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2 years ago

Tell whether the ordered pair (−1, 4) is a solution of the system.

Mathematics

1 answer:

lina2011 [118]2 years ago

6 0

Answer:

(-1,4) is a solution to the system.

Step-by-step explanation:

For this problem, we can simply identify if this point is a solution by verifying the plugged in point values allow the left hand side to equal the right hand side.

(1) -2x - 3y = -10

-2(-1) - 3(4) ?= -10

2 - 12 ?= -10

-10 == -10

(2) -3x + y = 7

-3(-1) + (4) ?= 7

3 + 4 ?= 7

7 == 7

Since both equations are satisfied by this point, then we can say the point (-1,4) is a solution to the system. Additionally, this means this is a crossing point of the system of equations.

Cheers.

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The circumference of the equator of a sphere was measured to be 82 82 cm with a possible error of 0.5 0.5 cm. Use linear approxi

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Answer:

The maximum error in the calculated surface area is approximately 8.3083 square centimeters.

Step-by-step explanation:

The circumference ( $s$ ), in centimeters, and the surface area ( $A_{s}$ ), in square centimeters, of a sphere are represented by following formulas:

$A_{s} = 4\pi\cdot r^{2}$ (1)

$s = 2\pi\cdot r$ (2)

Where $r$ is the radius of the sphere, in centimeters.

By applying (2) in (1), we derive this expression:

$A_{s} = 4\pi\cdot \left(\frac{s}{2\pi} \right)^{2}$

$A_{s} = \frac{s^{2}}{\pi^{2}}$ (3)

By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area ( $\Delta A_{s}$ ), in square centimeters: