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3 years ago

Please can someone just answer question 7C

Mathematics

2 answers:

GuDViN [60]3 years ago

5 0

Answer:

y = -2/3x - 1

Step-by-step explanation:

Step 1: The first thing that we need to do is to find the slope of a given line

The explicit equation of a given line is: y = 3/2x + 5/2

So the slope is m = 3/2:

Step 2: The perpendicular slope (m1) is negative reciprocal of the slope m.

m1 = -2/3

So the perpendicular line will have a slope of m1 = -2/3

Step 3: Now we have a point and the slope so we can use point-slope form, which is: y - y0 = m1(x - x0)

In this example we have: m1 = -2/3, x0 = 0 and y0 = -1. After substitution we have:

y - y0 = m1(x - x0)

y - (-1) = -2/3(x - 0)

y + 1 = -2/3x + 0

y = -2/3x + 0 - 1

y = -2/3x - 1

lbvjy [14]3 years ago

4 0

Answer:

y=-2/3*x-1

Step-by-step explanation:

3x-2y+5=0

Solving for y

-2y=-3x-5

y=3/2*x+5/2

-2/3 is perpendicular to 3/2, so the slope must be -2/3

y=-2/3*x+b

Substituting x=0 and y=-1,

-1=b

Therefore, the equation of the line is y=-2/3*x-1

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Suppose the value R(d) of d dollars in euros is given by R(d)-d The cost P(n) in dollars to purchase and ship n purses is given

S_A_V [24]

<u>Corrected Question</u>

Suppose the value R(d) of d dollars in euros is given by $R(d)=\dfrac67 d$ . The cost in dollars to purchase and ship n purses is given by P(n)=66n+23. Write a formula for the cost, Q(n) in euros to purchase and ship n purses.

Answer:

$Q(n)=\dfrac67(66n+23)$

Step-by-step explanation:

The value R(d) of d dollars in euros is given by $R(d)=\dfrac67 d$

Therefore:

$R(1)=\dfrac67$

$T$hat is, 1 dollars =\dfrac67$ euros$

The cost P(n) in dollars to purchase and ship n purses is given by:

$P(n) = 66n+23.$

Therefore, the cost, Q(n) in euros to purchase and ship n purses

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8 0

3 years ago

In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year. a) Find the exponential g

Angelina_Jolie [31]

Answer:

a) The exponential growth function

P(t) = 5,690,000(1.0287)^t

b) 6,742,868.7374 million

c) 12.04 years

d) 2439.0243902

Step-by-step explanation:

In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year.

The formula for exponential growth is given as:

P(t) = Po( 1 + r) ^t

Where P = Population size after time t

Po = Initial population size

r = Growth rate in percentage

t= time in years

a) Find the exponential growth function.

P(t) = Population size after time t

Po = Initial population size = 5.69 million

r = Growth rate in percentage = 2.87% = 0.0287

t= time in years

The Exponential growth function

P(t) = 5,690,000(1 + 0.0287)^t

P(t) = 5,690,000(1.0287)^t

b) Estimate the population of the city in 2018.

From 2012 to 2018 = 6 years

t = 6 years

Hence,

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^6

P(t) = 5,690,000(1.0287)^6

P(t) = 6,742,868.7374 million

c) When will the population of the city be 8 million?

P(t) = 8,000,000

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1.0287)^t

Divide both sides by 5,690,000

8,000,00/5,690,000 = 5,690,000(1.0287)^t/5,690,000

= 1.4059753954 = 1.0287^t

Take logarithm of both sides

log 1.4059753954 = log 1.0287^t

Log 1.4059753954 =t Log 1.0287

t = Log 1.4059753954/Log 1.0287

t = 12.041740264

t = 12.04 years

d) Find the doubling time.

The formula is given as 70/Growth rate

= 70/0.0287

= 2439.0243902

4 0

3 years ago