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Katen [24]
2 years ago
12

The distance from Greg's house to Tanya's house is 7/10 of a mile. Which number correctly shows the number of miles a decimal?*

Greg's house C Tanya's house Homile mile 07.10 7.0 0.7 0.07​
Mathematics
1 answer:
STALIN [3.7K]2 years ago
8 0

Answer:

<h2>7 divide by 10=0.7 so <em><u>0</u></em><em><u>.</u></em><em><u>7</u></em><em><u> </u></em> is the correct answer</h2>
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Is .07 closer to 1/2,0 or 1
Nikitich [7]
0, because 1/2 = 0.50. therefore .07 is more closer to 0
7 0
2 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

3 0
3 years ago
1/2x +1/4y =32 , then find 2x+y
NeX [460]

Answer:

128

Step-by-step explanation:

3 0
2 years ago
What is 3÷34<br><br> A. 2.25<br> B. 3<br> C. 4<br> D. 12
harina [27]

Answer:

I think it is 12

(D)

6 0
2 years ago
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Monica ramirez works at the hospital as a nursing assistant. she works 15 hours per week and earns $8.50 per hour. what is monic
nikklg [1K]
$127.50 because 15*8.50 is 127.50
6 0
3 years ago
Read 2 more answers
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