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PIT_PIT [208]
2 years ago
8

You can make a tent by throwing a piece of cloth over a clothesline, then securing the edge to the ground with stakes so that an

isosceles triangle is formed. How long would the cloth have to be so that the opening of the tent was 8 feet wide and 3 feet high?
Mathematics
1 answer:
4vir4ik [10]2 years ago
8 0

Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.

<h3>How long should the length of the cloth be?</h3>

The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.

That length - according to the Pythagoras theorem - would be:

= √(6² + (8 /2)²)

= √(36 + 16)

= 7.2 ft

As this is the length of one side of the cloth, the length of the entire cloth is:

= 7.2 x 2

= 14.4 ft

Find out more on the Pythagoras theorem at brainly.com/question/343682.

#SPJ1

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Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x(l
Pepsi [2]

I'm assuming the integral is

\displaystyle \int \frac{dx}{x (\ln(x^2))^5}

We have

\ln(x^2) = 2 \ln|x| \implies (\ln(x^2))^5 = 32 (\ln|x|)^5

Then substituting y=\ln|x| and dy=\frac{dx}x, the integral transforms and reduces to

\displaystyle \int \frac{dx}{x(\ln(x^2))^5} = \frac1{32} \int \frac{dy}{y^5} \\\\ ~~~~~~~~ = \frac1{32} \left(-\frac1{4y^4}\right) + C \\\\ ~~~~~~~~ = -\frac1{128(\ln|x|)^4} + C

which we can rewrite as

128 (\ln|x|)^4 = 8\cdot2^4(\ln|x|)^4 = 8 (2\ln|x|)^4 = 8 (\ln(x^2))^4

and so

\displaystyle \int \frac{dx}{x (\ln(x^2))^5} = \boxed{-\frac1{8(\ln(x^2))^4} + C}

7 0
1 year ago
Through: (-3,-5), parallel to y = 2x + 2​
Archy [21]

Answer:

y = 2x + 1

Step-by-step explanation:

Since you have an equation and a point, all you need to do is substitute the coordinates into the equation and then solve for the y-intercept (or "b"):

y = mx + b

y = 2x + 2

(-3, -5)

-5 = 2(-3) + b

-5 = -6 + b

-5 + 6 = b

b = 1

Now you have your final equation:

y = 2x + 1

*Remember that parallel lines have the same slope, so finding a new slope is not needed!

4 0
2 years ago
A woman bought some large frames for $16 each and some small frames for $7 each at a closeout sale. If she bought 24 frames for
8090 [49]

Answer:

20 big 4 small

Step-by-step explanation:

6 0
2 years ago
What is the value of x?
garik1379 [7]

Answer:

x=4

Step-by-step explanation:

3 0
2 years ago
Please answer correctly !!!!!!!! Will mark brianliest !!!!!!!!!!!
nexus9112 [7]

Answer:

x=6

Step-by-step explanation:

h(x) = -( x-2)^2 +16

We want when h(x) = 0

0 = -( x-2)^2 +16

Subtract 16 from each side

-16  = -( x-2)^2 +16-16

-16 = -( x-2)^2

Divide by -1

16= ( x-2)^2

Take the square root of each side

±sqrt(16) = sqrt(( x-2)^2 )

±4 = x-2

Add 2 to each sdie

2 ±4 = x-2+2

2+4 = x     2-4 =x

6 =x           -2 =x

since time cannot be negative

x=6

4 0
3 years ago
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