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3 years ago

for every 5 pounds of pasta served , 15 people can be fed. how many people can be fed with 4 pounds of pasta?

Mathematics

1 answer:

Sidana [21]3 years ago

7 0

Answer:

Step-by-step explanation:

its direct proportion. 15 divided by 5 is 3 so you must multiply 3 by 4 to get the amount of people, which is 12

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find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6

taurus [48]

Answer:

$f(x) = \frac{6}{x^2} -8$ or $f(x) = -\frac{6}{x^2} + 4$

Step-by-step explanation:

Given

$(x,y) = (1,-2)$ --- Point

$\int\limits^6_2 {(1 + 144x^{-6})} \, dx$

The arc length of a function on interval [a,b]: $\int\limits^b_a {(1 + f'(x^2))} \, dx$

By comparison:

$f'(x)^2 = 144x^{-6}$

$f'(x)^2 = \frac{144}{x^6}$

Take square root of both sides

$f'(x) =\± \sqrt{\frac{144}{x^6}}$

$f'(x) = \±\frac{12}{x^3}$

Split:

$f'(x) = \frac{12}{x^3}$ or $f'(x) = -\frac{12}{x^3}$

To solve fo f(x), we make use of:

$f(x) = \int {f'(x) } \, dx$

For: $f'(x) = \frac{12}{x^3}$

$f(x) = \int {\frac{12}{x^3} } \, dx$

Integrate:

$f(x) = \frac{12}{2x^2} + c$

$f(x) = \frac{6}{x^2} + c$

We understand that it passes through $(x,y) = (1,-2)$ .

So, we have:

$-2 = \frac{6}{1^2} + c$

$-2 = \frac{6}{1} + c$

$-2 = 6 + c$

Make c the subject

$c = -2-6$

$c = -8$

$f(x) = \frac{6}{x^2} + c$ becomes

$f(x) = \frac{6}{x^2} -8$

For: $f'(x) = -\frac{12}{x^3}$

$f(x) = \int {-\frac{12}{x^3} } \, dx$

Integrate:

$f(x) = -\frac{12}{2x^2} + c$

$f(x) = -\frac{6}{x^2} + c$

We understand that it passes through $(x,y) = (1,-2)$ .

So, we have:

$-2 = -\frac{6}{1^2} + c$

$-2 = -\frac{6}{1} + c$

$-2 = -6 + c$

Make c the subject

$c = -2+6$

$c = 4$

$f(x) = -\frac{6}{x^2} + c$ becomes

$f(x) = -\frac{6}{x^2} + 4$

3 0

3 years ago

In the given figure find the area of the shaded region if AC = 24 CM AB = 7cm and O is the centre

wariber [46]

See the attached figure to better understand the problem

we know that

The inscribed angle in a circle measures half of the arc it comprises.

in this problem
the inscribed angle= ∠ACB
and the arc it comprises measures 180°
then
the ∠ACB=180°/2-------> ∠ACB=90°

applying the Pythagorean theorem
AC²+CB²=AB²-------> AB²=24²+7²-------> AB²=625------> AB=25 cm

the diameter of circle is AB
radius=25/2--------> r=12.5 cm

[the area of a half circle]=pi*r²/2------> pi*12.5²/2--------> 245.44 cm²

[area of triangle ABC]=AC*CB/2--------> 24*7/2-------> 84 cm²

[the area of the shaded region]=[the area of a half circle]-[area of triangle ABC]

[the area of the shaded region]=245.44-84-------> 161.44 cm²

the answer is
the area of the shaded region is 161.44 cm²

5 0

3 years ago

Read 2 more answers

In the middle of a test Please answer!

vaieri [72.5K]

Answer:

umm... there is no problem

4 0

3 years ago

PLEASE ANSWER THIS

irinina [24]

Answer:

a) 1/4

b) 0.95

Step-by-step explanation:

0.25 is 25/100, which is 1/4

19/25 is 95/100, which is 0.95

3 0

3 years ago

Ree is 27 inches tall on her first birthday. She grows around 6 inches per year after that. What is the rate of change for the s

Archy [21]

It says "She grows around 6 inches per year."

This means that the rate of change is 6.

27 + (6 * y)

y = how many years pass.

Hope This Helped! Good Luck!

6 0

4 years ago