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3 years ago

Which statements are true about the linear inequality y > Three-fourthsx – 2? Select three options.

Mathematics

2 answers:

sertanlavr [38]3 years ago

6 0

Answer:

The correct answer choices are B, D, and E.

=))))))))))))))))))))))))))

can i get brainliest answer?? please!! i need it :p

Rashid [163]3 years ago

3 0

Answer:

The graph of y > Three-fourthsx – 2 is a dashed line

One solution to the inequality is (0, 0)

The graph intercepts the y-axis at (0, –2)

Step-by-step explanation:

we have

$y>\frac{3}{4}x-2$

The solution of the inequality is the dashed line above the solid line $y=\frac{3}{4}x-2$

The slope of the dashed line is positive and is equal to $m=\frac{3}{4}$

The y-intercept of the dashed line is (0,-2)

<u><em>Verify each statement</em></u>

Option 1) The slope of the line is –2

The statement is false

Because

The slope is equal to $m=\frac{3}{4}$

Option 2) The graph of y > Three-fourthsx – 2 is a dashed line

The statement is true (see the explanation)

Option 3) The area below the line is shaded

The statement is false

Because

The area above the line is shaded

Option 4) One solution to the inequality is (0, 0)

The statement is true

Because

If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality

Substitute the value of x and the value of y of the ordered pair in the inequality

For x=0, y=0

$0>\frac{3}{4}(0)-2$

$0>-2$ ---> is true

The ordered pair is a solution of the inequality

Option 5) The graph intercepts the y-axis at (0, –2)

The statement is true (see the explanation)

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Consider a propeller driven aircraft in forward flight at a speed of 150 mph: The propeller is set up with an advance ratio such

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a) The thrust of the propeller is 23,834 lbf

b) The induced velocity is 8.44 mph

c) The velocity in the downstream far field away from the propeller disc is 161.56 mph

d) The power absorbed by the fluid is 42.7 hp

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f) The propeller efficiency is 113.6%

a)The thrust of the propeller can be calculated using the equation,

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the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf

b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph

c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph

d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp

e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp

f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%

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