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2 years ago

What is the slope of the line that passes through the given points? (1,8) (8,9)

Mathematics

2 answers:

igor_vitrenko [27]2 years ago

6 0

9-8        1
----- =  -----.
8-1         7

The answer is 1/7.

masya89 [10]2 years ago

4 0

Answer:

1/7

Step-by-step explanation:

The slope of a line is the ratio of the vertical distance and horizontal distance between two points on a line.

Note that zero is tangible if the line is horizontal, and undefined if it is vertical.

Slope = ∆y / ∆x

Coordinates given: (1,8) and (8,9)?

Slope = 9 - 8 / 8 - (1)

Slope = 1 / 7

= 1 / 7

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Need help plz !!!!!!! Due today

Serggg [28]

Answer:

I know a little of this

Step-by-step explanation:

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7 0

2 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

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2 years ago

Triangle ABC is an isosceles triangle, and side BC is congruent to side AC. If side AC equals 40 centimeters, and AB is one-half

Alik [6]

Answer:

100 cm

Step-by-step explanation:

Given:

AC = BC

AC = 40

2AB=AC

Simplify:

BC = 40

Simplify:

2AB = 40

Algebra:

AB = 20

Here's the sides:

AB = 20

AC = 40

BC = 40

Add all of them together:

100

8 0

2 years ago

Will Upvote you!

notka56 [123]

For x = 4, then it means 3 to the fourth power or 3 times 3 times 3 times 3 times 3. 3^4 = 81 and 8 times that is 648.

y(x) = 8 * 3^x where x = 4:

y(x) = 8 * 3^4 = 8 * 81
y(x) = 648

The Function Rule then being that for every value of x there is one and only one value of y. y is the dependent variable and x is the independent variable.

7 0

2 years ago

Direct and Indirect Proportions

ivanzaharov [21]

Answer:

Step-by-step explanation:

5 0

2 years ago