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antoniya [11.8K]
3 years ago
12

The price of a notebook was $3.70 yesterday. Today, the price fell to $3.20 . Find the percentage decrease. Round your answer to

the nearest tenth of a percent.
Mathematics
1 answer:
mario62 [17]3 years ago
6 0

Answer:

13.5% Decrease

Step-by-step explanation:

Use formula (change in value / original value) * 100

Change in value = 3.70 - 3.20 =0.50 Change in value is 0.50

Original Value = 3.70

Use the formula (0.50/3.70) * 100 = 13.5 % Decrease

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A piece if wire 40cm is bent to form a right angled triangle whose hypotenuse is 17cm long find the other two sides of triangle
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Answer: 150mm

Step-by-step explanation:

Take the two adjecent sides of the triangle to be x and y and X is the angle opposite the side, x.

From the trigonometric identities for a right-angled triangle, it is known that

x=170sin X and;

y=170cos X

Thus the perimeter of the triangle is given by

170sin X + 170cos X + 170 = 400

170(sin X + cos X) = 400 - 170

170(sin X + cos X) = 230

sin X + cos X = 230/170 = 1.3529

Squaring both sides hence,

sin^2(X) + 2sin X.cos X + cos^2(X) = 1.8304

Recall that sin^2(X) + cos^2(X) = 1 and 2sin X.cos X = sin 2X.

Thus, the former expression gives;

1 + sin 2X = 1.8304

sin 2X = 0.8304

2X = arcsin (0.8304)

2X = 56.14° or (180 - 56.14)° = 56.14° or 123.86° for X existing within a triangle.

X = 56.14/2 or 123.86/2

X = 28.07° or 61.93°

Thus the two adjacent sides are ;

x = 170 sin (28.07) = 80mm

y = 170 cos (28.07) = 150mm

Using the value of 61.93° as X would give the same values but interchanged for x and y.

I hope you find this useful.

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Step-by-step explanation:

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