1. (i) Express 2704 as a product of its prime factors.

Mathematics

1 answer:

lidiya [134]3 years ago

8 0

Answer:

all answers below

Step-by-step explanation:

(i) 2704 = 2^4 x 13^2

(ii) as both indices (the powers) are divisible by 2, it is a perfect square.

(iii) as both indices are not divisible by 3, it is not a perfect square.

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Tara standing 20 feet from a tree and the angle of elevation is 72°. About how tall is the tree?

Zinaida [17]

Answer:

Approx 61.554 feet

Step-by-step explanation:

Since we are dealing with the opposite and adjacent sides, we will use tangent as our ratio.

Since the angle of elevation is 72 degrees, the left side of our equation is $tan(72)$ .

The right side of the equation is opposite over adjacent.

$x/20$

Set these equal to each other.

$tan(72) = x/20$

Simplify.

$20 tan(72)=x$

$20(3.078) = x$

x is approximately 61.554.

4 0

3 years ago

Kitara has 100 quarters and dimes. Their total value is $19. How many of each coin does Kitara have?

Sedbober [7]

Q + d = 100 so q = 100 - d
0.25q + 0.10d = 19

substitute q = 100 - d into 0.25q + 0.10d = 19

0.25q + 0.10d = 19
0.25(100 - d) + 0.10d = 19
25 - 0.25d + 0.10d = 19
-0.15d = -6
d = 40

q = 100 - 40 = 60

answer
Kitara has 60 quarters and 40 dimes

4 0

3 years ago

Find the area between y = 8 sin ( x ) y=8sin⁡(x) and y = 8 cos ( x ) y=8cos⁡(x) over the interval [ 0 , π ] . [0,π]. (Use decima

Marina86 [1]

Answer:

0.416 au

Step-by-step explanation:

Let y1=8sin(x) and y2=8cos(x), we must find the area between y1 and y2

$\int\limits^\pi _0{(8cos(x)-8sin(x))} \, dx = 8\int\limits^\pi _0{(cos(x)-sin(x))} \, dx =\\8(sin(x)+cos(x)) evaluated(0-\pi )=\\8(sin(\pi )-sin(0))+8(cos(\pi )-cos(0))=\\8(0.054-0)+8(0.998-1)=8(0.054)+8(-0.002)=0.432-0.016=0.416$