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3 years ago

The area of a rectangle is 60 cm2 If the width of the

Mathematics

1 answer:

aleksklad [387]3 years ago

6 0

The length of the rectangle is 10 cm and perimeter of the rectangle is 32 cm.

Step-by-step explanation:

Given,

The area of rectangle = 60 sq cm

Width (b) of the rectangle = 6 cm

To find the length and perimeter of the rectangle.

Formula

The area of the rectangle = l×b

The perimeter of the rectangle = 2(l+b)

According to the problem,

l×b = 60

or, l×6 = 60

or, l = 60÷6 = 10

Length (l) = 10 cm

Perimeter = 2×(10+6) cm = 32 cm

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Use lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5).

horsena [70]

Lagrangian:

$L(x,y,z,\lambda)=x^2+(y-2)^2+(z-5)^2+\lambda(x-2y+3z-6)$

where the function we want to minimize is actually $\sqrt{x^2+(y-2)^2+(z-5)^2}$ , but it's easy to see that $\sqrt{f(\mathbf x)}$ and $f(\mathbf x)$ have critical points at the same vector $\mathbf x$ .

Derivatives of the Lagrangian set equal to zero:

$L_x=2x+\lambda=0\implies x=-\dfrac\lambda2$
$L_y=2(y-2)-2\lambda=0\implies y=2+\lambda$
$L_z=2(z-5)+3\lambda=0\implies z=5-\dfrac{3\lambda}2$
$L_\lambda=x-2y+3z-6=0$

Substituting the first three equations into the fourth gives

$-\dfrac\lambda2-2(2+\lambda)+3\left(5-\dfrac{3\lambda}2\right)=6$
$11-7\lambda=6\implies \lambda=\dfrac57$

Solving for $x,y,z$ , we get a single critical point at $\left(-\dfrac5{14},\dfrac{19}7,\dfrac{55}{14}\right)$ , which in turn gives the least distance between the plane and (0, 2, 5) of $\dfrac5{\sqrt{14}}$ .

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3 years ago

Carrie saved money to spend while on a one-month vacation to Europe. On day 8, she had $2,400 remaining. On day 16, she had $1,6

garik1379 [7]

If this is represented by a linear function, then we know that the amount of money decreases at an unchanging amount. Knowing this, and knowing that on day 8, she had 2400, we simply just add 2400 to 8 100's:

2400 + 8*100 = 2400 + 800

Carrie initially had $3200, or Option C.

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3 years ago

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A forest inhabited only by borogoves and mome raths contains eighty-two creatures. Borogoves are two-legged animals, while mome

evablogger [386]

A+b=82
2a+4b=324

Solve for a and b. a is the # of borogoves, b is the # of mome raths.

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3 years ago

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leonid [27]

Answer:

it is 69

Step-by-step explanation:

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3 years ago

Hi please help me!! thanks

Artist 52 [7]

Answer:

3.2 x 10^13

Step-by-step explanation:

(8x10^4)(4x10^8)

reorder the terms using the commutative property

(8x4)x(10^4x10^8)

multiply

32x (10^4 x 10^8)

= 32 x 10^4+8

= 32 x 10^12

now convert to scientific notation

=3.2 x 10^13

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2 years ago