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maxonik [38]
3 years ago
13

Find the measure of angle C of △ABC, if: m∠A=60°+α, m∠B=60°−α.

Mathematics
1 answer:
allochka39001 [22]3 years ago
7 0

Answer:

In a triangle, sum of three angles=180°

So, A+B+C=180

C=180-A-B

C=180-60-a-60+a

C=60°

Hope it helps :-)

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Can you find a strategy for splitting any number so that you always get the largest product?
Alex

9514 1404 393

Answer:

  split the number into equal pieces

Step-by-step explanation:

Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.

We have to assume that the number being split is positive and all of the parts are positive.

<h3>2 parts</h3>

If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.

<h3>3 parts</h3>

Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...

  p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4

This will be maximized where its derivative is zero:

  p' = (1/4)(3x^2 -4nx +n^2) = 0

  (3x -n)(x -n) = 0 . . . . . . . . . . . . . factor

  x = n/3  or  n

We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.

<h3>more parts</h3>

A similar development can prove by induction that the parts must all be equal.

6 0
3 years ago
Find the ordinary interest on $ 1,800 for two months at a rate of 12%
balandron [24]
<span>Divide 12% by 12 months to get 1% per month. Multiply by 2 months to get 2%. Multiply 1800 by 0.02 </span>
5 0
3 years ago
Given the quadratic equation below, determine which situation it could represent? x2 -4x = 60
yarga [219]

Answer:

The solution is x = 10 and x = -6. This quadratic could be represented in factored form as (x - 10)(x + 6) or on a graph with x-intercepts at (10,0) and (-6,0).

Step-by-step explanation:

To solve the quadratic, write the quadratic in standard form and factor the equation.

x² - 4x = 60

x² - 4x - 60 = 0

(x - 10)(x + 6) = 0

x = 10 and x = -6

4 0
3 years ago
Find the mode for the following distribution.
goldfiish [28.3K]

Answer:

24

Step-by-step explanation:

mode means most so 24 is written twice and the others only once.

you're welcome if I helped. :/ (not sure if I helped)

7 0
3 years ago
Help me find the answer
solmaris [256]
I possibly think it is c that is what I got
8 0
3 years ago
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