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vodka [1.7K]
2 years ago
6

Select the correct answer. Which sequences of transformations confirm the congruence of shape II and I?

Mathematics
1 answer:
statuscvo [17]2 years ago
8 0

Answer:

the answer is 3

Step-by-step explanation:

i just did this in school

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Use cylindrical coordinates to evaluate the triple integral ∭ where E is the solid bounded by the circular paraboloid z = 9 - 16
4vir4ik [10]

Answer:

\mathbf{\iiint_E  E \sqrt{x^2+y^2} \ dV =\dfrac{81 \  \pi}{80}}

Step-by-step explanation:

The Cylindrical coordinates are:

x = rcosθ, y = rsinθ and z = z

From the question, on the xy-plane;

9 -16 (x^2 + y^2) = 0 \\ \\  16 (x^2 + y^2)  = 9 \\ \\  x^2+y^2 = \dfrac{9}{16}

x^2+y^2 = (\dfrac{3}{4})^2

where:

0 ≤ r ≤ \dfrac{3}{4} and 0 ≤ θ ≤ 2π

∴

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} \int ^{9-16r^2}_{0} \ r \times rdzdrd \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 z|^{z= 9-16r^2}_{z=0}  \ \ \ drd \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 ( 9-16r^2})  \ drd \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0}  ( 9r^2-16r^4})  \ drd \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0}   ( \dfrac{9r^3}{3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0}  \ drd \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0}   ( 3r^3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0}  \ drd \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0}   ( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) d \theta

\iiint_E  E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) \theta |^{2 \pi}_{0}

\iiint_E  E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}})2 \pi

\iiint_E  E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{64}}-\dfrac{243}{320}})2 \pi

\iiint_E  E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{160}})2 \pi

\mathbf{\iiint_E  E \sqrt{x^2+y^2} \ dV =\dfrac{81 \  \pi}{80}}

4 0
3 years ago
Drag each title to the correct box. Not all tiles will be used
mestny [16]

Answer:

4, 1, 6.

See explanation

Step-by-step explanation:

You are given the equation

d=vt-\dfrac{1}{2}at^2

First subtract vt from both sides:

d-vt--\dfrac{1}{2}at^2

and multiply the equation by -1:

vt-d=\dfrac{1}{2}at^2\ \ \ \ (1)

Now multiply (1) by 2:

2(vt-d)=at^2\ \ \ \ \ (2)

At last, divide by a

t^2=\dfrac{2(vt-d)}{a}\ \ \ \ \ (3)

5 0
3 years ago
15 points, no messing around, please do it right
cupoosta [38]

Answer:

416 is your answer!!!

Step-by-step explanation:

mak me brainliest and add me as a fiend

8 0
2 years ago
The Best Company produces two commercial products : blenders and mixers. Both products require a two step production process inv
deff fn [24]

Answer:

Maximum profit is $87 when 3 blenders and 11 mixers are produced.

Step-by-step explanation:

let blender is represented by x_{1} and and mixer by x_{2}.

total time to deliver parts = 24 hrs

total time to assemble = 30 hrs

time taken by each blender to deliver parts = 1 hr

time taken by each mixer to deliver parts = 2 hr

time taken by blenders in final assembling= 2 hr

time taken by mixers in final assembling = 3 hr

Each blender produced nets the firm=  $7

Each mixer produced nets the firm=  $6

Using this all data linear system of equation will be:

x_{1} + 2x_{2} =24  ----- (1)\\2x_{1} + 2x_{2} = 30 ----- (2)\\

profit function:

z= 7x_{1} +6x_{2} --- (3)

from (1)\\x_{1} = 0 \implies x_{2}= 12\\x_{2}= 0 \implies x_{1}= 24\\

Coordinate points obtained from (1) are (0,12) and (24,0)

from (2)\\x_{1}=0 \implies x_{2}=10\\x_{2}=0 \implies x_{1}=15\\

Coordinate points obtained from (2) are (0,10) and (15,0)

plotting these on graph

points lying in feasible region are:

A(0,0)

B(0,10)

C(3,11)

D(12,0)

substituting these points in (3) to find the maximum profit:

for A (0,0)

z = 0

for B (0,10)

z = 60

for C (3,11)

z =  87

for D (12,0)

z=84

So maximum profit is $87 when 3 blenders and 11 mixers are produced.

4 0
3 years ago
What is the x-coordinate of the vertex of the parabola whose equation is y = 3x^2 + 12x + 5?
Genrish500 [490]

Answer:

(-2,-7)

Step-by-step explanation:

8 0
3 years ago
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