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3 years ago

Find the value of x, rounded to the nearest tenth?

Mathematics

1 answer:

Stolb23 [73]3 years ago

4 0

Answer:

Step-by-step explanation:

we can use the trigonometric function in a right triangle

cos x = adjacent side to the angle /hypothenuse

cos 36°= x/10 ; multiply both sides by 10

10 * cos 36° = x ; make sure your calculator mode is in degrees

8.1 = x

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Read 2 more answers

A closed-top cylindrical container is to have a volume of 250 in2. 250 , in squared , . What dimensions (radius and height) will

miv72 [106K]

Answer:

radius r = 3.414 in

height h = 6.8275 in

Step-by-step explanation:

From the information given:

The volume V of a closed cylindrical container with its surface area can be expressed as follows:

$V = \pi r^2 h$

$S = 2 \pi rh + 2 \pi r^2$

Given that Volume V = 250 in²

Then;

$\pi r^2h = 250 \\ \\ h = \dfrac{250}{\pi r^2}$

We also know that the cylinder contains top and bottom circle and the area is equal to πr²,

Hence, if we incorporate these areas in the total area of the cylinder.

Then;

$S = 2\pi r h + 2 \pi r ^2$

$S = 2\pi r (\dfrac{250}{\pi r^2}) + 2 \pi r ^2$

$S = \dfrac{500}{r} + 2 \pi r ^2$

To find the minimum by determining the radius at which the surface by using the first-order derivative.

$S' = 0$

$- \dfrac{500}{r^2} + 4 \pi r = 0$

$r^3 = \dfrac{500 }{4 \pi}$

$r^3 = 39.789$

$r =\sqrt[3]{39.789}$

r = 3.414 in

Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:

$S'' = - \dfrac{500(-2)}{r^3}+ 4 \pi$

$S'' = \dfrac{1000}{r^3}+ 4 \pi$

Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.

Thus, from $h = \dfrac{250}{\pi r^2}$

$h = \dfrac{250}{\pi (3.414) ^2}$

h = 6.8275 in

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3 years ago

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grin007 [14]

Answer:

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Step-by-step explanation:

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3 years ago

Suppose y is inversely proportional to x. When x is 0.5, y is 12. What is the rule for the inverse variation?

Korvikt [17]

We know that
if <span>y is inversely proportional to x
then
y=k/x
where k is the constant of variation
so
for x=0.5 y=12
find the value of k
12=k/0.5-----> k=12*.5----> k=6
y=6/x

the rule is the following
y=6/x
</span><span>
</span>

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3 years ago