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nekit [7.7K]
3 years ago
10

Need help on some math "pictures "

Mathematics
1 answer:
vekshin13 years ago
3 0
1: (-1,2)
2: (2,5)
3: (3,0)
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In this exercise, T: R2 → R2 is a function. For each of the following parts, state why T is not linear. (a) T(a1, a2)= (1, a2) (
DENIUS [597]

Answer:

  • a) T is not homogeneous
  • b) T is not additive
  • c) T is not homogeneous
  • d) T is not additive
  • e) T is not additive

Step-by-step explanation:

In each case there is an example where one property of linear functions fails.

  • a) T(2(1,0))=T((2,0))=(1,0); 2T((1,0))=2(1,0)=(2,0). These vectors are not equal, then T doesn't satisfy the condition of scalar multiplication (homogeneity).
  • b) T((1,2)+(2,3))=T(3,5)=(3,9); T((1,2))+T((2,3))=(1,1)+(2,4)=(3,5). Because these vectors are not equal, T doesn't satisfy the property of vector addition (additivity).
  • c) T(\frac{1}{2}(\pi,0))=T((\frac{\pi}{2},0))=(\sin(\frac{\pi}{2}),0)=(1,0); \frac{1}{2}T((\pi,0))=\frac{1}{2}(0,0)=(0,0) so T is not homogeneous.
  • d) T((-1,0)+(1,0))=T(0,0)=(0,0); T((-1,0))+T((1,0))=(1,0)+(1,0)=(2,0) then T is not additive.
  • e) T((0,0)+(1,0))=T(1,0)=(2,0); T((0,0))+T((1,0))=(1,0)+(2,0)=(3,0) then T is not additive.
8 0
3 years ago
Scientists researching amphibians put tags on 30 frogs in a wetland area. Later, the scientists captured 520 frogs, of which 12
aleksklad [387]

Answer:

I THINK THE ANSWER IS d or e

5 0
3 years ago
Determine whether the function f(x) = -9.5 + 6 + x² is even, odd or neither.
zimovet [89]

Answer:

The function f(x) = -9.5 + 6 + x² is neither odd or even.

Step-by-step explanation:

We know that a function is termed as 'even' when

f(-x) = f(x) for all x

We know that a function is termed as 'odd' when

f(-x) = -f(x) for all x

Given the function

f(x) = -9.5x⁵ + 6 + x²

substitute x with -x

f(-x) = -9.5(-x)⁵ + 6 + (-x)²

as (-x)⁵ = -x⁵, so

f(-x) = -(-9.5x)⁵ + 6 + (-x)²

Apply exponent rule: (-a)ⁿ = aⁿ, if n is even

f(-x) = -(-9.5x)⁵ + 6 + x²

Apply rule: -(-a) = a

f(-x) = 9x⁵ + 6 + x²

As

f(-x) ≠ f(x) ≠ -f(x)

Therefore, the function f(x) = -9.5 + 6 + x² is neither odd or even.

5 0
3 years ago
What is the circumference of the circle is the top is 6
kaheart [24]
C = d × pi
C = 6 × 3.14
C = 18.84
7 0
3 years ago
Colin buys a car for £45500. It depreciates at a rate of 6% per year. How much will it be worth in 3 years? Give your answer to
natali 33 [55]

Answer:

yes

Step-by-step explanation:

the answer is 37,490.00 because over the span of 3 years the car would be worth 8,010.00 less

7 0
2 years ago
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