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KengaRu [80]
3 years ago
12

Max and Sharifa are both saving to buy the same model of DVD player, which costs $99, including tax. Max already has $31.00 and

decides to save $8.50 per week from now on. Sharifa already has $25.50 and decides to save $10.50 per week from now on. Who can pay for the DVD player first? Explain.
(NEED TO SHOW WORK)
Mathematics
1 answer:
gogolik [260]3 years ago
7 0

Answer:

Sharifa can pay for the DVD player first.

Step-by-step explanation:

<u>Max:</u>

99 - 31 = $68 remaining

68 / 8.5 = <em>8 weeks</em>

<u>Sharifa:</u>

99 - 25.5 = $73.50 remaining

73.5 / 10.5 = <em>7 weeks</em>

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baherus [9]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = \frac{\sqrt3}{2}

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}

Proof LHS → RHS:

LHS                          cos 165

Double-Angle:        cos (2 · 165) = 2 cos² 165 - 1

                             ⇒ cos 330 = 2 cos² 165 - 1

                             ⇒ 2 cos² 165  = cos 330 + 1

Given:                        2 \cos^2 165  = \dfrac{\sqrt3}{2} + 1

                              \rightarrow 2 \cos^2 165  = \dfrac{\sqrt3}{2} + \dfrac{2}{2}

Divide by 2:               \cos^2 165  = \dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \dfrac{2\sqrt3+4}{8}

Square root:             \sqrt{\cos^2 165}  = \sqrt{\dfrac{4+2\sqrt3}{8}}

Scratchwork:            \cos^2 165  = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2

                             \rightarrow \cos 165  = \pm \dfrac{\sqrt3+1}{2\sqrt2}

             Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

                             \rightarrow \cos 165  = - \dfrac{\sqrt3+1}{2\sqrt2}

LHS = RHS \checkmark

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4 years ago
The square pyramid has a volume of 768 cubic inches. The height equals 1/6x and the base is just x. What is the value of x ?
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Step-by-step explanation:

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