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Keith_Richards [23]
3 years ago
15

10 POINTS!! HELP ASAP!! What is the length of AC?

Mathematics
2 answers:
il63 [147K]3 years ago
8 0

Answer:

D.  144

Step-by-step explanation:

Triangle BAC is similar to triangle DEC, so you can set up a ratio:

\frac{84}{156-x} = \frac{7}{x}

Then cross multiply

84x = 7 (156 - x)

84x = 1092 - 7x

Add 7x to both sides.

91x = 1092

Divide both sides by 91.

x = 12

AC = 156 - x

AC = 156 - 12

AC = 144

My name is Ann [436]3 years ago
4 0

Answer:

D

Step-by-step explanation:

Δ CED and Δ CAB are similar thus the ratios of corresponding sides are equal, that is

\frac{CE}{CA} = \frac{ED}{AB} , substitute values

\frac{x}{156-x} = \frac{7}{84} = \frac{1}{12} ( cross- multiply )

12x = 156 - x ( add x to both sides )

13x = 156 ( divide both sides by 13 )

x = 12

Thus

AC = 156 - x = 156 - 12 = 144 → D

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pav-90 [236]

Answer:

The rule for the transformation is (x, y) + (-X, -Y)

The coordinates of L'are (-2,-2).

The coordinates of N' are (-1,-6)

Step-by-step explanation:

90 degree rotation from (x,y) results in (-x, y) and 180 degree results in (-x,-y)

The coordinates will change accordingly

L(2,2) will become L'(-2,-2)

M(4,4) will become M'(-4,-4)

and

N(1,6) will become N'(-1,-6)

So the correct statements are:

The rule for the transformation is (x, y) + (-X, -Y)

The coordinates of L'are (-2,-2).

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3 years ago
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Help plz most of points!
dmitriy555 [2]
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3 0
3 years ago
Consider the function f(x)=xln(x). Let Tn be the nth degree Taylor approximation of f(2) about x=1. Find: T1, T2, T3. find |R3|
Fynjy0 [20]

Answer:

R3 <= 0.083

Step-by-step explanation:

f(x)=xlnx,

The derivatives are as follows:

f'(x)=1+lnx,

f"(x)=1/x,

f"'(x)=-1/x²

f^(4)(x)=2/x³

Simialrly;

f(1) = 0,

f'(1) = 1,

f"(1) = 1,

f"'(1) = -1,

f^(4)(1) = 2

As such;

T1 = f(1) + f'(1)(x-1)

T1 = 0+1(x-1)

T1 = x - 1

T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2

T2 = 0+1(x-1)+1(x-1)^2

T2 = x-1+(x²-2x+1)/2

T2 = x²/2 - 1/2

T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3

T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3

T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)

Thus, T1(2) = 2 - 1

T1(2) = 1

T2 (2) = 2²/2 - 1/2

T2 (2) = 3/2

T2 (2) = 1.5

T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)

T3(2) = 4/3

T3(2) = 1.333

Since;

f(2) = 2 × ln(2)

f(2) = 2×0.693147 =

f(2) = 1.386294

Since;

f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).

Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,

Since;

f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2

Finally;

R3 <= |2/(4!)(2-1)^4|

R3 <= | 2 / 24× 1 |

R3 <= 1/12

R3 <= 0.083

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