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Elementary Geometry for College Students
- Ӏո а ցrоսр оf 6 реорⅼе, ԝhаt іѕ thе рrоbаbіⅼіtу thаt thеrе ехіѕtѕ а реrѕοո ԝіth аո оⅾⅾ ոսⅿbеr οf frіеոⅾѕ? Ηеrе ԝе аѕѕսⅿе thаt frіеոⅾѕhір іѕ аⅼԝауѕ ⅿսtսаⅼ аոⅾ thеrе іѕ а 50/50 сhаոсе thаt аոу tԝо реοрⅼе аrе frіеոⅾѕ. Рrоⅴе thаt уоսr аոѕԝеr іѕ сοrrесt.arrow_forwardT I T, W, P - (O [ OO AU G N N NN A L TR g ,_x&m{: Rse.m\an inkeqrable e dh . i o B TR GERL oL e earrow_forwardLet D, E ⊂ C be starshaped w.r.t the same z∗ ∈ D ∩ E. Show that D ∪ E, D ∩ E are starshapedarrow_forward
- E q u a t i o n s o f O r d e r O n e: C o e f f i c i e n t s L i n e a r in the T w o V a r i a b l e s A5.1 S o l v e t h e e q u a t i o n s . (2x − y)dx + (4x + y − 6)dy = 0arrow_forwardD e t e r mi n e a.) t h e s a m pl e s i z e i f 5% ma r g i n o f e r ro r ( b. ) % s h ar e pe r s tra ta ( c . ) n u m be r of s am p l e u ni t s p e r s t r at a . U s e S t r a t i f ie d Pr o p o r ti on al R an d om m e t h o d. Departments Employees % share # Samples units Administrative 230 Manufacturing 130 Finance 95 Warehousing 25 Research and Development 10 Totalarrow_forwardFind the Jacobian ∂(x, y) / ∂(u, v) for the indicated change of variables. x = u cos(?) − v sin(?), y = u sin(?) + v cos(?) ∂(x, y) / ∂(u,v)=arrow_forward
- M.a.k.e. .a. .r.e.p.o.r.t. .a.b.o.u.t. .v.o.l.l.e.y.b.a.l.l. .s.c.o.r.e.k.e.e.p.e.r. .a.n.d. .F.o.u.r. .(.t.w.o.). .l.i.n.e. .j.u.d.g.e.s... .P.l.s. .m.a.k.e. .i.t. .d.e.t.a.i.l.e.d. .f.o.r. .m.e. .t.o. .u.n.d.e.r.s.t.a.n.d. .m.o.r.e.,. .g.i.v.e. .e.x.a.m.p.l.e.arrow_forwardC o n s i d e r t h e p a r a b o l a C : z − 4 = − ( x − 2 ) 2 o n t h e x z - p l a n e. 1. F i n d t h e c e n t e r - r a d i u s f o r m o f t h e e q u a t i o n o f t h e s p h e r e h a v i n g a s d i a m e t e r t h e l i n e s e g m e n t j o i n i n g t h e v e r t e x o f C a n d t h e p o i n t P ( − 2 , − 4 , 2 ) . 2. S k e t c h t h e p o r t i o n o f t h e c y l i n d e r w i t h d i r e c t r i x C b e t w e e n t h e p l a n e s y = 0 a n d y = 3 i n t h e f i r s t o c t a n t. 3. G i v e a n e q u a t i o n f o r t h e s u r f a c e o f r e v o l u t i o n g e n e r a t e d w h e n C i s r e v o l v e d a b o u t t h e x - a x i s.arrow_forwardWrite x'' + y^2y' − x^3 = ?sin(t), y'' +(x' +y')^2 −x? = 0 as a first order system of ODEs.arrow_forward
- If w = f(x, y) and x = r cos θ, y = r sin θ, find formulas for ∂w/∂r, ∂w/∂θ, and ∂2w/∂r2.arrow_forwardE q u a t i o n s o f O r d e r O n e: C o e f f i c i e n t s L i n e a r in the T w o V a r i a b l e s A5.2 S o l v e t h e e q u a t i o n s . (x + y − 1)dx + (2x + 2y + 1)dy = 0arrow_forwardThe temperature at a point (x,y,z) is given byarrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning