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7nadin3 [17]
3 years ago
8

Please help me I need the answers in 30 minutes!!

Mathematics
1 answer:
Crank3 years ago
6 0

Answer:

a.7

b.6.8

Step-by-step explanation:

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y
Yuri [45]

Let the curve C be the intersection of the cylinder  



16x^2+y^2=16



and the plane



x+y+z=1



The projection of C on to the x-y plane is the ellipse



16x^2+y^2=16



To see clearly that this is an ellipse, le us divide through by 16, to get



\frac{x^2}{1}+ \frac{y^2}{16}=1



or  



\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1,



We can write the following parametric equations,



x=cos(t), y=4sin(t)



for  



0\le t \le 2\pi



Since C lies on the plane,



x+y+z=1



it must satisfy its equation.



Let us make z the subject first,  



z=1-x-y



This implies that,



z=1-sin(t)-4cos(t)



We can now write the vector equation of C, to obtain,



r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))



The length of the curve of the intersection of the cylinder and the plane is now given by,



\int\limits^{2\pi}_0 {|r'(t)|} \, dt



But  



r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))



|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}



\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184



Therefore the length of the curve of the intersection  intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0
3 years ago
Please help me with both! would really appreciate it
Tamiku [17]
Jus look and the answer above
7 0
3 years ago
Alice Correa bought three yards of cloth to make a dress the cloth was on sale for a dollar 93 per yard how much did Alice pay f
alexandr1967 [171]
To solve for the total amount that Alice paid for the 3 yards cloth, multiply the cost per yard with the additional 5% to number of yards. 5% of 93 is 4.65. The total cost per yard of cloth is 97.65. Multiplying the total cost with 3 will give 292.95. Thus, Alice paid 292.95 dollars in total. 
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3 years ago
ABCD is a quadrilateral. <br> AB=CD<br> Angle ABC = angle BCD<br> Prove that AC = BD
maks197457 [2]
  • Answer:

compare the triangles ΔABC and ΔBCD

∡ABC = ∡BCD (given)

AB = CD (given)

BC = BC (common)  } = > (SAS) ΔABC ≡ ΔBCD = > AC = BD

5 0
3 years ago
Please help me on this geometry!! i’ll mark you the brainliest
Gnoma [55]

Answer:

Median

Step-by-step explanation:

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Hope this helps! Please tell me if I did anything wrong, thank you and have a great day!

4 0
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