I need help explaining, I know the answer, but I don't know how I got the answer

The angle measures and/or side lengths of a triangle are described. Determine whether the conditions given

(a) One unique triangle. This is an equilateral triangle since all sides are the same length. Through the SSS property, we can prove that only one triangle is possible here.

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(b) Cannot make a triangle. The triangle inequality theorem says that adding any two sides of a triangle must result in a value larger than the third side. Add up the first two sides (1 and 2) to get 1+2 = 3, which is not larger than the third side (3 units long). I recommend cutting out strips of paper that are 1 inch, 2 inches and 3 inches long, and trying to form a triangle. You'll find that a triangle is not possible. The 1 inch and 2 inch strips will line up to form a straight line that is 3 inches long, and basically you have a flat line (or a triangle with area 0)

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(c) More than one triangle. The angles add up to 180 since 35+60+85, so we can form a triangle. It turns out we can form infinitely many of them. The AA (angle angle) similarity theorem allows us to scale any triangle to make it larger or smaller compared to the original.

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(d) Cannot make a triangle. I'm assuming the 509 should actually be 50°. If so, then a triangle is not possible because the three angles (50, 50, 50) do not add to 180. We have instead 50+50+50 = 150. For any triangle, the three angles must always add to 180 degrees.

8 0

3 years ago

What is a equivalent to 25/45

bezimeni [28]

5 0

3 years ago

Read 2 more answers

Since at t=0, n(t)=n0, and at t=[infinity], n(t)=0, there must be some time between zero and infinity at which exactly half of t

Ostrovityanka [42]

An expression for this timet-half will be given as ln(2) / λ ≈ 0.693 / λ

<h3>What is an expression?</h3>

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The complete question is:

Suppose a radioactive sample initially contains N0unstable nuclei. These nuclei will decay into stable nuclei, and as they do, the number of unstable nuclei that remain, N(t), will decrease with time. Although there is no way for us to predict exactly when any one nucleus will decay, we can write down an expression for the total number of unstable nuclei that remain after a time t:

N(t)=No e−λt,

where λ is known as the decay constant. Note that at t=0, N(t)=No, the original number of unstable nuclei. N(t) decreases exponentially with time, and as t approaches infinity, the number of unstable nuclei that remain approaches zero.

Part (A) Since at t=0, N(t)=No, and at t=∞, N(t)=0, there must be some time between zero and infinity at which exactly half of the original number of nuclei remain. Find an expression for this time, t half.

Express your answer in terms of N0 and/or λ.

1) Equation given:

← I used α instead of λ just for editing facility..

Where No is the initial number of nuclei.

2) Half of the initial number of nuclei: N (t-half) = No / 2

So, replace in the given equation:

$N9t) = Ne^{-\lambda t}$