Answer:
Sin of x does not change
Step-by-step explanation:
Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.
From trigonometry,
Sin(x)=opposite/hypotenose
Where x=4/5
Sin(4/5)= opposite/hypotenose
But we were given the scale factor of 2 which means the dilation is to two times big.
Then we have
Sin(x)=(2×opposite)/(2×hypotenose)
Then,if we divide by 2 the numerator and denominator we still have
Sin(x)=opposite/hypotenose
Which means the two in numerator and denominator is cancelled out.
Then we still have the same sin of x. as sin(4/5)
Hence,Sin of x does not change
Answer: 0.6065
Step-by-step explanation:
Given : The machine's output is normally distributed with


Let x be the random variable that represents the output of machine .
z-score : 
For x= 21 ounces

For x= 28 ounces

Using the standard normal distribution table , we have
The p-value : 

Hence, the probability of filling a cup between 21 and 28 ounces= 0.6065
Answer:
x ≈ 15.9
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 6² = 17²
x² + 36 = 289 ( subtract 36 from both sides )
x² = 253 ( take the square root of both sides )
x =
≈ 15.9 ( to the nearest tenth )
The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.
1.

We want to find
such that
. This means



so
is conservative.
2.

Then




so
is conservative.
3.

so
is not conservative.
4.

Then




so
is conservative.