From 590b61cdc1120315197f65dd780c919b6e13e385 Mon Sep 17 00:00:00 2001
From: thing1 <thing1@seacrossedlovers.xyz>
Date: Mon, 24 Mar 2025 18:35:17 +0000
Subject: maths and comp sci

---
 maths/hw/eq17/eq17.ms | 90 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 maths/hw/eq17/eq17.ms

(limited to 'maths/hw/eq17/eq17.ms')

diff --git a/maths/hw/eq17/eq17.ms b/maths/hw/eq17/eq17.ms
new file mode 100644
index 0000000..850bbdc
--- /dev/null
+++ b/maths/hw/eq17/eq17.ms
@@ -0,0 +1,90 @@
+.TL
+Exam Questions 17
+.AU
+Lucas Standen
+.AI
+QMC
+
+.PP
+1)a)
+
+.EQ
+dx over dt = 2cos(t)
+.EN
+
+.EQ
+dy over dt = 2sin(2t)
+.EN
+
+.EQ
+dy over dx = 2cos(t) over 2sin(2t)
+.EN
+
+.EQ
+"when " t = pi over 6
+.EN
+
+.EQ
+dy over dx = {2cos({pi over 6})} over {2sin(2({pi over 6}))}
+.EN
+
+.EQ
+dy over dx = 1
+.EN
+
+.PP
+1)b)
+
+.EQ
+x = 2sin(t) 
+.EN
+
+.EQ
+x over 2 = sin(t)
+.EN
+
+.EQ
+1 = cos(2t)
+.EN
+
+.EQ 
+1 = 1 - cos sup 2 (t)
+.EN
+
+.EQ 
+y = cos sup 2 (t)
+.EN
+
+.EQ
+({x over 2}) sup 2 + y sup 2 = 1
+.EN
+
+.EQ
+{x over 4} sup 2 + y sup 2 = 1
+.EN
+
+.EQ
+{x over 4} sup 2 - 1 = - y sup 2 
+.EN
+
+.EQ
+- {x over 4} sup 2 + 1 = y sup 2 
+.EN
+
+.EQ
+sqrt {- {x over 4} sup 2 + 1} = y sup 2 
+.EN
+
+.EQ
+-2 <= x <= 2 
+.EN
+
+.PP
+1)c)
+
+.EQ
+0 <= f(x) <= 1
+.EN
+
+
+
-- 
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