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Mathematics Questions & Answers

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1. \( a^{2}-2 a b+b^{2} \)
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ASK YOUR TEACHER \( [ \) PRACTICE ANOTHER \( \frac{4}{1-\sqrt{3}} \) Simplify by rationalizing the denominator. \( \frac{4}{2} \)
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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. \( 8 y=5 x \). Direct variation Constant of variation: \( k=\square \) Neither variation
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b. Para hallar la altura de un globo, se realizaron las mediciones indicadas en la figura. ¿Cuánto dista el slobo del punto \( A \) ? ¿Cuánto del punto \( B \) ? ¿A que altura está el globo?
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What value of \( b>-1 \) maximizes the integral? \( \int_{-1}^{b} x^{2}(4-x) d x \)
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Al reducir la expresión CscaTanaCosa-Csc \( 2 a ~ a ~ u n a ~ s o l a ~ f u n c i o ́ n ~ t r i g o n o m e ́ t r i c a ~ s e ~ o b t i e n e: ~ \) \( 2 \operatorname{sen}^{2} a \) \( -\sec ^{2} a \) \( -\cot ^{2} a \)
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\( 7 x=\frac{14}{y} \) Direct variation Constant of variation: \( k=\square \) Inverse variation Constant of variation: \( k=\square \) Neither
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Simplify the following expression by rationalizing the denominator. \( \frac{6+\sqrt{5}}{2-\sqrt{5}} \)
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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: \( \sin (5 \theta)=\cos \left(\theta-40^{\circ}\right) \)
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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: \( k=\square \)
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