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Lynna [10]
3 years ago
9

Find the equations of all lines tangent to y = 9–x^2 that pass through the point (1, 12). ...?

Mathematics
1 answer:
Oksanka [162]3 years ago
4 0
The slope of the tangent at a given point can be found by differentiating the given equation and substituting the value of x at the point as such:
y = 9 - x²
dy/dx = -2x; x = 1
dy/dx = -2

For a line with the slope of -2 and passing through point (1 , 12)
y -12 = -2(x - 1)
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Find the third, fourth, and tenth terms of the sequence describe by the rule below
Sophie [7]

The third term, fourth term and tenth term are -1, -3, -15 respectively.

<h3>What is a sequence?</h3>

A sequence is a pattern of numbers in which successive terms differ by an constant term called the common difference or ratio.

Analysis:

For a sequence defined by the rule A(n) = 3 + (n-1)(-2)

Third term, n = 3

A(3) = 3 + (3-1)(-2) = -1

Fourth term, n = 4

A(4) = 3 + (4-1)(-2) = -3

Tenth term, n = 10

A(10) = 3 + (10-1)(-2) = -15

In conclusion, the third, fourth, tenth terms are -1, -3 and -15 respectively.

Learn more about sequence: brainly.com/question/6561461

#SPJ1

4 0
2 years ago
Help me please i have the homework for today
Vlad1618 [11]

Hello there i hope you are having a good day :)

So you have got AB in a straight line this for a straight line would equal to 180° Then all you would have to do is to work out angle X you would do

42° + 29° = 71° and then you would take away it from 180° -  70° = 109°

So X would equal to 109°

Hopefully that helps you ❤

4 0
4 years ago
Read 2 more answers
What is the expression for f(x) when we rewrite 64^x/4^5x-1 as 4^f(x)
Sav [38]

Answer: f(x)= -2x+1

Step-by-step explanation:

4 0
3 years ago
1/3 (4+2)=-2/5(x-9) and x=4
VladimirAG [237]
So it will be
1/3(6)=-2/5(-5)
then will remove minus
1/3*6=2/5*5
then cancle 3 and 6 will be 2 and remove 5
So it become like this 2=2 it is True
5 0
3 years ago
You invested a total of $9,000 at 4 1/2 % and 5% simple interest. During one year, the two accounts earned $435. How much did yo
KonstantinChe [14]

Answer:

The amount invested at 4.5% was \$3,000

The amount invested at 5% was \$6,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x -----> the amount invested at 4.5%

9,000-x -----> the amount invested at 5%

in this problem we have

t=1\ year\\ P1=\$x\\ P2=\$(9,000-x)\\I=\$435\\r1=0.045\\r2=0.05

substitute

435=x(0.045*1)+(9,000-x)(0.05*1)

435=0.045x+450-0.05x

0.05x-0.045x=450-435

0.005x=15

x=\$3,000

so

9,000-x=\$6,000

therefore

The amount invested at 4.5% was \$3,000

The amount invested at 5% was \$6,000

5 0
4 years ago
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