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3 years ago

10

The ratio of kangaroos to koalas in the Australian zoo is 6 to 8 . If there are 132 koalas in the zoo how many kangaroos are in

the gym

1 answer:

dolphi86 [110]3 years ago

8 0

Answer:

99

Step-by-step explanation:

set it up as a proportion 6/8 = x/132. then solve

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Two similar rectangles have a scale factor of 3:2 the perimeter of the small rectangle is 50 feet.What is the perimeter of the l

Katyanochek1 [597]

Answer: 75 feet

Step-by-step explanation:

From the question, we are informed that two similar rectangles have a scale factor of 3:2 and that the perimeter of the small rectangle is 50 feet.

The perimeter of the large rectangle measured in feet will be calculated as:

= 3/2 × 50

= 150/2

= 75 feet

7 0

3 years ago

Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

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3 years ago

Which type of parent function is f(x) =^3cubed x

sergij07 [2.7K]

Answer:

Cube Root

Step-by-step explanation:

Because there is a 3 outside the symbol.

That means the equation is stating: y * y * y = x

Hope this helps :)

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2 years ago

The sum of the measures of two complementary angles is 90°. If one angle measures 24° more than twice the measure of the other,

geniusboy [140]

X + y = 90

Let's make 'x' the bigger angle and 'y' the smaller.
X is 24 more than twice y.
x = 24 + 2y

Now plug that into the x of the first equation.
(24 + 2y) + y = 90

Combine like terms.
24 + 3y = 90

Subtract 24 from both sides.
3y = 66

Divide both sides by 3.
y = 22

The measure of the smaller angle is 22°

3 0

3 years ago

Find m ab <br> Find m acb

gulaghasi [49]

MAB = 110
mACB = 360 - 110 = 250

hope it helps

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3 years ago