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Mathematics Questions & Answers

Q:
Simplify the following expression by rationalizing the denominator. \( \frac{6+\sqrt{5}}{2-\sqrt{5}} \)
Q:
value of: \( \frac{\sin \theta+\cos \theta}{2 \sin \theta} \) without using a calculator. \( 4.2 .1 \tan \left(-32^{\circ}\right) \) \( 4.2 .2 \sin 412^{\circ} \) Simplify the following fully and without using a calculator: \( \frac{\sin 120^{\circ} \cdot \tan 300^{\circ}}{\cos \left(-60^{\circ}\right) \cdot \tan 225^{\circ}} \) Prove the following identity: \( \frac{\cos 2 x-\cos x-\sin x}{2 \sin x \cos x+\sin x}=\frac{1}{\tan x}-\frac{1}{\sin x} \) Determine the general solution of: \( \sin (5 \theta)=\cos \left(\theta-40^{\circ}\right) \)
Q:
Eor each equation, determine whether it represents a direct variation, an inverse variation, or neither. Find the constant of variation when one exists and write it in simplest form. \( -3 x+\delta y=-1 \) Constant of variation: \( k=\square \) Dinverse variation Constant of variation: \( k=\square \)
Q:
21. Una caja tiene 60 bombones. Eva se comió \( \frac{1}{5} \) de la caja y Ana \( \frac{1}{2} \). ¿Qué fracción de bombones queda? A) \( \frac{3}{10} \) B) \( \frac{5}{10} \) C) \( \frac{3}{10} \)
Q:
La distancia desde el punto \( Q(1,5,-4) \) al plano dado por \( 3 x-y+2 z=6 \) es: 4.2762 1.0690 1.1547 4.6188
Q:
Let \( H(x)=\int_{0}^{x} \sqrt{64-t^{2}} d t \), for \( -8 \leq x \leq 8 \) a. Evaluate \( H(0) \) b. Evaluate \( H^{\prime}(3) \) c. Evaluate \( H^{\prime}(8) \) d. Use geometry to evaluate \( H(8) \) e. Find the value of \( s \) such that \( H(x)=s H(-x) \).
Q:
\( \left\lvert\, \begin{array}{l}-5 x+4 y=-3 \\ \text { Direct variation } \\ \text { Constant of variation: } \quad k=\square \\ \text { Inverse variation } \\ \text { Constant of variation: } \quad k=\square \\ \text { Neither }\end{array}\right. \)
Q:
Multiply the following binomials. \[ \left(b+\frac{8}{5}\right)\left(b+\frac{2}{5}\right) \]
Q:
La distancia desde el punto \( Q(3,-1,4) \) a la linea dada por \( x=-2+3 t, y=-2 t y z=1+4 \) tes: 2.4495 2.2014 5.0200 - 5.3104
Q:
For each equation, determine whether it represents a direct variation, an Inverse variation, or neither. Find the constant of variation when one exists and write it in simplest form. \( 16 x+2 y=0 \) Direct variation Constant of variation: \( \quad k=\square \) Inverse variation Constant of variation: \( \quad k=\square \)
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