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2 years ago

In radian measure, the angles of a 30-60-90 triangle are;

Mathematics

1 answer:

blagie [28]2 years ago

7 0

We know that
180 degrees is equal to pi radians
so
for 30 degrees
180°--------> pi radians
30°--------> x
x=30*pi/180------> x=pi/6 radians

for 60 degrees
180°--------> pi radians
60°--------> x
x=60*pi/180------> x=pi/3 radians

for 90 degrees
180°--------> pi radians
90°--------> x
x=90*pi/180------> x=pi/2 radians

the answer is the option c
pi/6,pi/3,pi/2

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Answer:

IV. A+{1, 2, 3, 6, 12}

Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

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1 year ago

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more tha

Fofino [41]

Answer:

Largest possible length is <em>21 inches</em>.

Step-by-step explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length = $l$ inches and

Width = $w$ inches

As per given condition:

$l = 2w+3$ ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

$P = 2 \times (Width + Length)$

Putting the given values and conditions as per equation (1):

$60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch$

Putting in equation (1):

$l = 2\times 9+3\\\Rightarrow l = 21\ inch$

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Largest possible length is <em>21 inches</em>.

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2 years ago

Consider a single spin of the spinner.

alex41 [277]

Answer:

"landing on a shaded portion and landing on a 3"

"landing on an unshaded portion and landing on a number less than 2 "

Step-by-step explanation:

Mutually exclusive means the events will have no intersection.

Let's look at your first choice:

"landing on a shaded portion and landing on an even number"

Landing on a shaded portion would be 1 or 4.

Landing on an even number would be 2 or 4.

There is an intersection (they contain a common element), the 4.

These events are not mutually exclusive.

Let's look at your second choice:

"landing on a shaded portion and landing on a number greater than 3"

Landing on a shaded portion would be 1 or 4.

Landing on a number greater than 3 would be just 4.

There is an intersection; they both contain 4.

These events are not mutually exclusive.

Let's look at your third choice:

"landing on a shaded portion and landing on a 3"

Landing on a shaded portion would be 1 or 4.

Landing on 3 would just be 3.

There is no common elements in the lists listed. These events have no intersection.

These events are mutually exclusive.

Let's look at your fourth choice:

"landing on an unshaded portion and landing on an odd number"

Landing on a unshaded portion would be 2 or 3.

Landing on an odd number would be 1 or 3.

There is an intersection; they both have 3 in common.

These events are not mutually exclusive.

Let's look at your fifth choice:

"landing on an unshaded portion and landing on a number less than 2 "

Landing on an unshaded portion would 2 or 3.

Landing on a number less than 2 would be 1.

There is no intersection.

These events are mutually exclusive.

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2 years ago

Read 2 more answers

Which statements are true about circle Q? Select three options. The ratio of the measure of central angle PQR to the measure of

kkurt [141]

Answer:

<h3>- The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth. </h3><h3>- The area of the shaded sector depends on the length of the radius. </h3><h3>- The area of the shaded sector depends on the area of the circle</h3>

Step-by-step explanation:

Given central angle PQR = 45°

Total angle in a circle = 360°

Ratio of the measure of central angle PQR to the measure of the entire circle is $\frac{45}{360} = \frac{1}{8}$ . This shows ratio that <u>the measure of central angle PQR to the measure of the entire circle is one-eighth</u>.

Area of a sector = $\frac{\theta}{360}*\pi r^{2}$

$\theta$ = central angle (in degree) = 45°

r = radius of the circle = 6

Area of the sector

$= \frac{45}{360}*\pi (6)^{2}\\ = \frac{1}{8}*36 \pi\\ = 4.5\pi units^{2}$

<u>The ratio of the shaded sector is 4.5πunits² not 4units²</u>

From the formula, it can be seen that the ratio of the central angle to that of the circle is multiplied by area of the circle, this shows <u>that area of the shaded sector depends on the length of the radius and the area of the circle.</u>

Since Area of the circle = πr²

Area of the circle = 36πunits²

The ratio of the area of the shaded sector to the area of the circle = $\frac{4.5\pi }{36 \pi } = \frac{1}{8}$

For length of an arc

$= \frac{45}{360}*2\pi r\\= \frac{45}{360}*2\pi (6)\\= \frac{45}{360}*12 \pi \\= \frac{12\pi }{8} \\= \frac{3\pi }{2} units$

ratio of the length of the arc to the area of the circle = $\frac{\frac{3\pi}{2} }{36\pi} = \frac{3}{72} =\frac{1}{24}$

It is therefore seen that the ratio of the area of the shaded sector to the area of the circle IS NOT equal to the ratio of the length of the arc to the area of the circle

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2 years ago

Read 2 more answers