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4 years ago

Y=2x X+Y=-9 What's the answer ?

Mathematics

1 answer:

Elan Coil [88]4 years ago

3 0

$y=2x\\
x+y=-9\\\\
x+2x=-9\\
3x=-9\\
x=-3\\\\
y=2\cdot(-3)\\
y=-6\\\\
\boxed{(x,y)=(-3,-6)}$

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Solve for x: 5x\10=2 is it (a) 1 (b) 4 (c) 5 (d) 20

OleMash [197]

(b) 4

5(4)/10=20/10=2

6 0

3 years ago

22: A 2.0 kg object moves along the x-axis under the influence of an unknown force. Its potential energy due to the force is U(x

aleksandr82 [10.1K]

Answer: a) -13.25 N, b) 1.78 m/sec

Step-by-step explanation:

Since we have given that

$U(x)=ax^4+bx^2$

where

$a=2.5\ J/m^4\\\\b=12\ J/m^2$

As we know that

$F=\dfrac{-dU}{dx}=-(4ax^3+2bx)$

Here, x= 0.5 m

So, it becomes,

$F=-(4\times 2.5\times (0.5)^3+2\times 12\times 0.5)=-13.25\ N$

Now, we need to find the velocity when it crosses the origin,

$F=mg\\\\F=m\dfrac{dv}{dt}\\\\F=mv\dfrac{dv}{dx}\\\\-(4ax^3+2bx)dx=mvdv\\\\\int\limits^{0.5}_0 {-(4ax^3+2bx)} \, dx =\int\limits {mv} \, dv\\\\ \dfrac{-4ax^4}{4}+\dfrac{2bx^2}{2}|_0^{0.5}=\dfrac{mv^2}{2}\\\\ax^4+bx^2|_0^{0.5}=\dfrac{mv^2}{2}\\\\2.5(0.5)^4+12(0.5)^2=\dfrac{2v^2}{2}\\\\0.15625+3=v^2\\\\3.15625=v^2\\\\\sqrt{3.15625}=v\\\\v=1.78$

Hence, a) -13.25 N, b) 1.78 m/sec

7 0

4 years ago

PLEASE HELP ME I WILL CHOOSE BRAINLIEST!!!!

kakasveta [241]

Answer:

Exact height = 8*sqrt(3) mm

Approximate height = 13.856 mm

=============================================================

Explanation:

If you do a vertical cross section of the cylinder, then the 3D shape will flatten into a rectangle as shown in the diagram below.

After flattening the picture, I've added the points A through F

point A is the center of the sphere and cylinder
points B through E are the corner points where the cylinder touches the sphere
point F is at the same horizontal level as point A, and it's on the edge of the cylinder.

Those point labels will help solve the problem. We're told that the radius of the sphere is 8 mm. So that means segment AD = 8 mm.

Also, we know that FA = 4 mm because this is the radius of the cylinder.

Focus on triangle AFD. We need to find the height x (aka segment FD) of this triangle so we can then double it later to find the height of the cylinder. This in turn will determine the height of the bead.

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

As the hint suggests, we'll use the pythagorean theorem

a^2 + b^2 = c^2

b = sqrt(c^2 - a^2)

x = sqrt(8^2 - 4^2)

x = sqrt(48)

x = sqrt(16*3)

x = sqrt(16)*sqrt(3)

x = 4*sqrt(3)

This is the distance from D to F

The distance from D to E is twice that value, so DE = 2*(FD) = 2*4*sqrt(3) = 8*sqrt(3) is the exact height of the bead (since it's the exact height of the cylinder).

Side note: 8*sqrt(3) = 13.856 approximately.