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Serggg [28]
3 years ago
7

Express √ − 100 - 100 in terms of i i

Mathematics
2 answers:
Hunter-Best [27]3 years ago
4 0

Answer:

14.1421*i

Step-by-step explanation:

barxatty [35]3 years ago
4 0

Answer:

The answer would be 10i.

Step-by-step explanation:

Given expression,

\sqrt{-100}

=\sqrt{-(10)^2}  

=\sqrt{-1}\times \sqrt{10^2}    (\because \sqrt{ab}=\sqrt{a}\times \sqrt{b})

=\sqrt{-1}\times (10^2)^\frac{1}{2}   (\because \sqrt{a}=a^\frac{1}{2})

=i\times (10)^{2\times \frac{1}{2}}    (\because (a^m)^n = a^{mn})

=10i

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Answer: 1st one

Step-by-step explanation:

8 0
3 years ago
The straight line, Line L has an equation of 4x+y=7. Find the equation of the straight line perpendicular to Line L that passes
Jobisdone [24]

Answer:

Step-by-step explanation:

y = -4x + 7

perp. 1/4

y - 3 = 1/4(x + 8)

y - 3 = 1/4x + 2

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3 0
2 years ago
Consider the following region R and the vector field F. a. Compute the​ two-dimensional curl of the vector field. b. Evaluate bo
Shalnov [3]

Looks like we're given

\vec F(x,y)=\langle-x,-y\rangle

which in three dimensions could be expressed as

\vec F(x,y)=\langle-x,-y,0\rangle

and this has curl

\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle

which confirms the two-dimensional curl is 0.

It also looks like the region R is the disk x^2+y^2\le5. Green's theorem says the integral of \vec F along the boundary of R is equal to the integral of the two-dimensional curl of \vec F over the interior of R:

\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA

which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of R by

\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle

\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt

with 0\le t\le2\pi. Then

\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt

=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0

7 0
3 years ago
On a number line, what is x-4<-3?
goblinko [34]

Add 4 to both sides

x - 4 < -3

x-4+4 < -3+4

x < 1

To graph this on a number line, plot an open circle at 1 on the number line. Do not fill in the open circle. Shade to the left of the open circle. The shaded region represents all x values smaller than 1.

The graph is shown below.

3 0
3 years ago
Triangle DEF is a right triangle. What is the measure of ZEFD?<br> D<br> 57°<br> F<br> E
creativ13 [48]

Answer:

<h3>                33°</h3>

Step-by-step explanation:

Sum of measures of angles in any triangle is 180°

The maesure of right angle is 90°

So:  m∠EFD = 180° - 90° - 57° = 33°

6 0
3 years ago
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