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2 years ago

a local city collects 8% sales tax if the total purchase was $216 then how much was collected for sales tax

Mathematics

1 answer:

Fudgin [204]2 years ago

6 0

When typing the equation : $216x8% the 8% become .08 so multiply .08 by $216 and your final answer is $17.28

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(a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩r→1(t)=⟨x(t),y(t),z(t)⟩ for the shadow of the circular cylinder x2

motikmotik

Answer: (a) r1(t) = <2cost , 0 , 2sint>

(b) <2cost , (1 - 12sint - 10cost)/8 , 2sint>

Step-by-step explanation:

x2+z2=4

Now, in the xz plane, we know that y = 0...

So, x^2 + z^2 = 4 will simply be a circle centered at (0,0)..

This can be easily parameterized as

x = 2cos(t)

z = 2sin(t)

So, the required parameterization is :

r1(t) = <2cost , 0 , 2sint>

Cylinder : x^2 + z^2 = 4

Plane : 5x+8y+6z=1

Easily enough, the x^2 + z^2 = 4 can again be parameterized as

x = 2cost , z = 2sint

With this, we can find y using plane equation...

5x+8y+6z=1

5(2cost) + 8y + 6(2sint) = 1

8y = 1 - 12sint - 10cost

y = (1 - 12sint - 10cost)/8

So, the parameterization is :

<2cost , (1 - 12sint - 10cost)/8 , 2sint>

6 0

2 years ago

Which of the following graphs could be the graph of the function f(x) = x4 + x3 – x2 – x?

Sav [38]

For this case we have the following function:
$x ^ 4 + x ^ 3 - x ^ 2 - x
$
We can rewrite the function to identify the zeros of it.
When rewriting the function factoring we have: $x (x-1) (x + 1) ^ 2
$
Therefore, the zeros of the function are:
$x = 0

x = 1

x = -1$
Thus, the graph that contains intersections on the x axis in the points mentioned, will be the graph of the function.
Answer:
See attached image.

8 0

2 years ago

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Nancy's 50-meter freestyle swim time was 28.004 seconds. Betty’s 50-meter freestyle swim time was 27.949 seconds. What was the d

loris [4]

The difference between the 2 times would be .055 seconds...

6 0

2 years ago

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Solve for x:<br> 3(5x + 10) + 10 = 6x - (x + 10)

34kurt

Answer:

x= -5

Step-by-step explanation:

3(5x+10)+10=6x-(x+10)

15x+30+10=6x-x-10

15x+40=5x-10

15x-5x=-10-40

10x=-50

x=-5

8 0

2 years ago

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a patio is shaped like a golden rectangle. it's length ( the longer side) is 16ft. what is the patios width? write your answer i

Trava [24]

$a\ golden\ rectangle:\ \ \ \frac{a+b}{a}= \frac{a}{b} \\----------------\\a+b=16\ [ft]\ \ \ \ \Rightarrow \ \ \ b=16-a\\\\ \frac{16}{a} = \frac{a}{16-a} \ \ \ \ \Leftrightarrow\ \ \ 16(16-a)=a^2\\\\a^2+16a-256=0\\\\\ \ \ \Rightarrow\ \ \ \Delta=16^2-4\cdot(-256)=256\cdot5\ \ \ \Rightarrow\ \ \ \sqrt{\Delta} =16 \sqrt{5} \\\\a_1= \frac{-16-16 \sqrt{5} }{2} =-8-8 \sqrt{5} 0\\\\$

$a=8( \sqrt{5} -1)\ \ \Rightarrow\ \ b=16-8( \sqrt{5} -1)=16-8\sqrt{5} +8=8(3- \sqrt{5} )\\\\Ans.\ This\ golden\ ractangle\ has\ sides:\\.\ \ \ \ \ \ \ 8( \sqrt{5} -1)\ [ft]\ \ and\ \ 8(3- \sqrt{5} )\ [ft]$

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2 years ago