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3 years ago

Triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tenth if necessary. OPQR

Mathematics

1 answer:

Andrews [41]3 years ago

3 0

Answer:

RS = 75.3

Step-by-step explanation:

You need to set up the proportion of corresponding sides.

$\frac{PQ}{ST} = \frac{PO}{RS}$

$\frac{7}{31} = \frac{17}{RS}$

7(RS) = 31(17)

= 527

RS = 527/7 = 75.2857...

= 75.3

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A closed cylindrical can of fixed volume V has radius r.a) Find the surface area, S, as a function of r.b) What happens to the v

andrey2020 [161]

Answer:

Step-by-step explanation:

This question is incomplete; here is the complete question.

A closed cylindrical can of fixed volume V has radius r. (a) Find the surface area, S, as a function of r. (b) What happens to the value of S approaches to infinity? (c) Sketch a graph of S against r, if V=10 cm³.

A closed cylindrical can of volume V is having radius r and height h.

a). Surface area of a cylinder is given by

S = 2(Area of the circular sides) + Lateral area of the can

S = 2πr² + 2πrh

S = 2πr(r + h)

b). Since surface area is directly proportional to radius of the can

S ∝ r

Therefore, when r approaches to infinity (r → ∞)

c). If V = 10 cm³ Then we have to graph S against r.

From the formula V = πr²h

10 = πr²h

h = $\frac{10}{\pi r^{2}}$

By placing the value of h in the formula of surface area,

S = $2\pi r(r+\frac{10}{\pi r^{2}})$

Now we can get the points to plot the graph,

r -2 -1 0 1 2

S -13.72 -13.72 0 26.28 35.13

7 0

3 years ago

8.45 At some point in the season, the Unicorns had won 60% of their basketball games. After that point, they won 8 more games an

ololo11 [35]

Answer:

The total number of games won by Unicorn is 40.

Step-by-step explanation:

We are given with a word problem
We are asked to find the number of unicorns played during the season
We can do this in two steps

Step 1: Finding the win percentage

Step 2: Finding the number of unicorns played during the season

Step 1 of 2

Let the number of games played by unicorn be x.The unicorn won 60% of the first x-10 games That is $\frac{60}{100} \times(x-10)$

Combining the 8 games we get,

$\begin{gathered}\frac{60}{100}(x-10)+8=\frac{60}{100} \times x-\frac{60}{100} \times 10+8 \\0.6 x-6+8=0.6 x+2\end{gathered}$

Step 2 of 2

The unicorn totally won 65% of the games played.

That is $\frac{65}{100} \times x=0.65 x$

Equating both the equation gives

$\begin{gathered}0.6 x+2=0.65 x \\2=0.65 x-0.6 x \\2=0.05 x \\\frac{2}{0.05}=x \\40=x\end{gathered}$

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2 years ago

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Answer:

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