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2 years ago

What is the scale factor of XYZ to UVW

Mathematics

2 answers:

Varvara68 [4.7K]2 years ago

8 0

Answer:
$\boxed {\frac{1}{5}}$
<span>
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Solution-
$60 * \frac{1}{5} = 12$

$90 * \frac{1}{5} = 18$

$75 * \frac{1}{5} = 15$
<span>━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━<span>━━
</span></span>Hence, the answer would be $\boxed {\frac{1}{5}}$

solong [7]2 years ago

7 0

Answer:

$\frac{1}{5}$

Step-by-step explanation:

We want to find the scale factor of the dilation from ΔXYZ to ΔUVW.

The scale factor is given by the formula;

$k=\frac{Image\:Length}{Corresponding\:Object\:Length}$

Since the dilation is from ΔXYZ to ΔUVW, our image triangle is ΔUVW.

We can now use any of the corresponding sides to determine the scale factor.

$k=\frac{|UV|}{|XY|}$

$\Rightarrow k=\frac{12}{60}$

We simplify to get;

$\Rightarrow k=\frac{12}{12\times5}$

We cancel the common factors to get;

$\Rightarrow k=\frac{1}{5}$

Therefore the scale factor is $\frac{1}{5}$

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Serga [27]

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3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

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Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
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Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

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2 years ago

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inna [77]

Answer:

p=-1/2

Step-by-step explanation:

4(4p+6)=16

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2 years ago

Another one that is even more confusing because it is a fraction.

kogti [31]

Answer:

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Step-by-step explanation:

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Maksim231197 [3]

<h2>Answer:</h2>

The equation that is used to model the length of ladder in terms of x is:

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<h2>Step-by-step explanation:</h2>

We can model this problem with the help of a right angled triangle whose hypotenuse is 13 meters and the other two legs are x meters and (x-7) meters.

where x is the distance between the top of the ladder and the ground.

and (x-7) is the distance between the foot of the ladder and the wall.

Hence, using Pythagorean Theorem we have:

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Hence, the answer is:

$x^2-7x-60=0$

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2 years ago

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