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Mathematics

1 answer:

bogdanovich [222]3 years ago

5 0

Answer:

(7, -10)

(-1, 1)

(2, -7)

Step-by-step explanation:

Points that are in Quadrant II will have a negative x-value and a positive y-value. (-, +)

Points that are in Quadrant IV will have a positive x-value and a negative y-value. (+, -)

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The ratio of two numbers is 8:7. The product of these numbers is 896. What is the smaller of these two

Darina [25.2K]

Answer:

Step-by-step explanation:

You want the smaller of the two factors of 896 that have the ratio 8:7.

<h3>Setup</h3>

Let x represent the smaller of the two factors (the one we want to find). Then the larger factor is (8/7)x, and their product is ...

x(8/7)x = 896

(8/7)x² = 896

<h3>Solution</h3>

Multiplying by the inverse of the coefficient of x², we have ...

x² = (7/8)(896) = 784

x = √784 = 28 . . . . . . . . take square root

The smaller of the two numbers is 28.

Additional comment

The larger is (8/7)(28) = 32.

5 0

2 years ago

An atrium is being designed to house an exhibit of tropical birds. The atrium must enclose 250,000 cubic feet of space, and the

9966 [12]

The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium.

<h3>Can this atrium be built in the rectangular plot of land?</h3>

The atrium with the maximum allowable radius (R), in feet, is represented in the image attached. The real atrium is possible if and only if the real radius (r) is less than the maximum allowable radius and therefore, the real volume (V), in cubic feet, must be less than than maximum possible volume (V'), in cubic feet.

First, we calculate the volume occupied by the maximum allowable radius:

V' = (8 · π / 3) · (45 ft)³

V' ≈ 763407.015 ft³

The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium. $\blacksquare$