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kirill [66]
4 years ago
11

Is 6/15 equivalent to 2/3​

Mathematics
1 answer:
Archy [21]4 years ago
6 0

Answer:

yes they are both divisible by three

Step-by-step explanation:

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What is the distance from the pair of points (7,3) and (-1,-4)
mafiozo [28]

Answer:

The distance between the two points is 10.63015

D=10.63015

8 0
4 years ago
Calculate the slope of the line given the points (2,1) and (1,-4)
Dmitrij [34]

The equation for the slope of a line is:

y2-y1/x2-x1

So:

-4-1/1-2 = -5/-1 =5

The slope of the line is 5.

8 0
3 years ago
Read 2 more answers
Lin is reading a 47-page book. She read the first 20 pages in 35 minutes. Rounding to the nearest minute, how long will it take
Kruka [31]

Answer: 82.25 minutes

Step-by-step explanation:

First convert the minutes she took to hours. This would be:

= 35/60

She is reading at a speed of 20 pages per 35/60 hours.

To finish 47 pages therefore, she will take:

= (47 * 35/60) / 20

= 1.37083 hours

Converted to minutes that would be:

= 1.37083 * 60 mins

= 82.25 minutes

7 0
3 years ago
Find the minimum and maximum of f(x,y,z)=x2+y2+z2 subject to two constraints, x+2y+z=7 and x−y=6.
sweet-ann [11.9K]
Use the method of Lagrange multipliers. We have Lagrangian

L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-7)+\lambda_2(x-y-6)

with partial derivatives (set equal to 0) of

L_x=2x+\lambda_1+\lambda_2=0
L_y=2y+2\lambda_1-\lambda_2=0
L_z=2z+\lambda_1=0
L_{\lambda_1}=x+2y+z-7=0
L_{\lambda_2}=x-y-6=0

As x+2y+z=7, and x-y=6, we can obtain

\dfrac12L_x+L_y+\dfrac12L_z=0\implies3\lambda_1-\dfrac12\lambda_2=-7
L_x-L_y=0\implies\lambda_1-2\lambda_2=12
\begin{cases}3\lambda_1-\frac12\lambda_2=-7\\\lambda_1-2\lambda_2=12\end{cases}\implies\lambda_1=-\dfrac{40}{11},\lambda_2=-\dfrac{86}{11}

From this, we find a single critical point:

2x-\dfrac{40}{11}-\dfrac{86}{11}=0\implies x=\dfrac{63}{11}
\dfrac{63}{11}-y=6\implies y=-\dfrac3{11}
\dfrac{63}{11}-\dfrac6{11}+z=7\implies z=\dfrac{20}{11}

At this point, we have a value of

f\left(\dfrac{63}{11},-\dfrac3{11},\dfrac{20}{11}\right)=\dfrac{398}{11}

To determine what kind of extremum occurs at this point, we check the Hessian of f(x,y,z):

\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}

We observe that \det\mathbf H(x,y,z)=8>0 at any point (x,y,z), and that the eigenvalues of this matrix are all positive (2 with multiplicity 3), so \mathbf H is positive definite. By the second partial derivative test, this means f(x,y,z) attains a minimum at this critical point. Meanwhile, f has no maximum value.
5 0
3 years ago
Can someone help me with this problem please:((
NNADVOKAT [17]
P= perimeter = 62 = 15+10+13+x = 38+x
then x=62-38= 24

A= 1/2 * (10+24) *h
204 = 1/2 * 34 * h
204*2 * 1/34 = h
12= h

then h= 12
8 0
3 years ago
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