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2 years ago

Please help me as soon as possible!

Mathematics

1 answer:

S_A_V [24]2 years ago

4 0

Answer:

9.53 AU

Step-by-step explanation:

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A car travels 2.83 km in the x-direction, then turns left 65.3 ◦ to the original direction and travels an additional distance of

umka21 [38]

Answer:

4.24 km

Step-by-step explanation:

The x-component of the displacement after the turn is ...

d2·cos(θ) = (3.38 km)cos(65.3°) ≈ 1.41239 km

Adding this to the displacement before the turn, we have ...

x-component of displacement = 2.83 km + 1.41 km = 4.24 km

4 0

3 years ago

Simplify (5x^3 - 7x^2 + 3x - 4) - (8x^3 + 2x^2 + 3x - 7)

muminat

Answer:

-3x^4 - 14x^3 + 3x^2 - 10

Step-by-step explanation:

6 0

3 years ago

Select the correct product (x2+4) (x2-4) x4 16 x4+16 x2+8x+16 x2 8x 16

natka813 [3]

The answer would be x^4 -16
Explanation: use the FOIL method.
(x^2 +4)(x^2 -4)= x^4 +4x -4x -16. 4x and -4x cancel each other out. You are left with x^4 -16.
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8 0

3 years ago

A recipe to make 12 cupcakes includes: ¼ cup of butter, 1¼ cups of flour, and 2/3 cup of sugar. What amount of each ingredient i

Korolek [52]

Answer: Use the same recipe but just throw away 4 cupcakes

5 0

3 years ago

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the bin is constructed from 48 square feet of sheet metal, so:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

$\frac{dv}{dx} = 48-3x^{2} =0$

Solving for x:

$x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4$

Solving for y:

$y = \frac{48- 4^{2} }{(4)(4)} = 2$

Then, the dimensions of the largest volume of such a bin is:

Length = 4 ft
Width = 4 ft
Height = 2 ft

And its volume is:

$V = (4^{2} )(2) = 32 ft^{3}$

8 0

3 years ago