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matrenka [14]
3 years ago
15

Cw 11.1 backside v. V.

Mathematics
1 answer:
nika2105 [10]3 years ago
3 0

Answers:

10.  28.3 cm²

11. 7.3 cm²

12. P: 32 yds, A: 76.8 sq yds

13. P: 64 units, A: 220.8 units

14.  50.3 cm²

15. 132.7 cm²

16. 9.7 in

17. 5.9 cm

18.  324.08 sq inches.

19. 39 cm²

20. 36.6 cm²

Step-by-step explanation:

10. Find the area of the shaded region.

It's a circle, let's first calculate its area, with the formula A = π * r²

A = π  * 6² = 36 π  = 113.1 cm²

The shaded area has a 90 degrees angle... so it's 1/4 of the whole circle.

The area of the shaded area of this circle is then: 113.1 * 1/4 = 28.275 cm²

Rounded to the tenths, that's of course 28.3 cm²

11. Find the area of the shaded region.

Again, let's first find the area of the complete circle, with A =  π * r²

A =  π * 4² = 16π  = 50.27 cm²

Now, let's find the angle for the shaded area.

A circle has 360 degrees, and we know the angles of 2 segments... so we can easily find the missing angle:

360 - 203 - 105 = 52

The shaded area has an arc of 52 degrees, so we multiply the area of the full circle by 52/360 to get the area of that shaded area:

(50.27 * 52) / 360 = 7.26 cm², rounded to the tenths: 7.3 cm²

12. Find perimeter AND area of this regular polygon.

The figure is a regular octagon (8 sides).

To calculate its perimeter, it's simply 8 times one side, so: 8 * 4 yd = 32 yds

For the area, you can view an octagon as 8 triangles joined together.  In this case, we have a base of 4 yds and a height of 4.8 yds, so the area of each triangle is: (4 * 4.8) /2 = 9.6, the total area of the octagon is then 8 * 9.6 = 76.8 yds

13. Find perimeter AND area of this regular polygon.

The figure is a regular octagon (8 sides).

To calculate its perimeter, it's simply 8 times one side, so: 8 * 8 = 64 units

For the area, you can view an octagon as 8 triangles joined together.  In this case, we have a base of 4 yds and a height of 4.8 yds, so the area of each triangle is: (8 * 6.9) /2 = 27.6, the total area of the octagon is then 8 * 27.6 = 220.8 units

14. Find the area of a circle of <u>radius</u> = 4 cm

We have a circle with a radius of 4 cm, we need to find its area.

The area of a circle is obtained by the formula: A = π * r²

We already have the value of r, so we will input it in the formula:

So, we'll have A = π * 4² = 16 * π = 50.27 cm²

Rounded to the tenths: 50.3 cm²

15. Find the area of a circle of <u>diameter</u> 13 cm

We have a circle with a diameter of 13 cm, we need to find its area.  To use the formula for the area, we need the radius, not the diameter.  Since the diameter is 13 cm, the radius is 6.5

The area of a circle is obtained by the formula: A = π * r²

So, we'll have A = π * 6.5² = 42.25 * π = 132.73 cm²

Rounded to the tenths: 132.7 cm²

16. Find the diameter of a circle with an area of 75 in².

We just used the area formula for a circle, based on the radius.  We'll process it in reverse from the area to get the radius... which will give us the diameter, so r² = A / π

We then have:  r² = 75 / π = 23.87

So, r = 4.88 (square root of 23.87), which we double to get the diameter: 9.76 in, rounded to 9.7 in.

17. Find the radius of a circle with an area of 108 cm².

We just used the area formula for a circle, based on the radius.  We'll process it in reverse from the area to get the radius, so r² = A / π

If we input the area given in the question into the formula, we have:  r² = 108 / π = 34.38 cm

So, r = 5.86 (square root of 34.38), rounded to 5.9 cm.

18. Find the area

We have here a half-circle with a triangle.

We just used the formula for the area of a circle, and we know the radius of that half-circle: 8 inches.

A = π * 8² = 64 * π = 201.06 sq inches, for the whole circle.

But we only have half of it, so 201.06 / 2 = 100.08 sq inches.

Now the triangle.  To calculate the area of a triangle, you multiply its base by its height, then you divide by 2, so:

A = 16 x 28 = 224 sq inches.

Which we add to the half-circle area (100.08 sq inches) to get 324.08 sq inches. So 324.1 sq inches once rounded to the tenths.

19. Find the area

We have a triangle on top of a rectangle.

Area of a triangle: (base * height) / 2.

Area of a rectangle: base * height

So, for the triangle: A = (6 * 3) / 2 = 9 cm²

And for the rectangle: A = 6 * 5 = 30 cm²

Total: 9 + 30 = 39 cm²

20. Find the area

We have a rectangle and a half circle.  The radius of the half-circle is: 2 cm (half of the height of the rectangle).

Area of the rectangle: base * height, so 6 * 4 = 24 cm²

Area of the circle:  π * r² = π * 2² = 4π = 12.56 cm²

Total for the figure: 24 + 12.56 = 36.56, or 36.6 cm² once rounded.

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Jorden leaves home for school on his bike everyday at 6:00 AM, traveling at 32 km/h. one day he forgot his homework, which his m
densk [106]

Answer:

She caught up with Jordan at 6:39 AM

Step-by-step explanation:

We solve this question making linear functions for the distances that Jorden and his mom have driven, and then we equalize them to find the moment they caught up.

Jorden leaves home for school on his bike everyday at 6:00 AM, traveling at 32 km/h.

Her mom will have left 15 minutes after he left, when he will already have traveled \frac{15*32}{60} = \frac{32}{4} = 8\text{km}

So, his position after t minutes can be modeled by the following function:

J(t) = 8 + 32t

His mom

His mom goes after him starting from home, so the initial position is 0, with a velocity of 52 km/h. So her position can be modeled by the following function:

M(t) = 52t

At what time did she catch up with Jorden,

She catches up t minutes after 6:15 AM.

t is found when

M(t) = J(t)

So

8 + 32t = 52t

20t = 8

t = \frac{8}{20}

t = 0.4

0.4 of an hour is 0.4*60 = 24 minutes.

So she catched up with Jordan after 6:15 AM + 24 minutes = 6:39 AM

4 0
2 years ago
Which of the following would eliminate the variable on the left side of the given equation? 36 - 19w = -6w + 41.  1. add -19w  2
Paladinen [302]
W=5/13 you just eliminate the negative sign
5 0
3 years ago
Drag the tiles to the correct boxes to complete the pairs.
Delvig [45]

16/-8=-2

Whenever dividing a -negative number and +positive number= number will be always -

3  3/7 / 1  1/7= 24/7 *7/8= 3 ( Cross out 7 and 7, divide by 1). Cross out 8 and 24 and divide by 8) ( Also always flip over the second fraction only when dividing)

3 3/7= 24/7 because multiply the denominator and whole number. 3*7=21

Add 21 with the numerator (3)= 21+3=24

-12.2 / (-6.1)=2

Whenever dividing two - negative numbers= + positive number

-2 2/5 / 4/5= -12/5*5/4=-3 Cross out 5 and 5- divide by 5. Cross out 4 and -12, divide by 4

Answers:

- 2 = 16/-8=-2

3= 3  3/7 /( dividing )1 1/7= 3

2= -12.2 / (-6.1)=2

-3=-2 2/5 / ( dividing) 4/5=-3

6 0
3 years ago
Read 2 more answers
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
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