate the volume of the solid resembling an ice cream cone, we can use the method of double integration in polar coordinates. Because we're dealing with a cone, polar coordinates are suitable as they're related to circular symmetry.

The limits of the cone are given by the functions z = sqrt(x^2 + y^2) and z = sqrt(50 - x^2 - y^2). In polar coordinates these become z = r and z = sqrt(50 - r^2).

To evaluate the volume of the cone, we need to subtract the volume of the lower cone (given by z = r) from the volume of the upper cone (given by z = sqrt(50 - r^2)). We convert the values to polar coordinates and use double integration as follows:

V = ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ

This integral, once solved, will give the volume of the ice cream shaped solid.

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Answer:

77%

Step-by-step explanation:

Answer:

[tex]f^{-1}=4(x+2)[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{x}{4} -2[/tex]

To find inverse function , replace f(x) with y

[tex]y=\frac{x}{4} -2[/tex]

Swap the variables x and y

[tex]x=\frac{y}{4} -2[/tex], nbw we solve for y

Add 2 on both sides

[tex]x+2=\frac{y}{4}[/tex]

Now to eliminate 4, we multiply 4 on both sides

[tex]y=4(x+2)[/tex]

Replace y with f^-1

[tex]f^{-1}=4(x+2)[/tex]

Final answer:

The second partial derivatives of v = e⁵x * ey are ∂²v/∂x² = 25e⁵x * ey and ∂²v/∂x² = 5e⁵x * e^y.

Explanation:

To find the second partial derivatives of the function v = e⁵x * ey, we need to differentiate twice with respect to x and y. Let's start with the first partial derivative with respect to x:

∂v/∂x = ∂(e⁵x * ey)/∂x

= 5e⁵x * ey

Next, we differentiate the first partial derivative with respect to x to find the second partial derivative with respect to x:

∂²v/∂x² = ∂(5e⁵x * ey)/∂x

= 25e⁵x * ey

Similarly, the second partial derivative with respect to y is:

∂²v/∂x² = ∂(5e⁵x * ey)/∂y

= 5e⁵x * e^y

The total number boxes of juice are 768 in the display.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that in each variety pack of fruit juice, there are 3 voxes of apple juice, 2 boxes of grape juice, and 1 box of orange juice.

In a display in the store, there are 16 cases of juice with 8 variety packs in each case therefore,

Each variety pack of fruit juice = 3 + 2 + 1 = 6 juice

8 variety packs = 8 x 6 = 48

Now, the total number boxes of juice are in the display

16 x 48

= 768

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2:9 means for every 2 men there are 9 women

36/9 =4

4*2 = 8

 there are 8 men