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Volgvan
3 years ago
12

Cristina uses a ruler to measure the length of her math textbook. She says that the book is 4/10 meters long. Is her measurement

in simplest form? If not, what is the length of the book in Simplest form?
Mathematics
1 answer:
a_sh-v [17]3 years ago
4 0

Answer:

2/5

Step-by-step explanation:

You could still divide by 2

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The answer is c all the others are 1/3 fractions
3 0
3 years ago
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Evaluate Dx / ^ 9-8x - x2^
Solnce55 [7]
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
4 0
3 years ago
Find the surface area of the pyramid. The side lengths of the base are equal. Square pyramid with base edge of 12 centimeters, a
sdas [7]

Answer:

the surface area of the square pyramid is 576.66 cm^2

Step-by-step explanation:

The computation of the surface area of square pyramid is given below:

A = a^2  + 2a × √a^2 ÷ √4 + √h^2

where

a = 12 cm

h = 17 cm

Now put the value of a and h in the above formula

= 12^2 + 2(12) × √12^2 ÷ √4 + √17^2

= 576.66 cm^2

hence, the surface area of the square pyramid is 576.66 cm^2

8 0
2 years ago
It takes 16 minutes for 9 people to paint 8 walls . How many minutes does it take for 4 people to paint 6 walls?
Soloha48 [4]

Answer:

27 minutes to complete the painting of 4 walls

Step-by-step explanation:

since 16m with 9p --> 8 walls

x minutes with 4p --> 6 walls?

let x= minutes

6 walls painted=(8/144 walls painted per minute)x

simplify

x= 6 divided by (8/144)

x=108 minutes (to complete 6 walls)

108/4=

27 minutes to complete the painting of 4 walls

4 0
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Darina [25.2K]

Answer:

\frac{50 miles}{1 hour} * \frac{1 hour}{60 minutes}

Step-by-step explanation:

Since 1 hour contains 60 minutes, So 1 hour would by divided by 60

So, the required expression is,

=> \frac{50 miles}{1 hour} * \frac{1 hour}{60 minutes}

7 0
3 years ago
Read 2 more answers
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