<h3>Given</h3>
three numbers: a, b, c
a+b+c = 11
2a +5b +6c = 32
3a -b = 22
<h3>Find</h3>
a, b, c
<h3>Solution</h3>
The equations can be represented by the augmented matrix
![\left[\begin{array}{ccc|c}1&1&1&11\\2&5&6&32\\3&-1&0&22\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%261%2611%5C%5C2%265%266%2632%5C%5C3%26-1%260%2622%5Cend%7Barray%7D%5Cright%5D)
A graphing calculator gives the solution
(a, b, c) = (8, 2, 1)
The three numbers are 8, 2, and 1.
_____
If you want to solve this by hand, you could use Cramer's rule, or you could do the row operations by and. For example, subtract twice the first equation from the second to get
... 3b +4c = 10
Subtract 3 times the first equation from the third to get
... -4b -3c = -11
These two equations can be solved by your favorite method to find
... b = (-44 +30)/(-16 +9) = -14/-7 = 2 . . . . . using Cramer's rule
... c = (-40 +33)/-7 = 1
Then the first equation can be used to find <em>a</em>.
... a + 2 + 1 = 11
... a = 8 . . . . . . . . . . . as above
The volume of the sphere with a radius of 9 will be
v≈3053.63
Answer:
Step-by-step explanation:
<u>Given quadratic function:</u>
<u>Points on the graph:</u>
- (-2,-35), (1,-5), (3,- 15)
<u>Substitute values of x and y and solve the system of equations:</u>
- -35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
- -5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
- -15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3
<u>Subtract eq 2 from eq 1:</u>
- -35 - (-5) = 4a - 2b + c - a - b - c
- -30 = 3a - 3b
- b = a + 10 ⇔ eq 4
<u>Subtract eq 2 from eq 3:</u>
- -15 - (-5) = 9a + 3b + c - a - b - c
- -10 = 8a + 2b
- b = -4a - 5 ⇔ eq 5
<u>Compare eq 4 and eq 5, solve for a:</u>
- a + 10 = -4a - 5
- a + 4a = -5 - 10
- 5a = -15
- a = -3
<u>Find the value of b using eq 4:</u>
<u>Find the value of c using eq 2:</u>
- -5 = -3 + 7 + c
- c = -5 - 4
- c = -9
<u>We now have a, b and c:, the function is:</u>
Answer:
$40 million
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Current value = 125%
which means that current value is 25% more than its initial value.
Let Initial Value = X
So, Increase in investment value = 25% × X = 0.25X
Given, increase value = $10million
So, 0.25X = $10 million
= X = $10million
= X = $10million ÷ 0.25
= X = $40 million
Hence the initial value of investment is $40million.
