A straight line PQ cuts the x andy axis at M and N respectively. If the points A(-3,5) and B(4,7) lies on PQ , calculate

Mathematics

1 answer:

aivan3 [116]2 years ago

8 0

Could you show us a picture of the question

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14 yd

son4ous [18]

Answer:

The volume is 196 cubic yards

Step-by-step explanation:

Given

$Base\ Area = 7yd * 2yd$

$Height = 14yd$

Required

The volume

The volume is given as:

$Volume = Base\ Area * Height$

Where:

$Base\ Area = 7yd * 2yd$

$Height = 14yd$

So, the equation becomes

$Volume = 7yd * 2yd * 14yd$

$Volume = 196yd^3$

6 0

2 years ago

Suppose x is a real number and epsilon > 0. Prove that (x - epsilon, x epsilon) is a neighborhood of each of its members; in

kaheart [24]

Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let $y\in (x-\epsilon,x+\epsilon)$ . then we have that $x-\epsilon$ . Hence, it makes sense to define the positive number delta as $\delta=\min\{x+\epsilon-y,y-(x-\epsilon)\}$ (the inequality guarantees that these numbers are positive).

Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ , and if we prove this, we are done. To prove it, let $z\in (y-\delta,y+\delta)$ , then $y-\delta$ . First, $\delta \leq y-(x-\epsilon)$ then $-\delta \geq -y+x-\epsilon$ hence $z>y-\delta \geq x-\epsilon$

On the other hand, $\delta \leq x+\epsilon-y$ then $z$ hence $z$ . Combining the inequalities, we have that $x-\epsilon$ , therefore $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ as required.