I'm assuming that the lower case c and the upper case C are the same variables.
6C^2 + 2.5D - D + 2C^2 - 3D = 8C^2 - 1.5D
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
Answer:
192 cm
Step-by-step explanation:
You need to note first two things.
1. The function f(x) need to be a continuous function on [-3,-1] (indeed f(x) is a polynomial function, is continuous on every real number x)
2. Take the closed interval [-3,-1]
Now, evaluate f(-3) and f(-1).
So, we have f(-3) < 0 and f(-1). So, 
, then by the Intermediate Value Theorem, there exist 
such that 
.
Speed of boat in still water ---- x km/h
speed of current ------ y km/h
distance with the current = 4(x+y)
distance against the current = 5(x-y)
we know that 3.5(x+y) = 70
x+y = 20
but 4(x+y) = 4(20) = 80
then 5(x-y) = 80
x-y = 16
x+y=20
x-y=16
add them
2x = 36
x = 18 , then y = 2
