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just olya [345]
4 years ago
14

Jose is a child living in Argentina, where spring begins in September and ends in December. Because he sees the days getting lon

ger in these months, he makes a conjecture that the days are getting longer all over the world. Show that Jose’s conjecture is false by writing a counterexample.
Mathematics
1 answer:
IRISSAK [1]4 years ago
4 0
Jose is false because the sun which makes it a day only shines none side of the earth while the moon is on the other side so on the other half of the hemisphere the days would be getting shorter while the days get longer on the other half of the hemisphere.
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Prove the identity.
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Answer:

D. Pythagorean

Step-by-step explanation:

Given the identity

cos²x - sin²x = 2 cos²x - 1.

To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.

Starting from the left hand side

cos²x - sin²x ... 1

According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:

x = rcostheta

y = rsintheta

Substituting into the Pythagoras firnuka we have

(rcostheta)²+(rsintheta)² = r²

r²cos²theta+r²sin²theta = r²

r²(cos²theta+sin²theta) = r²

(cos²theta+sin²theta) = 1

sin²theta = 1 - cos²theta

sin²x = 1-cos²x ... 2

Substituting equation 2 into 1 we have;

= cos²x-(1-cos²x)

= cos²x-1+cos²x

= 2cos²x-1 (RHS)

This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM

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4 years ago
The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r
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Width of the rectangle is 9 units

Step-by-step explanation:

  • Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

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54 = x (x - 3)

54 = x² - 3x

x² - 3x - 54 = 0

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x(x + 6) - 9(x + 6) = 0

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x = -6, 9 (negative value is neglected)

x = 9 units

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