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erica [24]
3 years ago
15

Witch is greater 16.45 or 16.454

Mathematics
2 answers:
Leokris [45]3 years ago
6 0
16.45 is equal to 16.450, so 16.454 is grater.

Hope this helps!
Alex73 [517]3 years ago
5 0
16.454 because it has and extra .004 than 16.45
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2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.
likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4  + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

y = ^+_- \sqrt{-x^2+4x+4} -5

Thus

f(x) = \sqrt{-x^2+4x+4} - 5

g(x) = -\sqrt{-x^2+4x+4} - 5

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0

The quadratic has roots

\frac{52 ^+_-\sqrt{1664}}{26}

one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.

Also g(3.568) = - 7.354 and f(0.431) = -2.646

This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

5 0
2 years ago
Simplify the expression.<br><br> 7.5(–5.9)
Alex17521 [72]
7.5<span>(<span>−5.9</span>)</span><span>my answer is =<span>−<span>44.25
</span></span></span>
7 0
3 years ago
Read 2 more answers
John owes $829.30 to discover card. However his payment of $35 is late resulting in a late fee of $35. If his new balance $847.9
Orlov [11]

Answer:

Step-by-step explanation:

4 0
2 years ago
Solve the inequality for x. show each step of the solution <br> 12x&gt;7(4x+5)-19
STatiana [176]

Step-by-step explanation:

12x>7(4x+5)-19

12x>7*(4x+5)-19

12x>28x+35-19

12x-28x>16

-16x>16

16x>-16

x>-16/16

x<-1

3 0
2 years ago
Read 2 more answers
Someone pls help me i dont wanna fail.
sp2606 [1]
Top left : Unlike the others it is not displayed in a numerical form.
Bottom Left : It is the only item that goes above 1/100%.
5 0
2 years ago
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