1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Licemer1 [7]
3 years ago
11

Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 16x2 + 9y2 = 144. Cross-se

ctions perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
Mathematics
1 answer:
oee [108]3 years ago
7 0

In the x-y plane, the base has equation(s)

16x^2+9y^2=144\implies y=\pm\dfrac43\sqrt{9-x^2}

which is to say, the distance (parallel to the y-axis) between the top and the bottom of the ellipse is

\dfrac43\sqrt{9-x^2}-\left(-\dfrac43\sqrt{9-x^2}\right)=\dfrac83\sqrt{9-x^2}

so that at any given x, the cross-section has a hypotenuse whose length is \dfrac83\sqrt{9-x^2}.

The cross-section is an isosceles right triangle, which means the legs occur with the hypotenuse in a ratio of 1 to \sqrt2, so that the legs have length \dfrac8{3\sqrt2}\sqrt{9-x^2}. Then the area of each cross-section is

\dfrac12\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)=\dfrac{16}9(9-x^2)

Then the volume of this solid is

\displaystyle\frac{16}9\int_{-3}^39-x^2\,\mathrm dx=\boxed{64}

You might be interested in
Find the perimeter of each polygon 4cm
andriy [413]
Your answer is 12!!!!!
7 0
3 years ago
In the diagram, angle 1 = 4x + 30, and angle 3 = 2x +48.
iragen [17]

Answer:

Since we have the information for Angles 1 and 3, and they are vertical, we can set them equal to each other. Once we have done this we can find the measures of them combined, and subtract it from 360 in order to only have the measure of 2 and its vertical angle. Finally, all we need to do now is divide the remaining measure by 2, and this will give us the measure of angle 2.

Angle 1=Angle 3

4x+30=2x+48

2x+30=48

2x=18

x=9

Angle 1=4(9)+30

Angle 1=36+30

Angle 1=66

Angle 1=Angle 3

Angle 1+ Angle 3=132

360-132=228

228/2=114

Angle 2= 114

6 0
3 years ago
If n = 14m and m is 3% of b, then n is what percent of b?
Serjik [45]

Answer:

please mark me brainliesf if it is right

42 %

7 0
3 years ago
my mum was 27 when I was born,8 years she was twice as old as I shall be in 5 years time. how old am I now?​
jeyben [28]

Answer:

THIS IS HARD

Step-by-step explanation:

8 0
3 years ago
I need to find the correct measure of central tendency & dispersion with each variable. In addition, the 5-number summary &a
OLga [1]

Answer:

مرحبًا آمل أن يساعد هذا على أمل أن يكون لديك يوم كامل رائع ههههههه

3 0
3 years ago
Other questions:
  • What is the slope of any line parallel to y = 4x + 17
    13·2 answers
  • A bank account has a beginning balance of $560,00. After 6 months, the balance in the account has increased to
    5·1 answer
  • Austin is comparing the prices of two truck rental company company charges $4 per hour and an additional $70 as service charges
    9·1 answer
  • Slope intercept form
    12·1 answer
  • I want to know if mammals usually have more teeth than reptiles
    10·2 answers
  • Help me with this thanks​
    8·1 answer
  • HELP MY HOMIE OUT, MY HOMIE NEEDS SERIOUS HELP PLEEEEASE HELP ILL GIVE U A BRAINLIEST
    13·2 answers
  • Help ill mark brainliest
    14·2 answers
  • Find the area of each circle. Use 3.14 for the value of pi. Round your answer to the nearest tenth. Do NOT include units in your
    15·1 answer
  • Yeah ill give brain if correct
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!