1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tpy6a [65]
2 years ago
15

Can someone help me with these problems please! Im so confused

Mathematics
1 answer:
Schach [20]2 years ago
8 0

Step-by-step explanation:

why are you confused ?

the question is to get the area of the shaded (= grey) areas.

all the shapes are clearly combined shapes out of several basic shapes, and in some cases we need to add then, and in some we need to subtract them from each other (to eliminate any white content).

that is really all that needs to be done.

of course, it is important to notice the different metrics used for the lengths, which define the metrics to be used for the areas.

a.

a rectangle and 2 half-circles on the sides (they are together one full circle).

radius is always 1/2 of the diameter of a circle.

and the width of the rectangle is exactly the diameter (= 2×radius) of the circle(s).

grey area :

rectangle : 20×(6×2) = 20×12 = 240 m²

circle : pi×r² = pi×6² = pi×36 = 113.0973355... m²

in total :

240 + 113.0973355... = 353.0973355... m²

b.

a trapezoid minus a circle.

the area of a trapezoid is

(a+b)×h/2

and h (height) is again the diameter of the circle (2×radius).

grey area :

trapezoid : (9 + 15)(4×2)/2 = 24 × 4 = 96 ft²

circle : pi×r² = pi×4² = pi×16 = 50.26548246... ft²

in total :

96 - 50.26548246... = 46.26548246... ft²

c.

3 rectangles.

rectangle1 - rectangle2 + rectangle3.

grey area :

rectangle1 : 14×10 = 140 m²

rectangle2 : 10×6 = 60 m²

rectangle3 : 6×2 = 12 m²

in total :

140 - 60 + 12 = 92 m²

d.

a circle minus a square.

the only specialty here is the diameter and radius of the circle : the diagonal of the inner square.

we get the diagonal of the inner square via Pythagoras, because the diagonal makes 2 right-angled triangles out of the square.

diagonal² = 4² + 4² = 16+16 = 32

diagonal = sqrt(32)

radius = diagonal/2 = sqrt(32)/2 = sqrt(32/4) = sqrt(8)

grey area :

square : 4×4 = 16 cm²

circle : pi×r² = pi×(sqrt(8))² = pi×8 = 25.13274123... cm²

in total :

25.13274123... - 16 = 9.132741229... cm²

is there still anything unclear ?

please let me know.

but as you can see there is no need to panic. just use basic math and common sense.

You might be interested in
What happens to the distance between each billiard ball during this rigid<br><br> transformation?
Delicious77 [7]

The question is incomplete. Here is the complete question.

To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?

A. The distance remains constant throughout the transformation.

B. The distance decreases at the start and increases after all motion stops.

C. The distance stays the same at the start but decreasesexactly when motion ends.

D. The distance increases at the start and then decreases as the rack gets further from the player.

Answer: A. The distance remains constant throughout the transformation.

Step-by-step explanation: In a <u>rigid</u> <u>motion</u>, all moving points in the plane are moving in way such tha:

1)  relative distance between them stays the same and

2) relative position of the points stays the same

There are four types of rigid motions: translation, rotation, reflexion and glide reflection.

<u>Translation</u>: every point or object is moved by the same amount and in the same direction;

<u>Rotation</u>: the object rotates by the same amount around a fixed point;

<u>Reflexion</u>: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;

<u>Glide</u> <u>Reflection</u>: is a mirror reflection followed by a translation parallel to the mirror.

In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.

Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.

6 0
2 years ago
What is the value of the underlined digit in 16,403
Ilia_Sergeevich [38]
If the 1 were underlined it would be 10,000
If the 6 were underlined it would be 6,000
If the 4 were underlined it would be 400
If the 0 were underlined it would be 0
If the 3 were underlined it would be 3

8 0
3 years ago
True or False: In order to solve an equation, we must isolate the variable.
vaieri [72.5K]

Answer:

It is False

But it's not true

3 0
2 years ago
Read 2 more answers
3/8 + 1/4 + 1/2 - 2/3 =
Nostrana [21]

Answer:

\frac{11}{24}

Step-by-step explanation:

3/8 + 1/4 + 1/2 - 2/3

- > 1/4 =  2/8

3/8 + 2/8 + 1/2 - 2/3

5/8 + 1/2 - 2/3

- > 1/2 = 4/8

5/8 + 4/8 - 2/3

9/8 - 2/3

- > LCM of 8,3: 24

- > 9/8 = 27/24

- > 2/3 = 16/24

27/24 - 16/24

11/24

Hope this helps you.

7 0
3 years ago
Solve by square rooting : 3(X+2)^2:8​
dolphi86 [110]

The value of x is √8/3 - 2

Step by step explanation:

The given equation is

3(x+2)^2=8

To find x,

(x+2)²= 8/3

By taking square root on both sides

x+2= √8/3

x=√8/3 -2

x= -0.37

Thus the square root for the given value is -0.37

3 0
3 years ago
Other questions:
  • F(x) = -3x – 1<br> g(x) = 3x2 – 5x + 14<br> Find: f(g(x))
    11·1 answer
  • What are the slope and the Y intercept of the linear fractionThat is represented by the equation y= - 10x + 1
    6·2 answers
  • Giving 20 points ;(((((()
    8·2 answers
  • True or False if you took a true if then statement and inserted a not in each clause the new statement would also be true
    9·1 answer
  • Find the surface area of the regular pyramid
    7·1 answer
  • Kayla bought three pounds of strawberries for $14.40 what is the price in dollars per ounce of strawberries.
    14·1 answer
  • WHAT I KNOW?
    14·2 answers
  • A map show a town with an area of 3.5 inches.If the map has a scale of 1 inch:4 miles,what is the actual area of the town?
    11·1 answer
  • An altimeter records the height of a stunt man as he jumps from an airplane at
    9·1 answer
  • Question 5 of 5 Which inequality is true? O A. 1 - 3 &gt; 1 O B. B. &gt; 1 O C. 97 &gt; 27 D. TI +7 &lt; 10 SUBMIT​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!