All categories

2 years ago

Question 19 I know the answer is 1.5 but how

Mathematics

1 answer:

katrin2010 [14]2 years ago

5 0

Suppose the width of the path is x.
the dimensions of the extended rectangle are (12+x+x), and (16+x+x)
(12+2x)(16+2x)=285
4x²+56x+192=285
4x²+56x-93=0
Not easy to factor it, so use the quadratic formula to solve:
x={-56+√[(56²-4*4*(-93)]}/2*4 or x={-56-√[(56²-4*4*(-93)]}/2*4
x=1.5 (ignore the negative solution.)

You might be interested in

Debbie buys a tree for the holidays. She would like to determine the amount of space it will take up in her living room. The tre

Rina8888 [55]

Answer:

Volume = 200.96 cubic feet

Step-by-step explanation:

Volume of a cone is given by the formula $V=\frac{1}{3}\pi r^2 h$

Where r is the radius and h is the height

Given r = 4 and height is 3 times that. So height is 4*3 = 12

Plugging these into the formula we get:

Volume of Cone = $\frac{1}{3}\pi (4)^2 (12)\\=\frac{1}{3}(3.14)(16)(12)\\=200.96$

Thus, Volume = 200.96 cubic feet

3 0

2 years ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

3 years ago

Divide 33 photos into two groups so that the ratio is 4 to 7

Andre45 [30]

Total ratio = 4+7 = 11
33/11 = 3
4x3 = 12
7x3 = 21
so the two groups are 12:21
which is also = 4:7

3 0

2 years ago

Check all of the proper units of weight in the metric system kiloliter gram pound milligram

Over [174]

Gram
miligram
..................................

5 0

2 years ago

aalyn [17]

If a(n) = (39n^4 -506n^3 + 2341n^2 - 4610n + 3416) / 8 then

a(1) = 85 
a(2) = 17 
a(3) = 19 
a(4) = 4 
a(5) = 2

8 0

2 years ago