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3 years ago

Why is it not reasonable to say that 4.23 is less than 4.135?

Mathematics

2 answers:

OlgaM077 [116]3 years ago

6 0

If you round 4.135 it is 4.14 therefore 4.14 is less than 4.23

Elena L [17]3 years ago

5 0

Because 4.23 can be represented as: 423/100 and 4.135 as 413.5/100, because the denominators are equal then you can compare the numerators only, therefor 423 is bigger than 413.
(4.23 is bigger than 4.135)

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Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)

zavuch27 [327]

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

4 0

3 years ago

The weights of certain machine components are normally distributed with a mean of 8.04 g and a standard deviation of 0.08 g. Fin

NISA [10]

Answer:

The bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.

Step-by-step explanation:

We are given that

Mean, $\mu=8.04 g$

Standard deviation, $\sigma=0.08g$

We have to find the two weights that separate the top 3% and the bottom 3%.

Let x be the weight of machine components

$P(Xx_2)=0.03$

$P(X$

=0.03

From z- table we get

$P(Z1.88)=0.03$

Therefore, we get

$\frac{x_1-8.04}{0.08}=-1.88$

$x_1-8.04=-1.88\times 0.08$

$x_1=-1.88\times 0.08+8.04$

$x_1=7.8896$

$\frac{x_2-8.04}{0.08}=1.88$

$x_2=1.88\times 0.08+8.04$

$x_2=8.1904$

Hence, the bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.

5 0

3 years ago

Question 8

Lelechka [254]

Answer:

$695.88

Step-by-step explanation:

579 + 32 = 611

8% of 611 = 48.88

611 + 48.88 = 659.88

Stay safe! <3

6 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

3 years ago

What is the lowest form of 32:28?

BartSMP [9]

Answer:

to lowest terms of 32:28 is 8/7 or 8:7

Step-by-step explanation:

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3 years ago