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3 years ago

Write 57% as a ratio

Mathematics

2 answers:

PIT_PIT [208]3 years ago

5 0

The answer to this would be 57:100. this would be read as fifty seven to one hundred
hope this helps

Feliz [49]3 years ago

4 0

It’d be 0.57, hope this helps.

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jekas [21]

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2 years ago

Read 2 more answers

The volume (in cubic inches) of a shipping box is modeled by V =2x³ -19x² +39x, where x is the length (in inches). Determine the

yawa3891 [41]

Answer:

The values of x for which the model is 0 ≤ x ≤ 3

Step-by-step explanation:

The given function for the volume of the shipping box is given as follows;

V = 2·x³ - 19·x² + 39·x

The function will make sense when V ≥ 0, which is given as follows

When V = 0, x = 0

Which gives;

0 = 2·x³ - 19·x² + 39·x

0 = 2·x² - 19·x + 39

0 = x² - 9.5·x + 19.5

From an hint obtained by plotting the function, we have;

0 = (x - 3)·(x - 6.5)

We check for the local maximum as follows;

dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0

6·x² - 38·x + 39 = 0

x² - 19/3·x + 6.5 = 0

x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2

∴ x = 1.288, or 5.045

At x = 1.288, we have;

V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99

V ≈ 22.99 in.³

When x = 5.045, we have;

V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023

Therefore;

V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5

The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.

8 0

3 years ago

Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

for $0\le t\le1$ , which has differential

$\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

Then with $x(t)=y(t)=z(t)=1-t$ , we have

$\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r$

$=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt$

Complete the square in the quadratic term of the integrand: $t^2-2t+2=(t-1)^2+1=(1-t)^2+1$ , then in the integral we substitute $u=1-t$ :

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt$

$\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du$

Make another substitution of $v=u^2$ :

$\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv$

Integrate by parts, taking

$r=v+1\implies\mathrm dr=\mathrm dv$

$\mathrm ds=e^v\,\mathrm dv\implies s=e^v$

$\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv$

$\displaystyle=-(2e-1)+(e-1)=-e$

So, we have by the fundamental theorem of calculus that

$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

$\implies-e=f(1,1,1)-2$

$\implies f(1,1,1)=2-e$

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3 years ago

PYTHAGOREAN THEOREM IN 3D URGENT PLEASE PHOTO INSERTED

Andrews [41]

To find the length of the diagonal, we need to calculate the length of the base first and then use the value to calculate the diagonal since we are given the value of height of the triangle.

<h3>Pythagorean Theorem</h3>

This theorem is used to find the missing side of a right angle triangle given that we have the length of two sides.

To calculate the base of the triangle, let's use Pythagorean theorem here

$x^2 = y^2 + z^2\\x^2 = 2^2 + 3^2\\x^2 = 4 + 9 \\x^2 = 13\\x = \sqrt{13} \\x = 3.61$