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2 years ago

The diagram shows a right-angled triangle.

Mathematics

1 answer:

amm18122 years ago

4 0

The length of the hypotenuse and the opposite side to angle x of the right triangle are 8 cm and 3 cm respectively, which gives angle x as approximately 22.0°

<h3>Which of the trigonometric ratios can be used to find x°?</h3>

A description of the parts of the triangle are;

Length of the hypotenuse side = 8 cm

Length of the opposite side to x° = 3 cm

The trigonometric ratio of the sine of x° is presented as follows;

$sin(x) = \frac{Opposite}{Hypotenuse}$

Therefore;

$sin(x) = \frac{3}{8}$

Which gives;

${x}^{ \circ} = arcsine \left( \frac{3}{8} \right) \approx {22.0}^{ \circ}$

Angle x ≈ 22.0°

Learn more about trigonometric ratios of the cosine, sines, and tangent of angles here:

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3 years ago

1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

Anna11 [10]

Answer:

1.D) Procedure results in a binomial distribution.

2. B) Procedure results in a binomial distribution.

Step-by-step explanation:

The binomial distributions has following properties.

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3 years ago

The standard form of the equation of a circle is (x−5)2+(y−6)2=1.

Crank

Answer:

(A) $x^2+y^2-10x-12y+60=0$

Step-by-step explanation:

The standard form of the equation of a circle is given as:

$(x-5)^2+(y-6)^2=1$

Simplifying the above given equation, we get

$x^2+25-10x+y^2+36-12y=1$

$x^2+y^2-10x-12y+36+25=1$

$x^2+y^2-10x-12y+61=1$

$x^2+y^2-10x-12y+60=0$

which is the required general form of the equation.

Hence, option A is correct.

3 0

3 years ago

A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

3 years ago