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Anna007 [38]
3 years ago
5

Can somebody help me

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
6 0

cis(x)=\cos x+i\sin x\\\\cis15^o=\cos15^o+i\sin15^o\\\\\cos15^o=\dfrac{\sqrt6+\sqrt2}{4};\ \sin15^o=\dfrac{\sqrt6-\sqrt2}{4}\\\\\text{therefore}\\\\7cis15^o=7\left(\cos15^o+i\sin15^o\right)=7\cos15^o+7i\sin15^o\\\\=7\left(\dfrac{\sqrt6+\sqrt2}{4}\right)+7\left(\dfrac{\sqrt6-\sqrt2}{4}\right)i

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Step-by-step explanation:

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2 years ago
If a cannonball is shot directly upward with a velocity of 160 ft per​ second, its height above the ground after t seconds is gi
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Step-by-step explanation:

If a cannonball is shot directly upward with a velocity of 160 ft per​ second. Its height as a function of time is given by :

h(t)=160t-16t^2 .......(1)

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(a) Velocity is given by :

v=\dfrac{dh}{dt}\\\\v=\dfrac{d(160t-16t^2)}{dt}\\\\v=(160-32t)\ ft/s  

Acceleration is given by :

a=\dfrac{dv}{dt}\\\\a=\dfrac{d(160-32t)}{dt}\\\\a=-32\ ft/s^2

(b) For maximum height put \dfrac{dh}{dt}=0

i.e.

160-32t=0\\\\t=5\ s

Put t = 5 s in equation (1). So,

h(5)=160t-16t^2\\\\h(5)=160(5)-16(5)^2\\\\h(5)=400\ ft

(c) When the ball reaches ground, its height is equal to 0. So,

h(t) = 0

160t-16t^2=0\\\\t(160-16t)=0\\\\t=0,t=10\ s

Hence, this is the required solution.

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3 years ago
The ozone layer helps to sustain terrestrial life by __________.
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Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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(h, k) → (h + a, k +b)

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By applying rules of the translation,

Coordinates of image point A' → (-4 + 4, -2 + 3)

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Coordinates of B' → (1 + 4, -1 + 3)

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Coordinates of C' → (0 + 4, -5 + 3)

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Now plot these points on the graph.

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Let the shortest side be x.  Then the other two sides will be x+1 and x+2.

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