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Ostrovityanka [42]
1 year ago
12

1. Find the equation of a normal to the curve y= 2² - 2x +3 at the point (3,0)​

Mathematics
1 answer:
Gala2k [10]1 year ago
5 0

I think you meant to say the equation is

y = 2x² - 2x + 3

Differentiate both sides with respect to x :

dy/dx = 4x - 2

At the point (3, 0), the slope of the tangent line is dy/dx(3) = 4•3 - 2 = 10. Then the normal line to the curve at (3, 0) has slope -1/10.

Using the point-slope formula, the equation of the normal line is

y - 0 = -1/10 (x - 3)   ⇒   y = (3 - x)/10

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Triangle RST has vertices located at R (2, 3), S (4, 4), and T (5, 0).
LiRa [457]

The length of the sides are 2.24, 4.24 and 4.12 units while the slope are 0.5, -1 and -4.

<h3>Linear equation</h3>

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

For RS:

  • Length = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}=\sqrt{(4-3)^2+(4-2)^2}=2.24   \\&#10;\\&#10;slope=\frac{y_2-y_1}{x_2-x_1} =\frac{4-3}{4-2}=0.5

For RT:

  • Length = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}=\sqrt{(0-3)^2+(5-2)^2}=4.24   \\&#10;\\&#10;slope=\frac{y_2-y_1}{x_2-x_1} =\frac{0-3}{5-2}=-1

For ST:

  • Length = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}=\sqrt{(0-4)^2+(5-4)^2}=4.12   \\&#10;\\&#10;slope=\frac{y_2-y_1}{x_2-x_1} =\frac{0-4}{5-4}=-4

The length of the sides are 2.24, 4.24 and 4.12 units while the slope are 0.5, -1 and -4.

Find out more on linear equation at: brainly.com/question/14323743

5 0
2 years ago
Roger grew 42 plants with 14 seed packets. With 16 seed packets, how many total plants can Roger have in his backyard?
Step2247 [10]

Answer:

48 Plants

Step-by-step explanation:

3 per packet

42 / 14 = 3

3 x 16 = 48

48 Plants

Hope this helped!

5 0
2 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%20%5Chuge%20%5Cmathfrak%20%5Cred%7BQuEsTiOn%7D" id="TexFormula1" title=" \huge \mathfrak \red
trapecia [35]

Answer:

1. In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b.

2. The Thales theorem states that: If three points A, B, and C lie on the circumference of a circle, whereby the line AC is the diameter of the circle, then the angle ∠ABC is a right angle (90°).

Step-by-step explanation:

hope it helps

3 0
3 years ago
Read 2 more answers
If I have 7 and 5/6pounds of dog food each week we are use one and 2/ 3rd pound how many weeks will my dog food last
natulia [17]
I think it is 7 weeks



3 0
3 years ago
HELP PLEASE, I REALLY DONT UNDERSTAND THIS!
zubka84 [21]

Answer: Since 3−5+2=0, then 2

is the additive inverse of 3−5 is 2

 Since 5−3−2=0, then −2is the additive inverse of 5−3. is -2

Step-by-step explanation: additive inverse

The additive inverse of any number

x

is the number that gives zero when added to

x

. Example: the additive inverse of

5 is −5.

6 0
3 years ago
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