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3 years ago

Find the surface area of this net

Mathematics

1 answer:

Kay [80]3 years ago

7 0

Answer:

Umm what net? Edit your question and maybe I can Help

You might be interested in

Look at the formula for finding the volume of a rectangular prism below.

krek1111 [17]

V = LWH.....to find W, divide both sides by LH
V / LH = W <===

3 0

3 years ago

Determine whether the ratios are equivalent. 3:8 and 9: 24. are they equivalent or not?

Simora [160]

Answer:

Yes, they are equivalent.

Step-by-step explanation:

9 / 3 = 3

24 / 3 = 8

3:8 is just the simplified version of 9:24. This is due to 9:24 being divided by three, becoming 3:8.

8 0

2 years ago

A rectangular swimming pool is bordered by a concrete patio. the width of the patio is the same on every side. the area of the s

andre [41]

Answer:

$x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)$

where

l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Explanation:

Let

x = width of the patio
l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Since the pool is bordered by a complete patio,

Length of the pool (with the patio)
= (length of the pool (w/o the patio)) + 2*(width of the patio)
Length of the pool (with the patio) = l + 2x

Width of the pool (with the patio)
= (width of the pool (w/o the patio)) + 2*(width of the patio)
Width of the pool (with the patio) = w + 2x

Note that

Area of the pool (w/o the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
Area of the pool (w/o the patio) = lw

Area of the pool (with the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
= (l + 2x)(w + 2x)
= w(l + 2x) + 2x(l + 2x)
= lw + 2xw + 2xl + 4x²
Area of the pool (with the patio) = 4x² + 2x(l + w) + lw

Area of the patio
= (Area of the pool (with the patio)) - (Area of the pool (w/o the patio))
= (4x² + 2x(l + w) + lw) - lw
Area of the patio = 4x² + 2x(l + w)

Since the area of the patio is equal to the area of the surface of the pool, the area of the patio is equal to the area of the pool without the patio. In terms of the equation,

Area of the patio = Area of the pool (w/o the patio)
4x² + 2x(l + w) = lw
4x² + 2x(l + w) - lw = 0 (1)

Let

a = numerical coefficient of x² = 4
b = numerical coefficient of x = 2(l + w)
c = constant term = -lw

Then using quadratic formula, the roots of the equation 4x² + 2x(l + w) - lw = 0 is given by

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\ = \frac{-2(l + w) \pm \sqrt{(2(l + w))^2 - 4(4)(-lw)}}{2(4)} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l + w)^2) + 16lw}}{8} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2) + 4(4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2 + 4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 6lw + w^2)}}{8}$
$= \frac{-2(l + w) \pm 2\sqrt{l^2 + 6lw + w^2}}{8} \\= \frac{2}{8}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\x = \frac{1}{4}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right) \text{ or }}
\\\boxed{x = -\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

Since $(l + w) + \sqrt{l^2 + 6lw + w^2} \ \textgreater \ 0$ , $-\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2}\right)$ is negative. Since x represents the patio width, x cannot be negative. Hence, the patio width is given by

$\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

7 0

3 years ago

You want to go to graduate school, so you ask your math professor, Dr. Emmy Noether, for a letter of recommendation. You estimat

den301095 [7]

Answer:

$P(G) = 0.69$

$P(S | G) = 0.81$

$P(M|G') = 0.26$

Step-by-step explanation:

From the question we are told the

The probability of getting into getting into graduated school if you receive a strong recommendation is $P(G |S) = 0.80$

The probability of getting into getting into graduated school if you receive a moderately good recommendation is $P(G| M) = 0.60$

The probability of getting into getting into graduated school if you receive a weak recommendation is $P(G|W) = 0.05$

The probability of getting a strong recommendation is $P(S) = 0.7$

The probability of receiving a moderately good recommendation is $P(M) = 0.2$

The probability of receiving a weak recommendation is $P(W) = 0.1$

Generally the probability that you will get into a graduate program is mathematically represented as

$P(G) = P(S) * P(G|S) + P(M) * P(G|M) + P(W) * P(G|W)$

=> $P(G) = 0.7 * 0.8 + 0.2 * 0.6 + 0.1 * 0.05$

=> $P(G) = 0.69$

Generally given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as

$P( S|G) = \frac{ P(S) * P(G|S)}{ P(G)}$

=> $P(S|G) = \frac{ 0.7 * 0.8 }{0.69}$

=> $P(S | G) = 0.81$

Generally given that you didn't receive an offer to attend a graduate program the probability that you received a moderately good recommendation is mathematically represented as

$P(M|G') = \frac{ P(M) * (1- P(G|M))}{(1 - P(G))}$