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Dima020 [189]
2 years ago
15

If the length of each side of a cuboid decreases by 20%, find the percentage decrease in its volume.

Mathematics
1 answer:
just olya [345]2 years ago
6 0

Answer:

Step-by-step explanation:

(1+25 /100) (1-20/100) (1-50/100)  <1

5/4 x 4/5 x 1/2 <1

Decrease in volume (in percent)

(1+25 /100) (1-20/100) (1-50/100)  x 100

=48.8%

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1)-7
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4 0
3 years ago
Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496
coldgirl [10]

Answer:

(a) gcd(20, 12)=4

(b) gcd(100, 36)=4

(c) gcd(496,207 )=1

Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

<em>                                   Given integers </em>a, b<em>, find </em>d=gcd(a,b)<em />

Here is an outline of the steps:

  1. Let a=x, b=y.
  2. Given x, y, use the division algorithm to write x=yq+r.
  3. If r=0, stop and output y; this is the gcd of a, b.
  4. If r\neq 0, replace (x,y) by (y,r). Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find gcd(20, 12) we apply the Euclidean algorithm:

20 = 12\cdot 1 + 8\\ 12 = 8\cdot 1 + 4\\ 8 = 4\cdot 2 + 0

The process stops since we reached 0, and we obtain gcd(20, 12)=4.

(b) To find gcd(100, 36) we apply the Euclidean algorithm:

100 = 36\cdot 2 + 28\\ 36 = 28\cdot1 + 8\\ 28 = 8\cdot 3 + 4\\ 8 = 4\cdot 2 + 0

The process stops since we reached 0, and we obtain gcd(100, 36)=4.

(c) To find gcd(496,207 ) we apply the Euclidean algorithm:

496 = 207\cdot 2 + 82\\ 207 = 82\cdot 2 + 43\\ 82 = 43\cdot 1 + 39\\ 43 = 39\cdot 1 + 4\\ 39 = 4\cdot 9 + 3\\ 4 = 3\cdot 1 + 1\\ 3 = 1\cdot 3 + 0

The process stops since we reached 0, and we obtain gcd(496,207 )=1.

3 0
3 years ago
Anthony bought 3.4 pounds of Halloween candy that cost $6.95 a pound. How much money did he spend on candy?
ratelena [41]

Answer:

23.63

Step-by-step explanation:

3.4 x 6.95

8 0
3 years ago
Read 2 more answers
PLEASE HELP,, thank you so much if you do
taurus [48]

Answer:

(x)^2+(5)^2=(9)^2

Step-by-step explanation:

(a)^2+(b)^2=(c)^2

(x)^2+(5)^2=(9)^2

x^2+25=81

-25 -25

x^2=56

x=28

p.s. this ^2 means squared

3 0
3 years ago
Let O be an angle in quadrant III such that cos 0 = -2/5 Find the exact values of csco and tan 0.​
vivado [14]

well, we know that θ is in the III Quadrant, where the sine is negative and the cosine is negative as well, or if you wish, where "x" as well as "y" are both negative, now, the hypotenuse or radius of the circle is just a distance amount, so is never negative, so in the equation of cos(θ) = - (2/5), the negative must be the adjacent side, thus

cos(\theta)=\cfrac{\stackrel{adjacent}{-2}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - (-2)^2}=b\implies \pm\sqrt{25-4}\implies \pm\sqrt{21}=b\implies \stackrel{III~Quadrant}{-\sqrt{21}=b}

\dotfill\\\\ csc(\theta)\implies \cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{-\sqrt{21}}}\implies \stackrel{\textit{rationalizing the denominator}}{-\cfrac{5}{\sqrt{21}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies -\cfrac{5\sqrt{21}}{21}} \\\\\\ tan(\theta)=\cfrac{\stackrel{opposite}{-\sqrt{21}}}{\underset{adjacent}{-2}}\implies tan(\theta)=\cfrac{\sqrt{21}}{2}

4 0
2 years ago
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