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Stels [109]
3 years ago
6

The lengths of the sides of a triangle are in the extended ratio 5 ?: 9 ?: 10. The perimeter of the triangle is 48 cm. What are

the lengths of the? sides?
Mathematics
2 answers:
alexandr402 [8]3 years ago
6 0
A=10, B=18, C=20 are the lengths of the sides
Burka [1]3 years ago
5 0

Answer:

The correct answer is: a = 10 cm, b = 18 cm and c = 20 cm

Step-by-step explanation:

We will use triple proportion:

a : b : c = 5 : 9 : 10     from which is:

a = 5 k , b = 9 k and c = 10 k  where k is coefficient of proportion.

Formula for perimeter is:

P = a + b + c

When we replace value for a = 5 k , b = 9 k and c = 10 k in the formula for P we get:

5 k + 9 k + 10 k = 48  => 24 k = 48 => k = 48/24 = 2

Finally we get:

a = 5 · 2 = 10 cm

b = 9 · 2 = 18 cm

c = 10 · 2 = 20 cm

God with you!!!

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What complex number is represented by the polar coordinates (4, -pi/4)
nexus9112 [7]

Answer:

\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}

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