What's the area of this rectangular prism?
2 answers:
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Given:
To find:
The value of x.
Solution:
We know that, corresponding sides of similar triangles are proportional.
Since,, therefore
On substituting the values from the figure, we get
On cross multiplication, we get
Therefore, the value of x is 4.
For the first circle, let's use the pythagorean theorem
now, it just so happen that the hypotenuse on that triangle, is actually 17, but we used the pythagorean theorem to find it, and the pythagorean theorem only works for right-triangles.
so if the hypotenuse is actually 17, that means that triangle there is actually a right-triangle, meaning that the radius there, and the outside line there, are both meeting at a right-angle.
when an outside line touches the radius line, and they form a right-angle, the outside line is indeed a tangent line, since the point of tangency is always a right-angle with the radius.
now, let's check for second circle
well, low and behold, we didn't get our hypotenuse as 16 after all, meaning, that triangle is NOT a right-triangle, and that outside line is not touching the radius at a right-angle, therefore is NOT a tangent line.
let's check the third circle
this time, we did get our hypotenuse to 65, the triangle is a right-triangle, so the outside line is indeed a tangent line.
now, it just so happen that the hypotenuse on that triangle, is actually 17, but we used the pythagorean theorem to find it, and the pythagorean theorem only works for right-triangles.
so if the hypotenuse is actually 17, that means that triangle there is actually a right-triangle, meaning that the radius there, and the outside line there, are both meeting at a right-angle.
when an outside line touches the radius line, and they form a right-angle, the outside line is indeed a tangent line, since the point of tangency is always a right-angle with the radius.
now, let's check for second circle
well, low and behold, we didn't get our hypotenuse as 16 after all, meaning, that triangle is NOT a right-triangle, and that outside line is not touching the radius at a right-angle, therefore is NOT a tangent line.
let's check the third circle
this time, we did get our hypotenuse to 65, the triangle is a right-triangle, so the outside line is indeed a tangent line.
Answer:
So it would takes approximately 6.9 hours to reach 32 F.
Step-by-step explanation:
For this case we have the following differential equationÑ
We can reorder the expression like this:
We can use the substitution and
so then we have:
IF we integrate both sides we got:
If we apply exponential in both sides we got:
And if we replace w = u-T we got:
We can also express the solution in the following terms:
For this case we know that since w ehave a cooloing,
, we have this model:
And if we want that the temperature would be 32F we can solve for t like this:
If we apply natural logs on both sides we got:
So it would takes approximately 6.9 hours to reach 32 F.