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3 years ago

Traces of surface x2 + y2 − z2 = 1. Determine the equation for the family of traces in x = n.

Mathematics

1 answer:

pickupchik [31]3 years ago

6 0

Answer:

$\mathbf{y^2 -z^2 =1- n^2}$

Step-by-step explanation:

Give that:

the surface equation is $x^2 +y^2 -z^2 =1$

from the family of traces in x = n given that $x^2 +y^2 -z^2 =1$ , the equation can be represented as :

$n^2 +y^2 -z^2 =1$

$\mathbf{y^2 -z^2 =1- n^2}$

This represents a family of hyperbola for all values of n expects that n = ± 1

So, if n = ± 1,

Then

$y^2 - z^2 = 0$

(y-z) (y+z) = 0

y = ± z

So, for n = ± 1, it is a pair of line for y = z, y = -z

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Oscar has received a $4,000 gift and is looking for a bank to start a savings account. Which option

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Answer:

The best option for him would be a real interest rate of 5%.

Step-by-step explanation:

The nominal interest rate is the one that represents the percentage of increase of the money that is in a certain investment, without discounting the depreciation due to inflation or the payment of taxes.

On the other hand, the real interest rate is the one that represents the real increase in the money invested, after discounting inflation and any taxes to be paid.

Therefore, the best option for Oscar would be to invest his $ 4,000 in a savings account with a real interest rate of 5% per year.

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3 years ago

PLEASE HELP!! for 20 points<br> What is the area of the<br> composite figure?

belka [17]

Answer:

Step-by-step explanation:

Break the shape into smaller shapes, then solve:

Large Rectangle -> 4x8=32

Tiny Rectangle at the bottom ->2x3=6

Triangle at top can be broken into two right triangles ->

(4x2)(1/2)=4

Add: 32+6+4+4=46

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2 years ago

The volume of a right circular cone with radius r and height h is V = pir^2h/3.

Scorpion4ik [409]

The question is incomplete. The complete question is :

The volume of a right circular cone with radius r and height h is V = pir^2h/3. a. Approximate the change in the volume of the cone when the radius changes from r = 5.9 to r = 6.8 and the height changes from h = 4.00 to h = 3.96.

b. Approximate the change in the volume of the cone when the radius changes from r = 6.47 to r = 6.45 and the height changes from h = 10.0 to h = 9.92.

a. The approximate change in volume is dV = _______. (Type an integer or decimal rounded to two decimal places as needed.)

b. The approximate change in volume is dV = ___________ (Type an integer or decimal rounded to two decimal places as needed.)

Solution :

Given :

The volume of the right circular cone with a radius r and height h is

$V=\frac{1}{3} \pi r^2 h$

$dV = d\left(\frac{1}{3} \pi r^2 h\right)$

$dV = \frac{1}{3} \pi h \times d(r^2)+\frac{1}{3} \pi r^2 dh$

$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$

a). The radius is changed from r = 5.9 to r = 6.8 and the height is changed from h = 4 to h = 3.96

So, r = 5.9 and dr = 6.8 - 5.9 = 0.9

h = 4 and dh = 3.96 - 4 = -0.04

Now, $dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$

$dV = \frac{2}{3} \pi (5.9)(4)(0.9)+\frac{1}{3} \pi (5.9)^2 (-0.04)$

$dV=44.484951 - 1.458117$

$dV=43.03$

Therefore, the approximate change in volume is dV = 43.03 cubic units.

b). The radius is changed from r = 6.47 to r = 6.45 and the height is changed from h = 10 to h = 9.92

So, r = 6.47 and dr = 6.45 - 6.47 = -0.02

h = 10 and dh = 9.92 - 10 = -0.08

Now, $dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$

$dV = \frac{2}{3} \pi (6.47)(10)(-0.02)+\frac{1}{3} \pi (6.47)^2 (-0.08)$

$dV=-2.710147-3.506930$

$dV= -6.22$

Hence, the approximate change in volume is dV = -6.22 cubic units

8 0

2 years ago

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aksik [14]

Answer:

Step-by-step explanation:

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Both have 6 faces, so we will be adding six values together for each.

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Hopefully you can imagine the six different faces. It's kinda like a cereal box.

The front and back of a cereal box have the same area, as do the two sides and the top and bottom, so that makes it a little easier.

Front and Back: 28 * 36 = 1008

Sides: 36*6 = 216

Top and Bottom: 6*28 = 168

Let me know if you don't understand how I did any of that. Anyway, since there is a matching face for each we add them all together twice.

1008*2 + 216*2 + 168*2 = 2784 in^2

Container B has a similar setup, I won't write out everything like I did unless you want me to work it out with you.

2(16*12+16*22+22*12) = 1616 in^2

So since Container A has a surface area of 2784 and Container B has a surface area of 1616 it's obvious container A has a larger surface area

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3 years ago

A wave with a height of 5 feet and a wavelength of 10 feet has a wave base of

Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

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3 years ago

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