Correct and explain the grammatical error in this sentence: Les fleurs qu'elle a vu sont jolies.
The sentence should be: Les fleurs qu'elle a vues sont jolies. This sentence includes a case of the passé composé with avoir. There is no modification of the past particle when the auxiliary verb is avoir except when the complément objet direct (COD) is BEFORE the verb, as is the case in this sentence (elle a vu les fleurs --> les fleurs = COD). When the COD precedes the auxiliary verb "avoir" used in the passé composé, the past participle is changed in gender and number to agree with the COD. In this case, les fleurs is feminine and plural; therefore "vu" must be feminine and plural as well: "vues". -- En français: Quand le COD est AVANT le verbe "avoir" avec le passé composé, il existe un accord entre le COD et le participle passé. Dans cette phrase, le COD est "les fleurs" ; parce que "les fleurs" est avant "a vu" et c'est féminin et pluriel, le participle passé est changé à "vues".
Find the minimum value of the function f(x) = 4x^2 + 8x + 3
This is a quadratic function of the form f(x) = ax^2 + bx + c. The graph of a quadratic function is a parabola. Because a > 0, this parabola opens upward and the minimum value is given by the y-coordinate of the vertex. The formula for finding the x-coordinate of the vertex is x = -b/2a. Therefore, x = -8/(2*4) = -1. Find the y-coordinate by plugging x = -1 back into f(x): f(-1) = 4*(-1)^2 + 8*-1 + 3 = 4 - 8 + 3 = -1 The minimum value is -1.
Suppose a wave of pessimism sweeps across an economy, reducing aggregate demand. What is the effect on total output and average price levels? Can the Fed do anything to reverse or mitigate the effects of this wave of pessimism?
**I would include graphs in my real explanation to a student (not possible to include here)** This event would shift the aggregate demand (AD) curve to the left (from AD1 -> AD2) on the aggregate demand/aggregate supply graph, decreasing quantity of output (from Y1 -> Y2) and decreasing average price levels (from PL1 -> PL2). In the long run, however, output is determined only by real variables (supply of labor, capital, and natural resources), and a wave of pessimism does not actually change these real variables. Therefore, output would shift back from Y2 -> Y1 to its natural level as short-run aggregate supply shifts right (from SRAS1 -> SRAS2) to intersect with AD2 and with the long-run aggregate supply curve (which has not shifted) as the economy finishes adjusting to the change. Average price levels would decrease further to PL3. The Fed could reverse this by increasing the money supply, which would put downward pressure on interest rates, causing them to fall. This would stimulate investment spending, as it is now cheaper to borrow money, shifting the AD curve to the right, back to its original position.