In parallelogram RSTU, what is SU?

Find the area of a circle whose radius is 12 in. Round to the nearest 10

Ksivusya [100]

Answer:

Area = pi r²

area = 22/7 × 12 × 12 = 452.57 in²

7 0

3 years ago

Two angles of a triangle measure 48° and 97°. If the longest side is 12 cm, find the length of the shortest side to the nearest

sladkih [1.3K]

Answer:

B) 6.9 cm

Step-by-step explanation:

The remaining angle is the smallest, 180° -48° -97° = 35°. The shortest side is opposite this angle. The Law of Sines tells you its length is ...

short side = (longest side)·(sin(smallest angle)/sin(largest angle))

= (12 cm)sin(35°)/sin(97°) ≈ 6.9 cm

The shortest side is about 6.9 cm.

6 0

4 years ago

Will mark brainliest! Can something pls help me answer these showing there work? I offer 15 points

wariber [46]

Answer:

a) Third Quadrant

b) 7π/4 --> Option (4)

c) $-\frac{\sqrt{3} }{2}$ --> Option (1)

d) 1 --> Option (1)

e) $\frac{\sqrt{2} }{2}$ --> Option (2)

f) - $\frac{1}{2}$ --> Option (2)

g) $\frac{3}{2}$ --> Option (1)

h) $-\frac{\sqrt{3} }{2}$ --> Option(2)

Step-by-step explanation:

Ok, lets properly define some technical term here.

The terminal side of an angle is the side of the line after that it has made a turn (angle). I will drive my point home with the attachment to this solution

The initial side of an angle is the side of the line before the line made a turn(angle)

a) 1 complete revolution = $360^{0}$ = 2π rads

we can convert the radians to degrees using the above conversion rate

=> $\frac{7π}{6} rad \to degrees$ will be: $\frac{\frac{7π}{6} * 360}{2π}$

solving the expression above, 420π/2π = $210^{0}$

From the value of the angle in degree and having in mind that

$0^{0} - 90^{0} \to first \ quadrant\\ \\91^{0} - 180^{0} \to second\ quadrant\\\\181^{0} - 270^{0} \to third\ quadrant\\\\271^{0} - 360^{0} \to fourth\ quadrant$

$\frac{7π}{6} rad = 210^{0} \ is \ in \ third \ quadrant\\$

b) Co-terminal angles are angles which share the same initial and terminal side

To find the co-terminal of an angle we add or subtract 360 to the value if in degrees or 2π if in radians. From the value we want to find its co-terminal, because of the presence of π, its value is in radians and as such we add or subtract 2π from the value. If we perform subtraction, the negative co-terminal of the angle has been evaluated and the positive co-terminal is evaluated if we perform addition.

So, to get the positive co-terminal of -π/4, we add 2π and doing that, we get:

2π - π/4 = 7π/4

c) The value of sin(π/3) * cos(π) is ?

Applying special angle properties: (More on the special angle in the diagram attached to this solution)

sin(π/3) = $\frac{\sqrt{3} }{2}$

cos(π) = -1

substituting the values above into the expression, we have:

$\frac{\sqrt{3} }{2} * -1 = -\frac{\sqrt{3} }{2}$

d) if $f(x) = sin^{2}x + cos^{2} x$ , f(π/4) = ?

In trignometry, $sin^{2}x = (sin(x))^{2} ;\ cos^{2}x = (cos(x))^{2}$

Applying special angle properties again,

sin(π/4) = $\frac{\sqrt{2} }{2}$

cos(π/4) = $\frac{\sqrt{2} }{2}$

The expression becomes $(\frac{\sqrt{2} }{2} )^{2} + (\frac{\sqrt{2} }{2} )^{2}$ . Simplifying, we get:

2/4 + 2/4 = 1/2 + 1/2 = 1

e) cos(3π/4)

3π/4 is not an acute angle(angle < less than π/2 rad) and as such, we need to get its related acute angle. Now 3π/4 rads is in the second quadrant, this means that we will have to subtract 3π/4 from π to get the related acute angle.

π - 3π/4 = π/4

so instead of working with 3π/4, we work with its related acute angle which is π/4

cos(3π/4) is equivalent to cos(π/4) = $\frac{\sqrt{2} }{2}$ (special angle properties)

f) sin(11π/6)

11π/6 is not an acute angle(angle less than π/2 rad) and it is in the fourth quadrant. This means that to get its related acute angle, we have to subtract it from 2π

2π - 11π/6 = π/6

sin(11π/6) is equivalent to -sin(π/6) = -1/2 (special angle properties).

Note that there is a minus in the answer. That had nothing to do with the special angle properties but rather, the fact that:

At the fourth quadrant, only the cosine trignometric ratio is positive
At the first quadrant, all trignometric ratios are positive
At the second quadrant, only the sine trignometric ratio is positive
At the third quadrant, only the tangent trignometric ratio is positive

g) sin(π/6) + tan(π/4)

using special angle properties:

sin(π/6) = 1/2 and tan(π/4) = 1

the expression simplifies to: 1/2+1 = 3/2

h) cos(4π/3)

4π/3 is not an acute angle and it is in the third quadrant

To get its related acute angle, we have to subtract it from 3π/2

3π/2 - 4π/3 = π/6

so, cos(4π/3) = -cos(π/6) (The negative value is because of the fact that at the third quadrant, only the tangent trignometric ratio is positive)

using special angle properties, -cos(π/6) = $-\frac{\sqrt{3} }{2}$

7 0

3 years ago

A rectangular room is 3 times as long as it is wide and it’s perimeter is 56 m find the dimension of the room the length and wid

Lady bird [3.3K]

Answer:

Width = 3x So,

Length = x 3w + w = 56/2 = 28

3x + x = 4x

56 / 4 = 14 w = 7

x = 14

14 x 3 = 42

Answer: 42 meters Answer: dimension- 7 meters

6 0

3 years ago

Pls help with number 7,8,9 and 10

ella [17]

The answers to all the subparts of the multiplication problem are shown:

185 × 24 = 4440
1288 × 33 = 42504
6301 × 47 = 296147
3440 × 75 = 285000

<h3>What is multiplication?</h3>

Multiplying in math is the same as adding equal groups.
The number of items in the group grows as we multiply.
Parts of a multiplication issue include the product, the two factors, and the product.
The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

So, multiplication of the numbers:

185 × 24 = 4440
1288 × 33 = 42504
6301 × 47 = 296147
3440 × 75 = 285000

(Refer to the images attached below for calculations)

Therefore, the answers to all the subparts of the multiplication problem are shown:

185 × 24 = 4440
1288 × 33 = 42504
6301 × 47 = 296147
3440 × 75 = 285000

Know more about multiplication here:

brainly.com/question/10873737

#SPJ13

7 0

1 year ago