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3 years ago

I need help with these questions (see image). Please show workings.

Mathematics

2 answers:

Anton [14]3 years ago

5 0

Answer:

24 cm

Step-by-step explanation:

The chord, if the ends connected with the center, form an isosceles triangle with two sides being a radius of the circle.

We have:

Length of chord = x
Height of triangle = h = 5 cm
Radius = r = 26/2 = 13 cm

From the triangle we get:

(x/2)² + h² = r²
x²/4 + 5² = 13²
x²/4 = 144
x/2 = 12
x = 24

The length of the chord is 24 cm

denpristay [2]3 years ago

4 0

Answer:

24 cm

Step-by-step explanation:

The altitude from the centre to the chord is 5 cm and bisects the chord.

The radius of the circle is 26 cm ÷ 2 = 13 cm

There is a right triangle formed with legs 5 and x ( x is half the chord )

The hypotenuse is the radius, then using Pythagoras' identity

x² + 5² = 13²

x² + 25 = 169 ( subtract 25 from both sides )

x² = 144 ( take the square root of both sides )

x = $\sqrt{144}$ = 12

Then

length of chord = 2x = 2 × 12 = 24 cm

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3 years ago

The area of a circular oil slick on the surface of the sea is increasing at a rate of [150m^2/s] how fast is the radius changing

Akimi4 [234]

Answer with Step-by-step explanation:

We are given that

$\frac{dA}{dt}=150m^2/s$

a.Radius =25 m

We have to find rate of change of radius.

We know that

Area of circle, $A=\pi r^2$

Differentiate w.r.t time

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

Substitute the values then we get

$150=2\pi (25)\frac{dr}{dt}$

$\frac{dr}{dt}=\frac{150}{50\pi}=\frac{3}{\pi} m/s$

$\frac{dr}{dt}=\frac{3}{\pi} m/s$

b.A= $1000m^2$

Substitute the values then we get

$1000=\pi r^2$

$\pi=3.14$

$r^2=\frac{1000}{3.14}$

$r=\sqrt{\frac{1000}{3.14}}=17.8m$

$\frac{dA}{dr}=2\pi r\frac{dr}{dt}$

Substitute the values then we get

$150=2\pi(17.8)\frac{dr}{dt}$

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4 0

2 years ago

I need help with these questions (see image). Please show workings.​

I need help with these questions (see image). Please show workings.