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3 years ago

In the 3rd grade there are 60 kids and ten more girls than boys how many boy costumes and girl costumes will they need

Mathematics

2 answers:

Feliz [49]3 years ago

3 0

Answer: 35 girl costumes, 25 boy costumes.

Step-by-step explanation:

60 split into 2 groups is 30 each.

Add 5 to one group and subtract 5 from the other to get a difference of 10.

Girls group is 30+5=35

Boys group is 30-5=25

Mars2501 [29]3 years ago

3 0

Answer:

<em>They will need 25 boy costumes and 35 girls costumes.</em>

Step-by-step explanation:

There are x boys.

There are x + 10 girls.

Altogether, there are x + x + 10 students.

Altogether, there are 60 students, so

x + x + 10 = 60

2x + 10 = 60

2x + 50

x = 25 (boys)

x + 10 = 35 (girls)

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3 years ago

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Step-by-step explanation:

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Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

$\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

but the integrand is even, so this is really just

$\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

Substitute x = 1/2 arccot(u/2), which transforms the integral to

$\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du$

There are lots of ways to compute this. What I did was to consider the complex contour integral

$\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz$

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

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which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

$\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}$

and it follows that

$\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}$

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2 years ago

Does 10,15,20 form a right triangle

sveta [45]

A right triangle can only be formed when you use the 3/4/5 rule.
The 3/4/5 rule is a^2 + b^2 = c^2.

We will use 10 for a, 15 for b, and 20 for c.

a^2 + b^2 = c^2

Plug in 10 for a, 15 for b, and 20 for c.

10^2 + 15^2 = 20^2

10^2 = 100

15^2 = 225

20^2 = 400

100 + 225 = 400
This is not applicable, as 100 + 225 = 325.

Your answer is:

No, 10,15,20 does not form a right triangle.

I hope this helps!

5 0

3 years ago

A rectangle has an area of 822.4 square miles and a base of 32 miles. What is the height?

JulijaS [17]

I believe it would be 25.7 miles. I just divide 822.4 by 32.

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3 years ago

Read 2 more answers