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2 years ago

Evaluate (5 sin² 30ᴼ + cos² 45ᴼ - 4 tan² 30ᴼ) / ( 2 sin 30ᴼcos 30ᴼ + tan 45ᴼ)

1 answer:

4 0

Note that
sin(30°) = 1/2
cos(30°) = √3/2
tan(30°) = 1/√3
cos(45°) = 1/√2
tan(45°) = 1

Therefore
5 sin²(30°) + cos²(45°) - 4 tan²(30°)
= 5*(1/4) + 1/2 - 4*(1/3)
= 5/12
= 0.4167

2 sin(30°) cos(30°) + tan(45°)
= 2(1/2)(√3/2) + 1
= 1.866

$\frac{5sin^{2}(30)^{o}+cos^{2}(30^{o})-4tan^{2}(30^{o})}{2sin(30^{o})cos(30^{o})+tan(45^{o})} = \frac{0.4167}{1.866} =0.2233$

Answer: 0.223

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Chance can wash the car in 2 hours, while Sandy can wash the same car in 4 hours. How many hours would it take for them to wash

aliya0001 [1]

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

Number of hours Chance can wash the car = 2 hours

Number of hours Sandy can wash the car = 4 hours

Work done by Chance per hour is given by

$\frac{1}{2}$

Work done by Sandy per hour is given by

$\frac{1}{4}$

Work done by altogether per hour is given by

$\frac{1}{2}+\frac{1}{4}\\\\=\frac{2+1}{4}\\\\=\frac{3}{4}$

So, Number of hours they take if they together wash the car is given by

$\frac{4}{3}$

Hence, First Option is correct.

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2 years ago

Read 2 more answers

Maria has 37 pieces of fruit to make fruit baskets as gifts for her 5 teachers.

agasfer [191]

Answer: The answer would be C

Step-by-step explanation:

37 + 5 = 42

Each teacher needs 8 and there are 5 teachers

5 x 8 = 40

So each teacher can have 8 apples and there will be two left over

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2 years ago

Simplify : 48÷6 [-52 ÷2 {4 - 3 (2 - 15÷3)}]

garri49 [273]

Answer:

Step-by-step explanation:

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1 year ago

A rectangle has a length that is three feet more than twice it's width. The perimeter of the rectangle is 78 feet. State the val

ivann1987 [24]

Let the width of the rectangle be 'w'

According to the question length of the rectangle (l) is three feet more than twice it's width;

$\longrightarrow$ l = (2w + 3) ft

Perimeter of rectangle = 78 ft

Formula of perimeter of rectangle = 2(Length + Width)

So,

$\rm \implies 2(Length + Width) = 78 \\ \\ \rm \implies 2(2w + 3 + w) = 78 \\ \\ \rm \implies 2(3w + 3) = 78 \\ \\ \rm \implies 2 \times 3(w + 1) = 78 \\ \\ \rm \implies 6(w + 1) = 78 \\ \\ \rm \implies w + 1 = \dfrac{78}{6} \\ \\ \rm \implies w + 1 = 13 \\ \\ \rm \implies w = 13 - 1 \\ \\ \rm \implies w = 12 \: ft$

$\therefore$ Width of the rectangle (w) = 12 ft

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2 years ago