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2 years ago

Find the slope of the line that contains (-2,-2) and (-10,-9).

Mathematics

2 answers:

Digiron [165]2 years ago

6 0

Answer:

Step-by-step explanation:

slope of a line m= rise /run= (y1-y2)/ (x1-x2) = -2+9/-2+10 =7/8

Ivenika [448]2 years ago

6 0

Answer:7/8

Step-by-step explanation:

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For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Bond [772]

Given that $r=\theta$ , then $r'=1$

The slope of a tangent line in the polar coordinate is given by:

$m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}$

Thus, we have:

$m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}$

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

$\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

θ = 0

θ = 2.02875783811043

θ = 4.91318043943488

Part B:

For vertical tangent lines, $\frac{1}{m} =0$

Thus, we have:

$\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

θ = 4.91718592528713

3 0

3 years ago

I need help on number 6

Alona [7]

275 kg of copper. C.

4 0

2 years ago

The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of

Cloud [144]

Part a : you could draw a line from each corner to the middle
This would give you 7 triangles in total

Part b : area of one triangle : 4.5*7.8 = 35.1 / 2 = 17.55in <-- area of 1 triangle

Part c : so if there are 7 triangles and the area of 1 triangle is 17.55, you would do:
7 * 17.55 = 122.85

5 0

3 years ago

I need help finding the answers someone plz help

Harlamova29_29 [7]

Happy New Year from MrBillDoesMath!

Answer:

Proof by ASA congruence postulate. See below

Discussion:

Fact 1 : angle A = angle T (given)

Fact 2: The angles on both sides of point X are equal as vertical angles

are equal.

From these facts it follows that angle M = angle H (as all plane triangles have 180 degrees). Also AM = TH (given) so

In the left triangle In the right triangle

(angle M, side AM, angle A) = (angle H, side TH, angle T)

Hence the triangles have two congruent angles, and congruent sides included between the angles, so they are congruent by ASA.

Thank you,

MrB

8 0

2 years ago

Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two si

Phantasy [73]

x + y = 24 where x and y are the 2 parts of diagonal Other diagonal wil be smaller that 24.
x^2 + z^2 = 13^2
y^2 + z^2 = 20^2 where z = 0.5 * length of smaller diagonal)

form last 2 equations

y^2 - x^2 = 20^2 - 13^2 = 231
now y = 24-x so we have

(24 - x)^2 - x^2 = 231

576 - 48x = 231

48x = 345

x = 7.1875

z^2 = 13^2 - 7.1875^2 = 117.34
z = 1.83

so smaller diagonal = 21.66 cm

looks like its the third choice.

5 0

3 years ago