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3 years ago

In a 30° - 60° - 90° right triangle, the hypotenuse has a length of 8. what is the length of the longer leg?

Mathematics

1 answer:

Tatiana [17]3 years ago

5 0

Sin 30° = 1/2 = x/8
then x = 4

sin 60° = √3/2 = y/8
then y = 4√3

so the length of the longer leg is 4√3

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lana66690 [7]

Answer:

A, 210

Step-by-step explanation:

7 x 5 = 35 divided by 2 = 17.5 x 12 = 210

Formula of a triangle:

Bh x 1/2 (basically dividing by 2)

Your base is the length on the bottom your height is that line in the middle of the triangle. Multiply those then divide by two to get the area always. But since its long and its a prism you have to multiply by 12.

Volume will always have the unit 3 in it and the measuring unit will depend on what is says for example in this problem its inches so its inches cubed (3).

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3 years ago

g A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of pa

adoni [48]

Complete Question

A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of parts had a mean of 1.6 millimeters with a standard deviation of 0.03 millimeters. what standard deviation will be needed to achieve a process capability index f 2.0?

Answer:

The value required is $\sigma = 0.0133$

Step-by-step explanation:

From the question we are told that

The upper specification is $USL = 1.68 \ mm$

The lower specification is $LSL = 1.52 \ mm$

The sample mean is $\mu = 1.6 \ mm$

The standard deviation is $\sigma = 0.03 \ mm$

Generally the capability index in mathematically represented as

$Cpk = min[ \frac{USL - \mu }{ 3 * \sigma } , \frac{\mu - LSL }{ 3 * \sigma } ]$

Now what min means is that the value of CPk is the minimum between the value is the bracket

substituting value given in the question

$Cpk = min[ \frac{1.68 - 1.6 }{ 3 * 0.03 } , \frac{1.60 - 1.52 }{ 3 * 0.03} ]$

=> $Cpk = min[ 0.88 , 0.88 ]$

$Cpk = 0.88$

Now from the question we are asked to evaluated the value of standard deviation that will produce a capability index of 2

Now let assuming that

$\frac{\mu - LSL }{ 3 * \sigma } = 2$

$\frac{ 1.60 - 1.52 }{ 3 * \sigma } = 2$

=> $0.08 = 6 \sigma$

=> $\sigma = 0.0133$

$\frac{ 1.68 - 1.60 }{ 3 * 0.0133 }$

=> $2$

Hence

$Cpk = min[ 2, 2 ]$

$Cpk = 2$

So $\sigma = 0.0133$ is the value of standard deviation required

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3 years ago

Read 2 more answers