whats the mistake in this and why? 15+(√9•7)÷3 = 15+(3•7)÷3 =15+(21)÷3 =36÷3 =12

Mathematics

1 answer:

krok68 [10]3 years ago

4 0

Okay! So after you have 15+(21)÷3, you have to remember PEMDAS.

PEMDAS is the order in which you solve equations.

1. Parentheses: you solve everything in the parentheses first, all while following the rules of PEMDAS

2. Exponents: after you solve the things in the parentheses, you do the exponents.

3. Then you do Multiplication or Division, solving in the order from left to right.

4. After, you do Addition or Subtraction, solving in the order from left to right.

So using PEMDAS, we'll solve 15+(21)÷3.

We do division before addition, so 21/3 is 7.

Then you add 15 to 7 and get 22 as your final answer.

Hope this helps!

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What are the vertex , focus and directrix of the parabola with the equation x2+8x+4y+4=0?

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You can rewrite the equation in vertex form to find some of the parameters of interest.
x² +8x +4 = -4y
x² +8x +16 -12 = -4y
(x+4)² -12 = -4y
y = (-1/4)(x +4)² +3
From this, we see the vertex is (-4, 3).

The scale factor, (-1/4) is 1/(4p), where p is the distance from the vertex to the focus. Solving for p, we have
-1/4 = 1/(4p)
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So, the focus is 1 unit below the vertex. The focus is (-4, 2).

The directrix is the same distance from the vertex, but in the opposite direction, hence the directrix is y = 4.

_____
On a graph, if all you know is the vertex, you can draw a line with slope 1/2 through the vertex. It intersects the parabola at the y-value of the focus. Then the distance from that point of intersection to the axis of symmetry (where the focus lies) is the same as the distance from that point to the directrix.

Every point on the parabola, including the vertex and the point of intersection just described, is the same distance from the focus and the directrix. This point of intersection is on a horizontal line through the focus, so finding the distance is made easy.