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gavmur [86]
3 years ago
9

Ismail tried to prove that sin(θ) = cos(90°− θ) using the following diagram. His proof is not correct.

Mathematics
1 answer:
Anton [14]3 years ago
5 0

Answer:

  • C. Ismail used the wrong sides in his ratio for cos (90 - θ)

Step-by-step explanation:

<u>All steps correct apart from:</u>

  • cos (90° - θ) = AC/BC

<u>It should be</u>

  • cos (90° - θ) = AB/BC

Correct choice is C

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A piece of cardboard measures 10 ft by 10 ft. Four equal squares of size x are removed from the corners. After removing the squa
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Answer:

The value of x would be \frac{5}{3}

Step-by-step explanation:

Given,

The dimension of the cardboard = 10 ft by 10 ft,

∵ After removing four equal squares of size x ( in ft ) from the corners,

The dimension of the resultant box would be,

Length = ( 10 - 2x ) ft,

Width = ( 10 - 2x ) ft,

Height = x ft,

The volume of box,

V=(10-2x)\times (10 - 2x)\times x=x(10-2x)^2 = x(100 - 40x + 4x^2)=100x - 40x^2 + 4x^3

Differentiating with respect to x,

V'=100 - 80x + 12x^2

Again differentiating with respect to x,

V''=-80 + 24x

For maxima or minima,

V'=0

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\implies 3x^2 - 20x + 25=0

By quadratic formula,

x=\frac{20\pm \sqrt{20^2-4\times 3\times 25}}{6}

x=\frac{20\pm \sqrt{400 - 300}}{6}

x=\frac{20\pm \sqrt{100}}{6}

x=\frac{20\pm 10}{6}

\implies x = \frac{10}{6}=\frac{5}{3}\text{ or } x = 5

For x = 5/3, V'' = negative,

While for x = 5, V'' = Positive,

Hence, the value of x would be 5/3 ft for maximising the volume.

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