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2 years ago

Genuinely confused, how would you solve this? (will mark for brainliest!!)

Mathematics

1 answer:

Yanka [14]2 years ago

3 0

Answer:

Length of the bold sector: 40.3ft

Area of the bold sector: 282.08

Step-by-step explanation:

Finding the sector length: Assuming that pi=3.14, the diameter is 87.92 ft. The ratio of the bold section to the whole circumference is 165 to 360. So you need to multiply the circumference by the ratio. (87.92 x 165)/360=40.3

Finding the sector area: Assuming that pi=3.14, the area of the circle is 615.44 sq. ft. The ratio of the sector area to the area of the whole circle is 165:360. (615.44 x 165)/360=282.08, rounded to the nearest 100th.

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2 years ago

A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that la

weeeeeb [17]

Answer:

The correct option is D) $\frac{2}{3}$

Step-by-step explanation:

Consider the provided figure.

We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.

For this first find the total area as shown:

The given figure is a rectangle.

The area of rectangle is $l\times b$

Where, l = 6 cm + 3 cm = 9 cm and b = 5cm

Therefore the area of the rectangle is;

Area of rectangle = $9cm\times 5cm=45cm$

Now find the area of trapezoid.

The area of trapezoid is: $\frac{a+b}{2}h$

Where h is the height and a and b are the parallel sides.

Area of trapezoid = $\frac{9+3}{2}\times 5=30$

Thus, the area of trapezoid is 30 cm.

Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:

$Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}$

$Probability=\frac{30}{45}=\frac{2}{3}$

Hence, the correct option is D) $\frac{2}{3}$

3 0

3 years ago

In the figure below, Ray BD bisects angle ABC

viva [34]

Answer: 65 and 130

Step-by-step explanation:

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3 years ago

Determine the range

irina [24]

Answer:

-4, 2 i don't really know what to do

Step-by-step explanation:

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2 years ago

If (3-4i) (x+yi) = 1 + 0i. The value of x and y is

Black_prince [1.1K]

Step-by-step explanation:

$\textsf{\large{\underline{Solution}:}}$

<h3>Given That:</h3>

$\rm: \longmapsto (3 - 4i)(x + iy) = 1 + 0i$

$\rm: \longmapsto 3(x + iy) - 4i(x + iy)= 1 + 0i$

$\rm: \longmapsto 3x + 3iy - 4ix +4y= 1 + 0i$

On rearranging the terms, we get:

$\rm: \longmapsto (3x + 4y)+ (3y - 4x)i = 1 + 0i$

Comparing both sides, we get:

$\rm: \longmapsto 3x + 4y = 1 --- (i)$

$\rm: \longmapsto 3y - 4x = 0 --- (ii)$

Multiplying (i) by 4, we get:

$\rm: \longmapsto 12x + 16y = 4--- (iii)$

Multiplying (ii) by 3, we get:

$\rm: \longmapsto 9y - 12x = 0 --- (iv)$

Adding equations (iii) and (iv), we get:

$\rm: \longmapsto25y = 4$

$\rm: \longmapsto y =\dfrac{4}{25}$

From (ii), we get:

$\rm: \longmapsto 3y - 4x = 0$

$\rm: \longmapsto 3y = 4x$

$\rm: \longmapsto x = \dfrac{3}{4} y$

$\rm: \longmapsto x = \dfrac{3}{4} \times \dfrac{4}{25}$

$\rm: \longmapsto x = \dfrac{3}{25}$

Therefore:

$\rm: \longmapsto (x,y)= \bigg( \dfrac{3}{25}, \dfrac{4}{25} \bigg)$

★ Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

$\rm1.\ i^{4n} = 1$

$\rm2. \ i^{4n+1} = i$

$\rm3.\ i^{4n+2} = -1$

$\rm4.\ i^{4n+3} = -i$

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2 years ago