The sum of two numbers is 19. Their difference is 65. What are the numbers?

Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur

Bad White [126]

Looks like you have most of the details already, but you're missing one crucial piece.

$\sigma$ is parameterized by

$\vec r(u,v)=\langle u\cos3v,u\sin3v,v\rangle$

for $0\le u\le7$ and $0\le v\le\frac{2\pi}3$ , and a normal vector to this surface is

$\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left\langle\sin3v,-\cos3v,3u\right\rangle$

with norm

$\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{\sin^23v+(-\cos3v)^2+(3u)^2}=\sqrt{9u^2+1}$

So the integral of $f(x,y,z)=x^2+y^2+z^2$ is

$\displaystyle\iint_\sigma f(x,y,z)\,\mathrm dA=\boxed{\int_0^{2\pi/3}\int_0^7(u^2+v^2)\sqrt{9u^2+1}\,\mathrm du\,\mathrm dv}$

6 0

3 years ago

3. Write the equation. Slope: riset Run y intercept: equation: y=mx+b;

larisa [96]

Answer: y = 1/4 x – 4

OR y = x/4 –4

m is the slope. b is the y-intercept.

Without numbers on the x and y axis, it may not be correct. But assuming a normal scale, the slope is positive 1/4 and the y-intercept is -4

Step-by-step explanation: To find the slope, m, determine "rise over run"

Look for places where the graphed line crosses the grid at intersections. There seems to be such places at (–4,–5), (0,–4) and (4,–3)

The "rise" is the difference in y-values. Here, they increase by 1.

The "run" is the difference in x-values. Here they increase by 4.

So the slope is 1/4. Put that in place of m.

The graphed line crosses the y-axis at –4

That is the y-intercept. Use -4 in the place of b

Keep the y and x; substitute the values for m and b we found.

y = 1/4 x – 4

OR

y = x/4 – 4 This makes it clear that x is not in the denominator of the fraction, 1/4, and in calculations with given coordinates, the value of x will be divided by 4.

3 0

3 years ago

Write an algebraic equation for each question below and then solve the equation.

Aneli [31]

Answer:

$number = x \\ number \: decreaed \: by \: 8 = > x - 8 = 26 \\ x - 8 = 26 \\ x = 8 + 26 \\ x = 34 \\ thank \: you$

3 0

3 years ago

Read 2 more answers

2. what value of b makes the following equation true

Svetradugi [14.3K]

Answer:

2. 10

3. D. 1 for all n

Step-by-step explanation:

2. The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

a^b = 1/a^-b

__

$\dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}$

The value of n is 10.

__

3. Using the above rules of exponents, the expression simplifies to ...

6^(-n+n) = 6^0 = 1

The value is 1 for any n.

4 0

3 years ago

A boat sails for 5 hours at 30 mph in a direction 164°56'. How far south has it sailed (to the nearest mile)?

Valentin [98]

Total distance covered = 5 x 30 = 150 miles
Angle of travel with respect to south pole = 180 - 164°56' = 15°4'

Let the distance southwards covered be x, then
cos 15°4' = x/150
Thus, x = 150 cos 15°4' = 144.84

Therefore, the distance covered southwards = 145 miles to the nearest mile.

5 0

3 years ago