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3 years ago

the measurement of one angle of a right angle is 42 degrees what is the measurement of the third angle

1 answer:

8 0

The angles of a triangle all add up to 180°. In fact, it can be generalized that the sum of the interior angles of an n-sided polygon is equal to 180°(n–2).

A right triangle must have a right angle, which is equal to 90°. If the other angle is 42°, that means that we can find the third angle by subtracting 90° + 42° from 180°.

x = 180° – (90° + 42°) = 48°

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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

7 0

2 years ago

Take this brainlieslt! 20-20!

Irina-Kira [14]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What is the value for y?

NemiM [27]

The value of y is 28. Hope I helped!

3 0

3 years ago

Read 2 more answers

2. There were 35 children and 10 adults at a cookout.

qwelly [4]

Answer:

a.2:7

b.7:9

c.4:5

hope it helps

Explanation -

a. as original ratio is 10/35 , we reduce it to 2:7.

b. as original ratio is 35/45 , we reduce it to 7:9

c. as original ratio is 40:50 , we reduce it to 4:5

5 0

2 years ago

The exterior angle of a regular polygon is 15 degrees how many sides does it have

Komok [63]

The formula to use is
n = 360/E
where
n = number of sides
E = measure of exterior angle

In our case, E = 15 so
n = 360/E
n = 360/15
n = 24

This regular polygon has 24 sides

6 0

3 years ago