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3 years ago

Please help me please

Mathematics

1 answer:

Paha777 [63]3 years ago

8 0

Answer:

(b) Function B

Step-by-step explanation:

The exponent of 2 in Function B tells you it is nonlinear. A linear function will not have any product of variables or any roots.

You know function A is linear because the differences in x-values are all the same, and the differences in y-values are all the same. What makes it linear is that the ratio of y-differences to x-differences is a constant:

Δy/Δx = (8 -10)/(2 -0) = -1 = (6 -8)/(4 -2) = (4 -6)/(6 -4)

Function B is nonlinear.

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A model rocket is launched straight upward. The solid fuel propellant pushes the rocket off the ground at an initial velocity of

anastassius [24]

Answer:

a) 72.25sec

b) 6.25secs

c) after 10.5secs and 2 secs

Step-by-step explanation:

Given the height reached by the rocket expressed as;

s(t)= -4t^2 + 50t - 84

At maximum height, the velocity of the rocket is zero i.e ds/dt = 0

ds/dt = -8t + 50

0 = -8t + 50

8t = 50

t = 50/8

t = 6.25secs

Hence it will reach the maximum height after 6.25secs

To get the maximum height, you will substitute t - 6.25s into the given expression

s(t)= -4t^2 + 50t - 84

s(6.25) = -4(6.25)^2 + 50(6.25) - 84

s(6.25) = -156.25 + 312.5 - 84

s(6.25) = 72.25feet

Hence the maximum height reached by the rocket is 72.25feet

The rocket will reach the ground when s(t) = 0

Substitute into the expression

s(t)= -4t^2 + 50t - 84

0 = -4t^2 + 50t - 84

4t^2 - 50t + 84 = 0

2t^2 - 25t + 42 = 0

2t^2 - 4t - 21t + 42 = 0

2t(t-2)-21(t-2) = 0

(2t - 21) (t - 2) = 0

2t - 21 = 0 and t - 2 = 0

2t = 21 and t = 2

t = 10.5 and 2

Hence the time the rocket will reach the ground are after 10.5secs and 2 secs

3 0

3 years ago

Q2 - With decimals

Mila [183]

Answer:

Simplify the following algebraic expressions.

- 6x + 5 + 12x -6

2(x - 9) + 6(-x + 2) + 4x

3x2 + 12 + 9x - 20 + 6x2 - x

(x + 2)(x + 4) + (x + 5)(-x - 1)

1.2(x - 9) - 2.3(x + 4)

(x2y)(xy2)

(-x2y2)(xy2)

Solution

Group like terms and simplify.

- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - by

Solution

Use rules of exponential to simplify the numerator first.

(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)

Rewrite as follows.

(a4 / a2) (b3 / b3)

Use rule of quotient of exponentials to simplify.

= a2

Rewrite as follows.

(21 x5) / (3 x4) = (21 / 3)(x5 / x4)

Simplify.

= 7 x

(6 x4)(4 y2) / [ (3 x2)(16 y) ]

Multiply terms in numerator and denominator and simplify.

(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)

Rewrite as follows.

= (24 / 48)(x4 / x2)(y2 / y)

Simplify.

= (1 / 2) x2 y

Factor 4 out in the numerator.

(4x - 12) / 4 = 4(x - 3) / 4

Simplify.

= x - 3

Factor -5 out in the numerator.

(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)

Simplify.

= - 5

Factor numerator and denominator as follows.

(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]

Simplify.

= (x + 2) / (x + 4) , for all x not equal to 6

Solve for x the following linear equations.

2x = 6

6x - 8 = 4x + 4

4(x - 2) = 2(x + 3) + 7

0.1 x - 1.6 = 0.2 x + 2.3

- x / 5 = 2

(x - 4) / (- 6) = 3

(-3x + 1) / (x - 2) = -3

x / 5 + (x - 1) / 3 = 1/5

Solution

Divide both sides of the equation by 2 and simplify.

2x / 2 = 6 / 2

x = 3

Add 8 to both sides and group like terms.

6x - 8 + 8 = 4x + 4 + 8

6x = 4x + 12

Add - 4x to both sides and group like terms.

6x - 4x = 4x + 12 - 4x

2x = 12

Divide both sides by 2 and simplify.

x = 6

Expand brackets.

4x - 8 = 2x + 6 + 7

Add 8 to both sides and group like terms.

4x - 8 + 8 = 2x + 6 + 7 + 8

4x = 2x + 21

Add - 2x to both sides and group like terms.

4x - 2x = 2x + 21 - 2x

2x = 21

Divide both sides by 2.

x = 21 / 2

Add 1.6 to both sides and simplify.

0.1 x - 1.6 = 0.2 x + 2.3

0.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.6

0.1 x = 0.2 x + 3.9

Add - 0.2 x to both sides and simplify.

0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x

- 0.1 x = 3.9

Divide both sides by - 0.1 and simplify.

x = - 39

Multiply both sides by - 5 and simplify.

- 5(- x / 5) = - 5(2

What is the y intercept of the line - 4 x + 6 y = - 12?

Solution

Set x = 0 in the equation and solve for y.

- 4 (0) + 6 y = - 12

6 y = - 12

y = - 2

y intercept: (0 , - 2)

What is the x intercept of the line - 3 x + y = 3?

Solution

Set y = 0 in the equation and solve for x.

- 3 x + 0 = 3

x = -1

x intercept: (-1 , 0)

What is point of intersection of the lines x - y = 3 and - 5 x - 2 y = - 22?

Solution

A point of intersection of two lines is solution to the equations of both lines. To find the point of intersection of the two lines, we need to solve the system of equations x - y = 3 and -5 x - 2 y = -22 simultaneously. Equation x - y = 3 can be solved for x to give

x = 3 + y

Substitute x by 3 + y in the equation - 5 x - 2 y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

Substitute x by 3 + y in the equation -5 x - 2 y = - 22 and solve for y

x = 3 + y = 3 + 1 = 4

Point of intersection: (4 , 1)

For what value of the constant k does the line - 4 x + k y = 2 pass through the point (2,-3)?

Solution

For the line to pass through the point (2,-3), the ordered pair (2,-3) must be a solution to the equation of the line. We substitute x by 2 abd y by - 3 in the equation.

- 4(2) + k(-3) = 2

Solve the for k to obtain

k = - 10 / 3

What is the slope of the line with equation y - 4 = 10?

Solution

Write the given equation in slope intercept form y = m x + b and identify the slope m.

y = 14

It is a horizontal line and therefore the slope is equal to 0.

What is the slope of the line with equation 2 x = -8?

Solution

The above equation may be written as

x = - 4

It is a vertical line and therefore the slope is undefined.

Find the x and y intercepts of the line with equation x = - 3?

Solution

The above is a vertical line with x intercept only given by

(-3 , 0)

Find the x and y intercepts of the line with equation 3 y - 6 = 3?

Solution

The given equation may be written as

y = 3

The above is a horizontal line with y intercept only given by

(0 , 3)

What is the slope of a line parallel to the x axis?

Solution

A line parallel to the x axis is a horizontal line and its slope is equal to 0.

What is the slope of a line perpendicular to the x axis?

Solution

A line perpendicular to the x axis is a vertical line and its slope is undefined

Step-by-step explanation:

y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

8 0

3 years ago

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 oun

Ugo [173]

Answer: A) .1587

Step-by-step explanation:

Given : The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce.

i.e. $\mu=12.30$ and $\sigma=0.20$

Let x denotes the amount of soda in any can.

Every can that has more than 12.50 ounces of soda poured into it must go through a special cleaning process before it can be sold.

Then, the probability that a randomly selected can will need to go through the mentioned process = probability that a randomly selected can has more than 12.50 ounces of soda poured into it =

$P(x>12.50)=1-P(x\leq12.50)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{12.50-12.30}{0.20})\\\\=1-P(z\leq1)\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.8413\ \ \ [\text{By z-table}]\\\\=0.1587$

Hence, the required probability= A) 0.1587

6 0

3 years ago

A driver drove for 3 hours at a certain speed. If he drove 12 more miles at the same speed, the distance would be 132 miles. At

Zinaida [17]

Distance traveled in 3 hrs was (speed in mph)(3 hrs)

Then s(3 hrs) + 12 mi = 132 mi.

Therefore, 3s = 120, and s = 120 miles / 3 hrs = 40 mph (answer)

7 0

3 years ago

Please help asap!!!!

Lyrx [107]

Answer:

Step-by-step explanation:

8 0

3 years ago

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