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3 years ago

The values given in the table below are the coordinates of points on a line.

Mathematics

1 answer:

user100 [1]3 years ago

6 0

Answer:

slope = 5

Step-by-step explanation:

To calculate the slope m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (2, 8) ← ordered pairs from the table

m = $\frac{8-3}{2-1}$ = 5

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Prove the following statement.

gayaneshka [121]

Answer:

You can prove this statement as follows:

Step-by-step explanation:

An odd integer is a number of the form $2k+1$ where $k\in \mathbb{Z}$ . Consider the following cases.

Case 1. If $k$ is even we have: $(2k+1)^{2}=(2(2s)+1)^{2}=(4s+1)^{2}=16s^2+8s+1=8(2s^2+s)+1$ .

If we denote by $m=2s^2+2$ we have that $(2k+1)^{2}=8m+1$ .

Case 2. if $k$ is odd we have: $(2k+1)^{2}=(2(2s+1)+1)^{2}=(4s+3)^{2}=16s^2+24s+9=16s^{2}+24s+8+1=8(2s^{2}+3s+1)+1$ .

If we denote by $m=2s^{2}+24s+1$ we have that $(2k+1)^{2}=8m+1$

This result says that the remainder when we divide the square of any odd integer by 8 is 1.

6 0

3 years ago

Kelly spends 3/8 of her free time playing soccer. what percent of her free time was spent playing soccer?

lozanna [386]

I think it's 37.5 . I'm pretty sure cause I think you divide 3/8 . Then you go 2 to the right for your answer with the decimal. Not sure but . I think I'm right.

7 0

3 years ago

What is 18 minus 4 8/9

Step2247 [10]

The answer is 13.1111111111. Hope this helps!

7 0

3 years ago

Read 2 more answers

1. Let f(x, y) be a differentiable function in the variables x and y. Let r and θ the polar coordinates,and set g(r, θ) = f(r co

Olenka [21]

Answer:

$g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}\\$

Step-by-step explanation:

First, notice that:

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}cos(\frac{\pi}{4}),\sqrt{2}sin(\frac{\pi}{4}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}(\frac{1}{\sqrt{2}}),\sqrt{2}(\frac{1}{\sqrt{2}}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(1,1)\\$

We proceed to use the chain rule to find $g_{r}(\sqrt{2},\frac{\pi}{4})$ using the fact that $X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta)$ to find their derivatives:

$g_{r}(r,\theta)=f_{r}(rcos(\theta),rsin(\theta))=f_{x}( rcos(\theta),rsin(\theta))\frac{\delta x}{\delta r}(r,\theta)+f_{y}(rcos(\theta),rsin(\theta))\frac{\delta y}{\delta r}(r,\theta)\\$