9514 1404 393
Answer:
- 13 ft
- (a) 1 second; (b) t = 0, t = 1/2
Step-by-step explanation:
<h3>1. </h3>
Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...
5² +(w -1)² = w²
w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms
26 = 2w . . . . . . . . . . . . add 2w
13 = w . . . . . . . . . . . . divide by 2
The length of the wire is 13 feet.
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<h3>2. </h3>
(a) When h = 0, the equation is ...
0 = -16t^2 +8t +8
Dividing by -8 puts this into standard form:
2t^2 -t -1 = 0
Factoring, we get ...
(2t +1)(t -1) = 0
The positive value of t that makes a factor zero is t = 1.
It will take 1 second for the gymnast to reach the ground.
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(b) When h = 8, the equation is ...
8 = -16t^2 +8t +8
Subtract 8 and divide by 8 to get ...
0 = -2t^2 +t
0 = t(1 -2t) . . . . factor out t
Values of t that make the factors zero are ...
t = 0
t = 1/2
The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.
2x + 4y − 3z = −7 ---> first equation
3x + y + 4z = −12 ---> second equation
x + 3y + 4z = 4 ---> third equation
We try to eliminate z and make two equations
Multiply first equation by 4 and second equation by 3. then add both equations
8x + 16y -12z = -28
9x + 3y +12z = -36
----------------------------
17x + 19y = -64 ---------------> equation 4
multiply third equation by -1 and add second and third equation
3x + y + 4z = −12
-x - 3y - 4z = -4
-------------------------------------
2x -2y = -16 ---------------> equation 5
Multiply equation 4 by 2 and equation by 19
34x + 38y = -128
38x - 38y = -304
------------------------------------
72x = -432
Divide by 72 on both sides
x = -6
use equation 2x -2y = -16 ---------------> equation 5
2(-6) - 2y = -16
-12 -2y = -16
-2y = -4
So y = 2
Now plug in 2 for y and -6 for x
Using any one of the three equations
x + 3y + 4z = 4
-6 + 3(2) +4z = 4
4z = 4 (divide by 4 on both sides)
So z=1
So x= -6, y = 2 and z= 1
Answer:
-8 feet
Step-by-step explanation:
63 - 71 = -8
Answer:
Step-by-step explanation:
all you have to do is divide each number by 4, 41, 42, 43, 44, 45, 46, 47, 48, 49 ,and 50 until you get a remainder of 1. what I mean is do 2 divided by all the number from 40 50 and do the same with 4,5,8 and 10 until you find one of them that has a remainder of 1. (is a lot of work sorry could't tell you the anwer)
Answer:
Step-by-step explanation:
Recursive formula
a1 = -17
a^n = a^n-1 + 5
Explicit formula:
a^n = -17 + (n-1) * 5
