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ladessa [460]
4 years ago
12

Of the 216 students on the playground three-eighths are wearing white shoes how many children on the playground are not wearing

white shoes
Mathematics
2 answers:
natka813 [3]4 years ago
4 0
If 3/8 ARE wearing white schoes
Then 5/8 AREN'T wearing white shoes 
because

8/8 - 3/8 = 5/8
8/8 is the same as 1

Therefore, 
5/8 x 216/1 = y
If this is mental maths then,

You can cancel the 216 by 8 because the denominator of 5/8 is 8 to make 27

Therefore, the answer is 135

Len [333]4 years ago
3 0
First, you need to turn 3/8 in to a decimal. You can do that by dividing 3 by 8. You should get .375 now multiply that with 216. you should get 81. That means 81 kids are wearing white shoes. To find how many are not wearing white shoe, subtract 81 from 216. That gives you 135. 135 students are not wearing white shoes.
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What is the antiderivative of sin^2(x)cos^2(x)?
marin [14]

Answer:

\frac{x}{8}-\frac{\sin(4x)}{32}+C

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

\cos(2x)=2\cos^2x-1 \\ \cos(2x)=1 - 2\sin^2x.

And so inverting these,

\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x).

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

\sin^2x \cdot \cos^2x =\frac{1}{2} (1-\cos2x) \cdot \frac{1}{2} (1+\cos2x) = \frac{1}{4}(1-\cos^2(2x)).

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

\cos(2x)=2\cos^2x-1 \Rightarrow \cos(4x)=2\cos^2(2x)-1 \Rightarrow \cos^2(2x) = \frac{1}{2}(1+\cos(4x))

So then,

\sin^2x \cdot \cos^2x = \frac{1}{4}(1-\cos^2(2x)) = \frac{1}{4}(1-\frac{1}{2}(1+\cos(4x))) = \frac{1}{4}(1-\frac{1}{2}-\frac{1}{2}\cos(4x))=\frac{1}{8}(1-\cos(4x)).

This is now integrable (phew),

\int \sin^2x\cos^2x \ dx = \int \frac{1}{8}(1-\cos(4x)) \ dx = \frac{1}{8} \int (1-\cos(4x)) \ dx = \frac{1}{8}(x-\frac{1}{4}\sin(4x))+C.

7 0
3 years ago
What is the solution set for the equation (2x-1)(x+5)=0
satela [25.4K]

Answer:

x = 1/2    x=-5

Step-by-step explanation:

(2x-1)(x+5)=0

Using the zero product property

2x-1 =0  x+5 =0

2x= 1    x = -5

x = 1/2    x=-5

4 0
3 years ago
Read 2 more answers
Factor 5z^3+34z^2+53z-12 given that z+3 is a factor
Elis [28]
Do a long division 
the quotient comes to 

5z^2 + 19z - 4

this factors to

(5z - 1)(z + 4)

so factors are (z+3)(z+4)(5z-1)
8 0
3 years ago
The width of an extra large rectangle poster is 8 inches more than half its length.The area of this poster is 306 square inches
maria [59]

Answer:

a² + 16a - 612 = 0

Step-by-step explanation:

Here is the complete question :

The width of an extra large rectangle poster is 8 inches more than half its length. The area of this poster is 306 square inches

Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.

Area of a rectangle = length x width

Let length = a

width = 8 + 1/2a

Area =  (8 + 1/2a) x a

306 =  (8 + 1/2a) x a

multiply both sides of the equation by 2

612 = 16a + a²

a² + 16a - 612 = 0

the dimensions of the poster can be determined using quadratic formula

8 0
3 years ago
Write a fraction less than 1 with a demoninator of 6 that is greater than 3/4?
Dominik [7]
The most likely answer is 5/6
6 0
3 years ago
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