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3 years ago

a scale model of a human heart is 196 inches long. the scale is 32 to 1. how many inches long is the actual heart?

1 answer:

4 0

If the model is 196 inches, then the real heart is 196/32 inches long (6.125 and i guess just round to 6 if you need to)

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The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

3 0

3 years ago

Some help would be greatly appreciated

marusya05 [52]

I think it might be the second option

6 0

3 years ago

Why can you use cross products to solve the proportion 18/5 = x/100 for x ?

Tcecarenko [31]

Answer:

Yes, you can use cross products to solve for x in this proportion. Also, x is 360.

Step-by-step explanation:

Yes, you can use cross products to solve for x in that proportion.

Here's how you do it :

$\frac{18}{5} = \frac{x}{100}$

We cross product, getting :

18 * 100 = 5 * x

1800 = 5x

Divide by 5 on both sides to get x by itself.

360 = x

Yes, you can use cross products to solve for x in this proportion. Also, x is 360.

Hope this helps, please mark brainliest if possible. Have a great day.

4 0

3 years ago

Serial numbers for a product are to be made using 2 letters followed by 3 digits the letters are to be taken from the first 6 le

kipiarov [429]

Answer:

Step-by-step explanation:

We have to make 5 place serial number with first two as alphabets and last three as digits.

The alphabets are bonded to first 6 ( A, B, C, D, E, F) where as digits are 10 (say 1 to 10).

Let the serial number be S1 S2 S3 S4 S5.

For Alphabets

For S1 we have 6 alphabets.

Now for S2 we are left with 5 alphabets since there is no repetition one alphabet will be fix for S1.

So the possible combination for S1 S2= 6x5=30.

For Digits

We did the same as we did for alphabets, for S3 we have 10 possibilities, and for S4 and S5 9 and 8 respectively due to the no repetition condition.

So the possible combinations for S3 S4 S5 = 10x9x8=720

So the total number of serial numbers are 30+720=750.

7 0

3 years ago

The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16

Sergio [31]

Answer:

We can conclude that the result is significant and production differ in cost variance.

Step-by-step explanation:

Given :

n1 = 16

n2 = 16

s1² = 5.7

s2² = 2.8

α = 0.10

H0 : σ1² = σ2²

H1 : σ1² ≠ σ2²

The test statistic :

Ftest = s1² / s2² =

Ftest = 5.7 / 2.8

Ftest = 2.036

Using the Pvalue from Fratio calculator :

df numerator = 16 - 1 = 15

df denominator = 16 - 1 = 15

Pvalue(2.036, 15, 15) = 0.0898

Pvalue = 0.0898

Since the Pvalue is < α ; We can conclude that the result is significant and production differ in cost variance.

3 0

3 years ago