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Solnce55 [7]
3 years ago
8

Please also explain how you did it! Thank you

Mathematics
1 answer:
Tasya [4]3 years ago
8 0

Answer:

66 degrees

Step-by-step explanation:

360 degrees in a circle

102 and 144 make up the circumference of LPN

LMN however is still to be determined... which is 360-(102+144) = 114

Therefore, LMN = 114 degrees. Using a thereom (I forget which one), the corresponding angle to LMN is LPN.

To find angle LPN (180-114) = 66

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the average is 53.6

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There is a common denominator of 12 among those fractions.
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if area of a circle varies directly as the cube of the radius, when the area is 625cm the radius is 5cm. calculate the area of a
Maksim231197 [3]

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8 0
3 years ago
2 more questions thanks
sergey [27]
These are two questions and two answers.

1) Problem 17.

(i) Determine whether T is continuous at 6061.

For that  you have to compute the value of T at 6061 and the lateral limits of T when x approaches 6061.

a) T(x) = 0.10x if 0 < x ≤ 6061

T (6061) = 0.10(6061) = 606.1

b) limit of Tx when x → 6061.

By the left the limit is the same value of T(x) calculated above.

By the right the limit is calculated using the definition of the function for the next stage: T(x) = 606.10 + 0.18 (x - 6061)

⇒ Limit of T(x) when x → 6061 from the right = 606.10 + 0.18 (6061 - 6061) = 606.10

Since both limits and the value of the function are the same, T is continuous at 6061.

(ii) Determine whether T is continuous at 32,473.

Same procedure.

a) Value at 32,473

T(32,473) = 606.10 + 0.18 (32,473 - 6061) = 5,360.26

b) Limit of T(x) when x → 32,473 from the right

Limit = 5360.26 + 0.26(x - 32,473) = 5360.26

Again, since the two limits and the value of the function have the same value the function is continuos at the x = 32,473.

(iii) If  T had discontinuities, a tax payer that earns an amount very close to the discontinuity can easily approach its incomes to take andvantage of the part that results in lower tax.

2) Problem 18.

a) Statement Sk

You just need to replace n for k:

Sk = 1 + 4 + 7 + ... (3k - 2) = k(3k - 1) / 2

b) Statement S (k+1)

Replace

S(k+1) = 1 + 4 + 7 + ... (3k - 2) + [ 3 (k + 1) - 2 ] = (k+1) [ 3(k+1) - 1] / 2

Simplification:

1 + 4 + 7 + ... + 3k - 2+ 3k + 3 - 2] = (k + 1) (3k + 3 - 1)/2

                 k(3k - 1)/ 2 + (3k + 1) = (k + 1)(3k+2) / 2

Do the operations on the left side and  you will find it can be simplified to k ( 3k +1) (3 k + 2) / 2.

With that you find that the left side equals the right side which is a proof of the validity of the statement by induction.

4 0
3 years ago
Read 2 more answers
A student scored in the 54th percentile on her Calculus exam. What does this student's score mean in relation to those of the ot
o-na [289]

The student's score was higher than 54% of the students who took the test. Then the correct option is C.

<h3>What is the percentage?</h3>

The quantity of anything is stated as though it were a fraction of a hundred.

A student scored in the 54th percentile on her Calculus exam.

Then the student's score mean in relation to those of the other test takers will be

Let the student got the lowest scored in calculus.

Then the student's score was higher than 54% of the students who took the test.

Then the correct option is C.

More about the percentage link is given below.

brainly.com/question/8011401

#SPJ1

4 0
2 years ago
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