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2 years ago

Which of the following coordinates of points belong to the solution set of the inequality y <2x² +3x - 5?

Mathematics

1 answer:

bogdanovich [222]2 years ago

6 0

Answer:

Step-by-step explanation:

Check the inequality for each point.

For A. (-3,2)

$y < {2x}^{2} + 3x - 5 \\ 2 < {2 ( - 3)}^{2} + 3( - 3) - 5 \\ 2 < 2 \times 9 - 9 - 5 \\ 2 < 18 - 9 - 5 \\ 2 < 4 \\$

The inequality is satisfied.

For B. (-2,9)

$y < {2x}^{2} + 3x - 5 \\ 9 < 2 {( - 2)}^{2} + 3( - 2) - 5 \\ 9 < 2(4) - 6 - 5 \\ 9 < 8 - 6 - 5 \\ 9 < - 3 \\$

The inequality is not satisfied.

For C. (1,6)

$y < {2x}^{2} + 3x - 5 \\ 6 < {2(1)}^{2} + 3(1) - 5 \\ 6 < 2(1) + 3 - 5 \\ 6 < 2 + 3 - 5 \\ 6 < 0$

The inequality is not satisfied.

For D. (3,1)

$y < {2x}^{2} + 3x - 5 \\ 1 < {2(3)}^{2} + 3(3) - 5 \\ 1 < 2(9) + 9 - 5 \\ 1 < 18 + 9 - 5 \\ 1 < 22 \\$

The inequality is satisfied.

For E. (-1,5)

$y < {2x}^{2} + 3x - 5 \\ 5 < {2( - 1)}^{2} + 3( - 1) - 5 \\ 5 < 2(1) - 3 - 5 \\ 5 < 2 - 3 - 5 \\ 5 < - 6 \\$

The inequality is not satisfied.

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

$16x^2+y^2=16$

To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0

3 years ago

A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What pe

kicyunya [14]

Answer:

(a) 5.48%

(b) 17.82 years

(d) 15.21 years

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

µ=12 years and σ=2.5 years.

(a) What percent of the radios will function for more than 16 years?

For x = 16

z = 16 - 12/2.5

z = 1.6

Probability value from Z-Table:

P(x<16) = 0.9452

P(x>16) = 1 - P(x<16)

1 - 0.9452

= 0.054799

Converting to percentage = 0.054799 × 100

= 5.4799%

Approximately = 5.48%

(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.

find the z score of the 99th percentile = 2.326

Hence:z = (x-μ)/σ

2.326 = x - 12/2.5

Cross Multiply

2.326 × 2.5 = x - 12

5.815 = x - 12

x = 12 + 5.815

x = 17.815

Approximately = 17.82 years

When x < 10

Hence,

z = 10 - 12/2.5

z = -0.8

Probability value from Z-Table:

P(x<10) = 0.21186

Converting to percentage

0.21186 × 100

= 21.186%

Approximately = 21.19%

(d) If 10% of the radios will function for more than X years, find X.

The z score would be : 100 - 10%

= 90th percentile z score

We find the z score of the 90th percentile = 1.282

Hence:z = (x-μ)/σ

1.282 = x - 12/2.5

Cross Multiply

1.282 × 2.5 = x - 12

3.205 = x - 12

x = 12 + 3.205

x = 15.205

Approximately = 15.21 years

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2 years ago

Are these lines parallel perpendicular or neither

Natasha_Volkova [10]

Answer:

perpendicular

Step-by-step explanation:

start but putting each line into the standard line format

2x-y=-5

-y=-2x-5

y=2x+5

x+2y=-6

2y=-x-6

y=-(1/2)x-3

if lines are parallel the slopes would be the same. 2 is not equal to -1/2

if lines are perpendicular the slope of one would be the opposite inverse of the other.

negative inverse of 2 = - (1/2)

so the lines are perpendicular

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How many liters are there in a tank of volume 7.32m³?

Ivenika [448]

Answer: 3 liters in a tank of volume 7.32m^3

Step-by-step explanation:

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1 year ago

The theoretical probability of drawing a red card from a deck of cards is 1:2. Michael drew 20 cards and received 7 red and 13 b

Anon25 [30]

Answer and Step-by-step explanation:

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In the case above, the theoretical which is the expected probability that has not been experimented is 1/2 of getting Red cards. This probability is theoretical and therefore may change when tested. Hence the different result of 7 Red and 13 blacks with 20 cards picked when experimented

6 0

2 years ago