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2 years ago

Maya shaved her head and then began letting her hair grow. She represents the length

Mathematics

1 answer:

Svetach [21]2 years ago

4 0

Answer:

1.25 is the rate of growth of hairs per month.

Step-by-step explanation:

Given : L represents the length of hair.

m represents months after she shaved her head .

Equation :

To Find: What does 1.25 mean in this situation?

Solution:

Equation :

Since it is linear function . So, 1.25 is the slope

Slope is the rate of change per unit.

So, 1.25 is the rate of growth of hairs per month.

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Which expression is equivalent to -6(3x-2/3)

Fiesta28 [93]

Answer:

Solution given:

-6(3x-⅔)

distribute it

-18x+6*⅔

-18x+4 is a required answer.

3 0

3 years ago

Susan is 5.5 ft tall and casts a shadow that it is 4 ft long on the ground. She is walking through a park and finds the shadow o

Vika [28.1K]

Answer:

22 ft

Step-by-step explanation:

Height of Susan/Length of shadow = Height of sculpture/Length of Shadow of sculpture

5.5 ft/4 ft = x/16ft

Cross Multiply

4 × x = 5.5 × 16

x = 5.5 × 16/4

x = 22 ft

The height of the sculpture is 22 ft

4 0

3 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

4 years ago

A university's freshman class has 4800 students. 76% of those students are majoring in Economics. How many students in the fresh

IceJOKER [234]

Answer:

3648 Freshmen students major in economics.

Step-by-step explanation:

This is done by taking the whole class (4800) and multiply it by the percentage (.76 ((converted to decimal))) to get the amount.

5 0

3 years ago

HEY How Your Day?? MIne... Tired

Veseljchak [2.6K]

Answer:

good :-))

n ur ??????

.....

.. . ... .

8 0

3 years ago