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mel-nik [20]
3 years ago
15

Where does the normal line to the parabola y = x − x2 at the point (1, 0) intersect the parabola a second time?

Mathematics
1 answer:
Ksivusya [100]3 years ago
7 0
Find the line that is normal to the parabola at the given point
remember that normal means perpendicular
perpendicular lines have slopes that multiply to -1
we can use point slope form to write the equation of the line since we are given the point (1,0)

we just need the slope

take derivitive
y'=1-2x
at x=1
y'=1-2(1)
y'=1-2
y'=-1

the slope is -1
the perpendicular of that slope is what number we can multiply to get -1
-1 times what=-1?
what=1
duh
so
point (1,0) and slope 1
y-0=1(x-1)
y=x-1 is da equation

solve for where y=x-1 and y=x-x² intersect

set equatl to each other since equal y
x-1=x-x²
x²-1=0
factor difference of 2 perfect squares
(x-1)(x+1)=0
set to zero

x-1=0
x=1
we got this point already

x+1=0
x=-1
sub back
y=-1-(-1)²
y=-1-(1)
y=-1-1
y=-2

it intersects at (-1,-2)
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Akimi4 [234]

Angles ∠ACD and ∠CAB are congruent because they are alternate angles. Then the area of the triangle AOB will be 22.53 square cm.

<h3>What is the area of the right-angle triangle?</h3>

The area of the right-angle triangle is given as

A = 1/2 x B x H

Where B is the base and H is the height of the right triangle.

We know that angles ∠ACD and ∠CAB are congruent because they are alternate angles.

α₁ = 40°

AO = OC = 7.8 cm

Then the area of the triangle will be

Area = 1/2 x 7.8 x 7.8 x tan40°

Area = 22.53 square cm

More about the area of the right-angle triangle link is given below.

brainly.com/question/16653962

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5 0
1 year ago
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total
Fantom [35]

Answer:the number of coach tickets that she bought is 5

the number of first class tickets that she bought is 6

Step-by-step explanation:

Let x represent the number of coach tickets that she bought.

Let y represent the number of first class tickets that she bought.

The total number of people that went for the round trip is 11. This means that

x + y = 11

She was able to purchase coach tickets for ​$340 and first class tickets for ​$1190. She used her total budget for airfare for the​ trip, which was ​$8840. This means that

340x + 1190y = 8840 - - - - - - - 1

Substituting x = 11 - y into equation 1, it becomes

340(11-y) + 1190y = 8840

3740 - 340y + 1190y = 8840

- 340y + 1190y = 8840 - 3740

850y = 5100

y = 5100/850 = 6

x = 11 - y

x = 11 - 6 = 5

4 0
3 years ago
In a theater, there are 4 long rows of chairs,each with an equal number of chairs There are 5 ahort rows of chairs,each with an
Hoochie [10]
<span>There are 4 long rows and 5 short rows in the theater. x represents the number of chairs in each long row and y represents the number of chairs in each short row.

So, total number of chairs in 4 long rows= 4x
Total number of chairs in 5 short rows = 5y
Total number of chairs in the theater on a normal day = 4x + 5y

When 2 chairs are added to each long row, the number of chairs will change to (x+2).
So, total number of chairs in 4 long rows will be = 4(x+2)

When 3 chairs are added to each short row, the number of chairs will change to (y+3)
So, total number of chairs in 5 short rows will be = 5(y+3)

Thus, total number of chairs in the theater in rush day = 4(x+2) + 5(y+3)
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Thus we can say the number of chairs increase by 23 as compared to a normal day.
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7 0
3 years ago
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Karl is making a pot of chili. The recipe calls for 3/8 cup of chili powder, but Karl only wants to use half as much so it won’t
tresset_1 [31]

Answer:

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Step-by-step explanation:

Given that:

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Karl wants to use half : 1/2

The given question involves fractions. When the number of cups has to be divided into half, it will be multiplied with 1/2.

So,

Multiplying the chili powder requirement of the recipe to 1/2

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Hence,

KArl should use 3/16 cups of chili powder

4 0
3 years ago
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5 0
3 years ago
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