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2 years ago

A cylinder has a volume of 360 in^3. If the height and radius are multiplied by 2.5, what will the resulting volume be?

1 answer:

5 0

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=2.5r\\
h=2.5h
\end{cases}\implies V=\pi (2.5r)^2(2.5h)
\\\\\\
V=\pi \cdot 2.5^2\cdot r^2\cdot 2.5h\implies V=(2.5^2\cdot 2.5)\pi r^2 h
\\\\\\
V=15.625\pi r^2h\impliedby \textit{15.625 of the original}
\\\\\\
\textit{if the original was 360}\qquad 15.265\cdot 360$

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Simplify the expression and rewrite in rational exponent form.

Dahasolnce [82]

Answer:

$4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$

Step-by-step explanation:

The given expression: $4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}$

Step 1: Change radical to fractional exponent.

Formula for fractional exponent: $\sqrt[n]{a}=a^{\frac{1}{n}}$

The power to which the base is raised becomes the numerator and the root becomes the denominator.

$\Rightarrow 4 x^{\frac{3}{5}} \cdot y^{4} \cdot x^{\frac{1}{2}} \cdot y^{\frac{5}{3}}$

Step 2: Apply law of exponent for a product $a^{m} \times a^{n}=a^{m+n}$

Multiply powers with same base.

$\Rightarrow 4 x^{\frac{3}{5}+\frac{1}{2}} \cdot y^{4+\frac{5}{8}}$

Take LCM for the fractions in the power.

$\Rightarrow 4 x^{\frac{6}{10}+\frac{5}{10}} \cdot y^{\frac{12}{3}+\frac{5}{3}}$

$\Rightarrow 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$

Hence the simplified form of $4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}$ .

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2 years ago

Question 5 (1 point) 5 The Cool Shirts company prints personalized designs on T-shirts. The cost y for x shirts with the same de

Sergeeva-Olga [200]

Answer:

y = 8x + 25

Step-by-step explanation:

Using the coordinates (10, 105) and (20, 185)

The standard linear equation is expressed as y = mx+c

m is the slope

c is the intercept

m = 185 - 105/20-10

m = 80/10

m = 8

Get the y-intercept

Since y = mx+c

105 = 8(10) + c

105 = 80 + c

c = 105 - 80

c = 25

Get the required equation

Recall that y = mx+c

y = 8x + 25

Hence the required equation is y = 8x + 25

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2 years ago

What prime numbers make 32 being added up

Leviafan [203]

29 and 3

13 and 19

Hope this helps!

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2 years ago

Read 2 more answers

The sum of the first term of an ap is 240 and the sum of the next 4 term is 220 find the first term of the ap

Sindrei [870]

Answer:

The common difference is -5/4

T(n) = T(0) - 5n/4,

where T(0) can be any number. d = -5/4

Assuming T(0) = 0, then first term

T(1) = 0 -5/4 = -5/4

Step-by-step explanation:

T(n) = T(0) + n*d

Let

S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240

S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220

S2 - S1

= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)

= (5+6+7+8 - 1 -2-3-4)d

= 4(4)d

= 16d

Since S2=220, S1 = 240

220-240 = 16d

d = -20/16 = -5/4

Since T(0) has not been defined, it could be any number.

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2 years ago

Two bicyclists were racing toward each other when they were 98 miles apart. Three hours later they did not meet yet and the dist

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Let, speed of 1st bicyclist is x.

So, speed of 2nd bicyclist is x-3 .

We know, relative speed when two objects moves towards each other :

$v = x + ( x-3 )\\\\v = 2x - 3$

Now, distance travelled in 3 hours is (98-2) miles .

So,

$2x-3 = \dfrac{96}{3}\\\\2x - 3 = 32\\\\2x = 35\\\\x = 17.5\ mph$

Therefore, speed of bikes are 17.5 mph and 14.5 mph.

Hence, this is the required solution.

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2 years ago