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nekit [7.7K]
3 years ago
14

(a) (4,4) is a point on a locus whose equation is y2 = kx. Show that (16,8) is another point on the locus.

Mathematics
2 answers:
Vlad [161]3 years ago
6 0

Step-by-step explanation:

plug the coordinate points into the equations and solve for the remaining variable.

b) (2,3) - 5(2) + b(3) = 16

10 + 3b = 16. 3b= 6. b = 2

(0,8) - 5(0) + 2(8) = 16. 0+ 16 = 16. ☆

a) (4,4) assume based on results you meant y squared. (y^2)

(4)^2 = 4k. 16 = 4k. k = 4

(8)^2 = 4(16). 64 = 64. ☆

IgorLugansk [536]3 years ago
3 0

Answer:

Please check the explanation.

Step-by-step explanation:

a)

Given

(4,4) is a point on a locus whose equation is y²=kx

Putting (4, 4) in y²=kx

(4)² = k(4)

16 = 4k

k = 16/4

k = 4

Checking the point (16, 8) on the locus

y²=kx

Putting (16, 8) and k =4 in y²=kx

y²=kx

(4)² = 4×4

16 = 16

L.H.S = R.H.S

Therefore, (16, 8) is another point on the locus.

b)

Given

(2, 3) is a point on a locus whose equation is 5x +by= 16

Putting (2, 3) in 5x +by= 16

5x+by=16

5(2)+b(3)=16

10+3b=16

3b=6

b=6/3

b=2

Putting (0, 8) and b=2 in 5x +by= 16

5x +by= 16

5(0)+2(8)=16

0+16=16

16=16

L.H.S = R.H.S

Therefore, (0, 8) is another point on the locus.

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Answer:

6x² + 5x - 6

Step-by-step explanation:

Given

(2x + 3)(3x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(3x - 2) + 3(3x - 2) ← distribute both parenthesis

= 6x² - 4x + 9x - 6 ← collect like terms

= 6x² + 5x - 6

6 0
3 years ago
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Evaluate the function f(x) = sec(x - pi/2) for x = 0.
Anvisha [2.4K]
\sec\left(0-\dfrac{\pi}{2}\right)=\sec\left(-\dfrac{\pi}{2}\right)=\dfrac{1}{\cos \left(-\dfrac{\pi}{2}\right)}=\dfrac{1}{0}

So, the function f(x) for x=0 is undefined.
5 0
2 years ago
The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest
Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)

Calculation the value from standard normal z table, we have,  

P(x < 5) =0.7287= 72.87\%

b) P( port handles 3 or more million tons of cargo per week)

P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)

Calculating the value from the standard normal table we have,

1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%

c)P( port handles between 3 million and 4 million tons of cargo per week)

P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%

P(3 \leq x \leq 4) = 23.7\%

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)  

P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85  

= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85  

=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15  

Calculation the value from standard normal z table, we have,  

P( z \leq -1.036) = 0.15

\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

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2 years ago
What is the value of X?
rodikova [14]

Answer:

102

Step-by-step explanation:

triangle area = 180 degrees

straight line = 180 degrees

180 - 127 = 53

49

49 + 53 + 3rd angle = 180

3rd angle = 78

180-78 = x

x = 102

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notsponge [240]

Answer:

157.08

Step-by-step explanation:

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6 0
2 years ago
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