3 years ago

What is the projection of (4,4) onto (-7,3)?

1 answer:

3 0

Let's define the vectors:
u = (4,4)
v = (- 7.3)
The projection of u on v is:
P = ((u.v) / (v ^ 2)) v
We have then:
u.v = (4,4). (- 7.3)
u.v = (4) * (- 7) + (4) * (3) = -28 + 12 = -16
v ^ 2 = (- 7) ^ 2 + (3) ^ 2 = 49 + 9 = 58
Substituting we have:
P = ((- 16) / (58)) (- 7, 3)
Rewriting:
P = -0.28 (-7, 3)
Answer:
the projection of (4,4) onto (-7,3) is:
C) -0.28 (-7.3)

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The function y = x * ln(x + e) has two distinct x intercepts. One is at x = a and the other is at x = b. The value of a + b is

Snezhnost [94]

As points, x-intercepts take the form $(x,0)$ , so to find the intercepts we can set $y=0$ and solve for $x$ .

$x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}$

From the first equation alone, we already know that $x=0$ is a solution, which means one intercept is $(0,0)$ .

The second equation gives

$\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e$

so that the second intercept occurs at $(1-e,0)$ .

So if $a=0$ and $b=1-e$ , we have $a+b=1-e$ , giving C as the answer.