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Nikolay [14]
3 years ago
9

If you laid one of each size bolt 3/8, 1/2, 5/8, 7/8 and 1 1/4 end to end how long would the row of bolts be

Mathematics
1 answer:
Vaselesa [24]3 years ago
6 0
So 3/8 + 4/8 + 5/8 + 7/8 + 1 2/8 =


3 5/8
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Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = 4x − 4 at (1, 0).
larisa86 [58]
We are given the following:
          - parabola passes to both (1,0) and (0,1) 
<span>          - slope at x = 1 is 4 from the equation of the tangent line </span>

<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>

<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1 
<span>0 = a + b + 1
a + b = -1 </span>

<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the  equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b 
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b 
<span>4 = 2a + b </span>

So, we have two equations and  two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1 
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>

<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
6 0
3 years ago
Plz help me find this answer
cestrela7 [59]

Answer:

C

You have to check which of numbers is the lowest.

Cheers :D

3 0
2 years ago
a teacher and 10 students are to be seated along a bench in the bleachers at a basketball game. In how many ways can this be don
Veronika [31]

Wow !

OK.  The line-up on the bench has two "zones" ...

-- One zone, consisting of exactly two people, the teacher and the difficult student.
   Their identities don't change, and their arrangement doesn't change.

-- The other zone, consisting of the other 9 students.
   They can line up in any possible way.

How many ways can you line up 9 students ?

The first one can be any one of 9.   For each of these . . .
The second one can be any one of the remaining 8.  For each of these . . .
The third one can be any one of the remaining 7.  For each of these . . .
The fourth one can be any one of the remaining 6.  For each of these . . .
The fifth one can be any one of the remaining 5.  For each of these . . .
The sixth one can be any one of the remaining 4.  For each of these . . .
The seventh one can be any one of the remaining 3.  For each of these . . .
The eighth one can be either of the remaining 2.  For each of these . . .
The ninth one must be the only one remaining student.

     The total number of possible line-ups is 

               (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)  =  9!  =  362,880 .

But wait !  We're not done yet !

For each possible line-up, the teacher and the difficult student can sit

-- On the left end,
-- Between the 1st and 2nd students in the lineup,
-- Between the 2nd and 3rd students in the lineup,
-- Between the 3rd and 4th students in the lineup,
-- Between the 4th and 5th students in the lineup,
-- Between the 5th and 6th students in the lineup,
-- Between the 6th and 7th students in the lineup,
-- Between the 7th and 8th students in the lineup,
-- Between the 8th and 9th students in the lineup,
-- On the right end.

That's 10 different places to put the teacher and the difficult student,
in EACH possible line-up of the other 9 .

So the total total number of ways to do this is

           (362,880) x (10)  =  3,628,800  ways.

If they sit a different way at every game, the class can see a bunch of games
without duplicating their seating arrangement !

4 0
3 years ago
What is [nine x squared multiplied by thirty six y squared plus nine x squared multiplied by 4z squared?
Whitepunk [10]

Answer:

loading, please wait...

Step-by-step explanation:

8 0
2 years ago
8x + 3y + 6z = 43<br> -3x + 5y + 2z = 32<br> 5x – 2y + 5z = 24
kupik [55]

Answer:

Why do you want us to do??

Step-by-step explanation:

7 0
2 years ago
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