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)
40 is the correct answer for this
Answer:
Step-by-step explanation:
-5<x<4. The 3rd answer.
1. The winner threw the ball 175 ft, so what we want to do now is we convert (175) ft into yd.
We already know that 1ft= 1/3 yd, so the distance in yd is:
175 ft* (1/3 yd/ 1 ft) = 58 1/3 yd.
The answer is A. 58 1/3 yards.
2. 75 min* (4.5 miles/ 15 min)= 22.5 miles.
The correct answer is D. 22.5
3. Let's say that there are 4 weeks in a month. There are 5 weekdays in a week, so the number of weekdays in a month is:
5 weekdays/ 1 week* (4 weeks/ 1 month)= 20 weekdays/ 1 month.
Alex runs 5.9 miles/ 1 weekday, so the number of miles he runs every month is:
(5.9 miles/ 1 weekday)* (20 weekdays/ 1 month)= 118 miles/ month.
The nearest number to 118 is 120, so the answer is D.120 miles
4. 10 sweaters to 8 shirts:
10:8= 10/8= 5/4
The answer is B. 5/4
Hope this would help~
Answer:
The weight of the object is 3 kg.
Step-by-step explanation:
<u>Step 1:
</u>
Let object weight be x kg.
Now, as per the available data,
3/4 kg + 3/4 (x kg) = x kg
<u>Step 2:
</u>
3/4 (1 + x) = x
1 + x = 4x/3
1 = x (4/3 - 1)
x = 1 / (1/3)
x = 3
Weight of Object is 3 kg.
<u>Step 3:
</u>
Let's check if this value satisfies the first equation.
3/4 + 3/4 x 3 = 3/4 + 9/4 = 12/4 = 3
Hence proved.
