MATHEMATICS COLLEGE

Find the mass of the wire formed by the intersection of the sphere x 2 + y 2 + z 2 = 1 and the plane x + z = 0 if the density of the wire is 4x 2 grams per unit length.

Answers

Answer 1
Answer: Answer: x²+(â’xâ’z)²+z² = 1 → 2x²+2zx+(2z²â’1) = 0 Solve as a quadratic : x = { â’2z ± âš(4z²â’8(2z²â’1) } / 4 = { â’z ± âš(2â’3z²) } / 2 A more manageable form can be derived by setting z = âš(2/3).sint to remove âš This gives x = â’âš(1/6).sint + âš(1/2).cost (can omit ± sign since â’ is covered by Ď€â’t) Using x+y+z = 0 gives y = â’xâ’z = â’âš(1/6)sint â’ âš(1/2).cost So a parameterisation in terms of t â [0,2Ď€] is x = â’âš(1/6).sint + âš(1/2).cost, y = â’âš(1/6).sint â’ âš(1/2).cost, z = âš(2/3).sint (ds/dt)² = (â’âš(1/6).costâ’âš(1/2).sint)² + (â’âš(1/6).cost+âš(1/2).sint)² + (âš(2/3).cost)² = 1 â´ â« Ďds = â« ( â’âš(1/6).sint + âš(1/2).cost )²dt, [t=0,2Ď€] = 2Ď€/3

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HIGH SCHOOL

Robert climbed 775 steps in 12 1/2minutes. how many steps did he average per minute?

Answers

1162 is the awnser i believe
HIGH SCHOOL

Ali simplifies the expression 9y+y9y+y to 9y29y2. Use the drop-down menus to complete the statements below to explain why Ali's solution is correct or incorrect.

Answers

Answer with explanation:

The expression is: 9 y + y 9 y + y

Ali Simplifies it  

→→Incorrect simplification done by Ali.

Solution of the expression:

 

→→Correct Simplification of the expression

I say she is incorrect because the equation 9y+y9y+y should equal 19y if I am correct.  I am sorry if im not correct but i believe she is incorrect 
MIDDLE SCHOOL

What is the greatest common factor of 15 and 64

Answers

15 = 3*5
64= 2*2*2*2*2*2

There are no common factors so the GCF is 1
HIGH SCHOOL

CHECK MY ANSWER PLEASE A central angle θ in a circle with a radius of 5.5 centimeters intercepts an arc with a length of 7.7 centimeters.



What is the radian measure of θ ?

Enter your answer, as a decimal, in the box
I used 80.2

Answers

First you need to find the Circumference
C = 2 pi r = 2 * 3.14 * 5.5 = 34.54

Arc measure / 360 = 7.7 / 34.54
Arc measure = 7.7 * 360 / 34.54
Arc measure = 80.25

Answer:
80.25 if you are using pi = 3.14
80.2 if you are using pi = 3.141592....
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