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N76 [4]
3 years ago
8

(Find the distance between the points A(4, 3) and B(7,-1).​

Mathematics
2 answers:
murzikaleks [220]3 years ago
8 0
The answer to this problem is 5.
lana66690 [7]3 years ago
3 0

Answer:

5

Step-by-step explanation:

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I need help finding the values of the last boxes shown in the image.
Bingel [31]

The volume of the region R bounded by the x-axis is: \mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}

<h3>What is the volume of the solid revolution on the X-axis?</h3>

The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

In the graph, the given straight line passes through two points (0,0) and (2,8).

Therefore, the equation of the straight line becomes:

\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}

where:

  • (x₁, y₁) and (x₂, y₂) are two points on the straight line

Thus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:

\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}

y = 4x

Now, our region bounded by the three lines are:

  • y = 0
  • x = 2
  • y = 4x

Similarly, the change in polar coordinates is:

  • x = rcosθ,
  • y = rsinθ

where;

  • x² + y² = r²  and dA = rdrdθ

Now

  • rsinθ = 0   i.e.  r = 0 or θ = 0
  • rcosθ = 2 i.e.   r  = 2/cosθ
  • rsinθ = 4(rcosθ)  ⇒ tan θ = 4;  θ = tan⁻¹ (4)

  • ⇒ r = 0   to   r = 2/cosθ
  •    θ = 0  to    θ = tan⁻¹ (4)

Then:

\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}

\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}

Learn more about the determining the volume of solids bounded by region R here:

brainly.com/question/14393123

#SPJ1

5 0
2 years ago
Last Saturday jay spent 6 hours playing games,studying, and talking with friends. He spent 2/5 of the time playing and 1/2 of th
LenaWriter [7]
Jay spent 3/7 hours talking with his friends
7 0
3 years ago
to convert measurements in the metric system you can move the decimal point left or right why does this work?​
Lyrx [107]
The metric system is based on power os 10’s- brainest pls xx
4 0
2 years ago
Read 2 more answers
⚠️What is the slope of the line that passes through the points ( 4,9 ) and ( 14, 17)⚠️
EleoNora [17]


The answer is m=4/5 so the slope of the line is 4/5
5 0
3 years ago
Please find the surface area
nevsk [136]
4*(10*12/2)+4*(12*9)+(12*12)= 816 ft^2

the surface area is 816 ft^2.
5 0
3 years ago
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