I NEED HELP FAST
A colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm. Determine when the colony will reach a population of 2000.

logistic model:[tex]y(t)=\frac{c}{1+ae^-bt}[/tex]
I feel like I'm not given enough information. I'll assume that the limit is 10000

Answers

Answer 1

The colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

What is a mathematical function, equation and expression?                function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is that a colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm.

The logistic model is given as -

y(t) = {c/(1 + a[tex]e^{-bt}[/tex])}

For y(t) = 2000

2000 = {c/(1 + a[tex]e^{-bt}[/tex])}

(2000/c) = 1/(1 + a[tex]e^{-bt}[/tex])

(1 + a[tex]e^{-bt}[/tex]) = (2000/c)

a[tex]e^{-bt}[/tex] = (2000/c) - 1

a[tex]e^{-bt}[/tex] = (2000 - c)/c

[tex]e^{-bt}[/tex] = (2000 - c)/(ac)

(-bt)log{e} = log {(2000 - c)/(ac)}

- bt = log(2000 - c) - log(ac)

- bt = log(2000 - c) - log(a) + log(c)

t = - {log(2000 - c) - log(a) + log(c)}/b

Therefore, the colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

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Related Questions

find the equation of the tangent to the circle 4x²+4y²=25 what are parallel to the line 3x+5y+7=0​

Answers

Answer:

Step-by-step explanation:

To find the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0, we can use the following steps:

Rewrite the equation of the circle in standard form: (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius.

In this case, the equation of the circle is already in standard form, so we can skip this step.

Find the slope of the line 3x + 5y + 7 = 0. The slope is -3/5.

Find the slope of the tangent to the circle. The slope of the tangent will be equal to the slope of the line, which is -3/5.

Substitute the slope of the tangent and the coordinates of a point on the circle into the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the circle and m is the slope.

In this case, we can substitute the coordinates of the center of the circle (which is (0, 0)) and the slope of the tangent (-3/5) into the point-slope form to get:

y - 0 = (-3/5)(x - 0)

Simplify to get the equation of the tangent: y = -3/5x.

Therefore, the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0 is y = -3/5x.

6 people equally share 1/2 a pan of mac and cheese write a division expression to represent the situation

Answers

Answer:

6/1.5

Step-by-step explanation:

You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!

Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.

1204.2 + 4.72613 = [?] ​

Answers

The value of 1204.2 + 4.72613 is 1208.92613.

What is meaning of significant figures of a number?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Given number is 1204.2 and  4.72613.

If add zeros after the last digit of the decimal number, then the number will remains same.

The rewrite form of 1204.2 is 1204.20000.

Before combining two decimal integers, make sure they both have the same number of digits after the decimal point. If they don't, move a number's right by a number of zeros until they do.

Then, place the decimal points vertically and write one number on top of the other. Bring the decimal point directly below the decimal point and add as you would with full numbers.

The sum of 1204.20000 and 4.72613

1204.20000

    +4.72613

__________

1208.92613

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I've been unable to figure this out. Anyone able to assist on which is the correct answer?

Answers

The domain and range of the given function are  {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively

Domain and Range of a Function

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.

The given function is

f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)

The domain of the function can be given as;

Domain : {-2, 0, 1, 2, 3}

Range : {-3, 0, 2, 3, 4}

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Order the ratios from least to greatest.

5:8 11:16 18:32

Answers

The least to greatest of the ratio is 18 : 32, 5 : 8, and 11 : 16

Arrange from least to greatest

Least to greatest arrangement can also be referred to as ascending order. Ascending order is the order such that each element is greater than or equal to the previous element.

5 : 8

= 5/8

= 0.625

11 : 16

= 11/16

= 0.6875

18 : 32

= 18/32

= 0.5625

Therefore, the ratio can be arranged as 18 : 32, 5 : 8, and 11 : 16 in ascending order.

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Which of the following shows 12 more than a number, written as an algebraic expression?
A. 12-n
B.12+n
C.n-12
D.12n​

Answers

the answer is d i think, not totally sure

A man standing on the deck of a ship, h m above the sea level, observes that the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively. Find the height of the cliff in terms of A, B and h
give me the correct ans with clear explainnation and I will give u the BRAINLIEST!

Answers

The height of the cliff in terms of A, B and h are 40 meters.

What is a right-angled triangle?

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

A man standing on the deck of a ship.

Let C be the position of man.

And the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively 60° and 30°.

That means, ∠DCH = 60° and  ∠BCD = 30°.

The diagram is given in the attached image.

HD = x And BD = 10 meters.

In right-triangle ΔCDH,

we have,

tan60° = HD / CD

√3 = x / CD

CD = x/√3

In right-triangle  ΔCDB,

we have,

tan30° = BD/CD

CD = 10√3

So, the distance of the ship from the cliff is 10√3 meters.

Comparing, the both values of CD,

 10√3 =  x/√3

x  =  10√3 × √3

x = 10 × 3

x = 30 meters.

Now, the total height of cliff  = BD + DH

= 10 + 30

= 40 meters.

Therefore, the height of the cliff is 40 meters.

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a rectangle in the first and second quadrants of the coordinate plane has its base along the x-axis and two vertices on the parabola defined by y

Answers

The area of rectangle with has its vertices defined on parabola is 32 square units.

What is rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

What are other terms to describe rectangle?

Square, figure, oblong, parallelogram, plane a.re terms to describe rectangle

Equation of Parabola is y = 12 - x^2 is an even function.

Therefore, its rectangle form also is even at the origin.

We know area of rectangle = length × width

Here,

length = 2x, width = y

Area, A = 2x(12 - x2)

⇒ A = 24x - 2x^3

Take derivative of A with respect to x

⇒ A' = 24 - 6x^2

The area is largest when A' = 0

⇒ 24 - 6x^2 = 0

⇒ x^2 = 4

⇒ x = 2

Put the value of x in y = 12 - x^2

⇒ y = 12 - 4

⇒ y = 8

Area = 2(2)(8) = 32

Therefore, the largest area of a rectangle is 32 square units.

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Let K=[tex]20^{20}[/tex].Suppose that [tex]\frac{20^{k} }{k^{20} } =20^{n}[/tex].find the largest power of 20 that divides n?

Answers

Answer:

  20^2 = 400, the 2nd power of 20

Step-by-step explanation:

Given that k=20^20 and 20^k/k^20 = 20^n, you want the largest power of 20 that divides n.

Logarithms

Taking the base-20 logarithm of both equations, we have ...

  [tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]

Substituting for k and log(k), we get ...

  [tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]

This shows us the largest power of 20 that is a factor of n is 20².

can u answerr for me pls

Answers

Part A:

The graph of the line intersects the x-axis at the point (4, 0).

Part B:

The point represents the distance of Shari from the home.

After 4 minutes, Shari rushed past her house.

What is a graph?

A function graph is a visual representation of a relation. A function is actually equal to its graph in set theory and current mathematical foundations. For instance, when deciding whether or not a function is onto (surjective), a codomain should be taken into account. The graph of a function alone does not reveal the codomain. Although they relate to the same thing, the terms "function" and "graph of a function" communicate different perspectives on it, which is why they are commonly employed.

The line's x-intercept is 4 minutes.

The time Shari will arrive at her house is indicated by the 4 minutes.

Shari's distance from home on her run across town is represented by the line 6x - 3y = 24......... (1), where y stands for blocks, and x for minutes.

Therefore, when y = 0, we obtain 6x - 0 = 24, which equals x = 4, from equation (1) above.

As a result, 4 minutes is the x-intercept of the line (1).

It is stated that Shari will get at her house in 4 minutes, and there are no blocks between them.

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One student surveys the number of pens which are sold in two stationary shops.The pens of both shops are sold in a week.In the first shop 60 pens are sold in the first day and 6 pens are sold more in everyday as comparison of previous day.Similarly in the second shop 5 pens are sold in the first day and the double number of pens are sold in everyday as comparison of previous day.Now in which shop how manv nens are sold more? Find it.Ans: 89 more in second shop​

Answers

Answer: 224 pens more sold in 2nd shop

Step-by-step explanation:

Given,    

1st shop, 6 pens are sold more than previous day,

      1st day : 60

      2nd day : 60+6 =66

      3rd day : 66+6 =72

      4th day : 72+6 =78

      5th day : 78+6 =84

      6th day : 84+6 =90

      7th  day : 90+6 =96  

Then,

2nd shop, each day doubles the previous sold,

      1st day: 5

      2nd day:5*2 =10

      3rd day:10*2 =20

      4th day:20*2 =40

      5th day:40*2 =80

      6th day:80*2 =160

      7th day:160*2 =320

Therefore, second shop sells more in a week which is calculated by 320-96=224 more sold than the 1st shop.

Solve for x: −7 < x − 1 < 8
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9

Answers

The solution for the given inequality is -6 < x < 9.

What is linear equality?

In mathematics a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

The given inequality is:

         -7 < x - 1 < 8

       −7 + 1 < x − 1 + 1 < 8 + 1 -------- (Add 1 to all parts)

             -6 < x < 9

Hence, the solution for the given inequality is -6 < x < 9.

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Find the slope of the line y=5x+12.
Write your answer as an integer or as a simplified proper or improper fraction.

Answers

Answer:

5

Step-by-step explanation:

The slope or gradient of the line

using this formula as our guide line

y = mx +b

where m = slope

x = x intercept

b = y intercept

so

y = 5x + 12

the slope will be 5

i hope i helped pls rate as brainliest

Hello may I please get some help with this question

Answers

the answer is a , b , and c .

Task: Gym Membership
Instructions
Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.

Complete each of the 2 activities for this Task.
Activity 1 of 2
Find the value of c(7).

Activity 2 of 2
Explain what the value of c(7) you found means in this situation.

Answers

The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.

Finding p(a) from p(x)

To find p(a) for a given polynomial p(x) we need to substitute x = a in the given polynomial i.e in place of x.

Here we have

Function c is defined by the equation c(n) = 50 + 4n.

It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.  

Activity 1 of 2

Find the value of c(7).

=> c(7) = 50 + 4(7)

=> c(7) = 50 + 28

=> c(7) = 78

Activity 2 of 2

Explain what the value of c(7) you found means in this situation.

In c(n) = 50 + 4n, n represents the number of visits in a month and 50+4n will represent the monthly cost in dollars

If we apply the above statement to c(7) = 78

then 7 represents the number of visits and 78 represents the monthly cost of visiting the gym 7 times

Therefore,

The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.

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Im a bit stuck can I get some help

Answers

The relationship's slope and common difference are both 70 and constant.

What is the slope of the line?

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
As the  relationship given in the table is linear,
The slope of the relationship is given as,
M = (y₂ - y₁) /  (x₂ - x₁)
Now, putting values from the table,
m = 140 - 70 / 2 - 1
m = 70 jumps per minute

Now,
The common difference between the consecutive minutes of jumping,
d = 140 - 70 = 210 - 140
d = 70 = 70

From the above evaluation, it can be said that the common difference and rate are constant.

Thus, the slope of the relationship and the common difference is 70, as well as constant.

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Suppose the COMBINED area is known to be 0.10416, assume there is equal area on each side. Determine the corresponding Z-scores.
A) z=±1.62 B) z=±1.58 C) z=±1.72 D) z=±1.66 E) z=±1.69 F) z=±1.49 G) None of These

Answers

The solution is once more 1.28 since a combined area of 0.10416 to the right implies that it must also have an area of 0.90 to the left.

Since each normally distributed random variable has a slightly different distribution shape, standardizing the variable to give it a mean of 0 and a standard deviation of 1 is the only method to determine regions using a table. How do we go about doing that? Employ the z-score!

Z = ( x - μ)/σ

If a mean and standard deviation are present for the random variable X,

Then a random variable with a mean of 0 and a standard deviation of 1 is produced by converting X using the z-score!

With that in mind, all that remains is to understand how to find areas under the standard normal curve, which can then be applied to any random variable with a normal distribution.

Since an area of 0.10416 to the right means that it must have an area of 0.90 to the left, the answer is once again 1.28.

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The product of three consecutive integers n - 1, n, and n + 1 is 210. Write and solve an equation to find the numbers.

Answers

We can write an equation to represent the relationship between the three integers n - 1, n, and n + 1 by multiplying these three numbers together:

(n - 1) * n * (n + 1) = 210.

We can then solve this equation to find the value of n.

To solve the equation, we can first factor the left-hand side to get (n - 1) * (n + 1) * n = 210. This expression can be further simplified to n^2 - 1 = 210. We can then solve this equation by adding 1 to both sides to get n^2 = 211, and then taking the square root of both sides to get n = sqrt(211).

The value of n must be an integer, so the only possible value for n is 14. This means that the three consecutive integers are 13, 14, and 15.

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I need help with these 2 questions.

A) Write and solve a proportion to determine the height of the cell phone tower. Please show your work.

B) What is the height of the tower in meters?

Answers

Part (A)

Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.

P/Q = R/S

where,

P = height of the personQ = horizontal distance person is from the left-most cornerR = height of the towerS = horizontal distance the tower is from the left-most corner

In this case,

P = 1.8 metersQ = 6 metersR = unknown, we'll use variable hS = 60 meters

Therefore, we go from this

P/Q = R/S

to this

(1.8)/6 = h/60

Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.

--------------

Answer:   (1.8)/6 = h/60

====================================================

Part (B)

Let's cross multiply and solve for h.

(1.8)/6 = h/60

1.8*60 = 6h

108 = 6h

6h = 108

h = 108/6

h = 18

--------------

Answer:   18 meters

Answer:

A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

B). 18 meters tall

Step-by-step explanation:

We see TWO right triangles in this problem:

the one with the man and the 6m and the one with the phone tower and the 60m

These triangles are proportional so we can make a ratio out of them

the height of the man over the side of the triangle (6m)

and the height of the tower over the length of its triangle (60m)

Set these equal to each other to complete part A

[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

And by using cross multiplication (which is what you do for ratios), solve for h!

For a quick example of cross multiplication, I've attached a picture.

Now let's do it!

1.8 × 60 = 6 × h

108 = 6h

108/6 = h

h = 18

The height of the cell phone tower is 18 meters.

write an integral that expresses the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units

Answers

The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:

p(s) = 4s

Integral = ∫2s5s ds

= ∫2s5s dx

= [s2/2]2s5s

= (25/2) - (4/2)

= 20/2

= 10

Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.

To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.

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How to find the missing side Using Pythagoras Theorem?​

Answers

The legs are the two sides of the triangle that are labeled a and b . The hypotenuse is the longest side of a right triangle and is labeled c . There is a special relationship between the legs of a right triangle and its hypotenuse.

[tex]\int\limits^2_076e^4 {x} \, dx[/tex]

Answers

∫76^4•∫x dx
76e^4•∫x^2/2
38e^4x^2|^2. 0
38e^4•2^2-38e^4•0^2

152e^4

What is the slop in the equation

Answers

-2/3 (the number before x)

NO LINKS!!
A deposit pf $6000 is made in a college savings fund that pays 5.0% interest, compounded continuously. The balance will be given to a student after the money has earned interest for 40 years. How much (in dollars) will the student receive? (Round your answer to the nearest cent.)

Answers

Answer:

$44,334.34

Step-by-step explanation:

                         

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

P = $6000r = 5.0% = 0.05t = 40 years

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=6000e^{0.05 \times40}[/tex]

[tex]\implies A=6000e^2[/tex]

[tex]\implies A=6000(7.3890560...)[/tex]

[tex]\implies A=44334.33659...[/tex]

Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).

Hypothesis 1 H0: Receiving a 20 percent off coupon does not increase the number of customers visiting the Lotions and Potions soap store. Ha: Receiving a 20 percent off coupon increases customers visiting the Lotions and Potions soap store. Data Customers on file who visited the store during coupon promo: 32 percent Customers on file who visit the store during a typical week: 30 percent Sample size: 4,500 Questions Did you use a z-test or t-test? Why? What is the P value? Do you accept or reject the alternative hypothesis? Should Lotions and Potions continue to offer this promotion in order to increase visits? Why or why not?

Answers

The data Customers on file who visited the store during coupon promo is 32% .

a) We use Z-test for testing hypothesis in this case because it is single proportion.

b) The P-value is 0.0017.

c) As P value < α = 0.05 , So we reject the null hypothesis.

d) Yes, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.

The Null and Alternative hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.

Sample size ,n = 4,500

Significance level, 0.05

a) We use z-test, because this is single proportion hypothesis test.

Below are the null and alternative Hypothesis,

Null Hypothesis, H₀ : p = 0.3

Alternative Hypothesis, Hₐ : p > 0.3

b) Test statistic,

z = (p-cap - p)/sqrt(p×(1-p)/n)

z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)

z = 2.93

Using the Z-table, the P value at significance level 0.05 and z = 2.93 is 0.0017

As we see P-value < α = 0.05, so, reject the null hypothesis.

Yes, Lotions and Potions should continue to offer this promotion in order to increase visits.

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There are only 2.1 x 108 metric tonnes of usable fossil fuels existing on Earth.

Assuming an estimated rate of fossil fuel use of 1 x 105 metric tonnes per year, calculate an order of magnitude estimation of the time left before the fossil fuel reserves run out.

Give your answer to one significant figure.\

The answer is 2000 but I cannot figure out how they got it.

Answers

The time that is left before the fossil fuel reserves run out would be= 2000 years.

What is a fossil fuel?

A fossil fuel is defined as the type of fuel that is gotten from dead and decayed organic matter that has been buried for years underneath the earth surface.

The quantity of usable fossil fuel existing on earth = 2.1 x 10⁸metric tonnes.

The rate of fossil fuel used per year = 1 x 10⁵

Mathematically,

If 1 year = 1 x 10⁵

X years = 2.1 x 108

make X years the subject of formula;

X years = 2.1× 10⁸/1× 10⁵

X years = 2.1 × 10³ or 2100

X year = 2000( to one significant figure)

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What is the slope of (0,0) and (4,12)

Answers

Answer:

[tex] \Large{\boxed{\sf Slope = 3}} [/tex]

[tex] \\ [/tex]

Explanation:

The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.

[tex] \\ [/tex]

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]

Where m is the slope of the line.

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]

[tex] \\ [/tex]

Now, substitute these values into the formula:

[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer:

slope = 3

How to Solve:

The question is asking us to find the slope, given two points.

These points are (0,0) and (4,12).

We will use the slope formula:

[tex]\boldsymbol{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

m = slope(x₁,y₁) and (x₂,y₂) are points that the line passes through

Plug in the data:

[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]

[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]

Simplify the fraction to its lowest terms:

[tex]\boldsymbol{m=3}[/tex]

Therefore, the slope is 3.

To indirectly measure the distance across a river, Sebastian stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Sebastian draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

Answers

Sebastian uses the method of similar triangles to find the distance across the river, and the distance across the river is 372 foot.

What is a Triangle?

A triangle is a polygon with three sides and three vertices.

The triangle's total number of angles comes to 180°.

The distances between the formed the sight-lines are;

RB = 210 feet

OC = 275 feet

The distance between the point close to the river and the next point further from the river = 115 feet

In triangles ΔPRB and ΔPOC,

we have;

∠PRE = ∠POC = 90°

Given;

∠PER ≅ ∠PCO

By corresponding angle formed between two parallel lines and a common transversal.

Using angle-angle similarity theorem;

∴ ΔPRE is similar to ΔPOC Which gives;

PR / PO = RE / OC

Let x represent the distance across the river,

we have;

PR = x

PO = 115 + x

Which gives;

x / (115+x) = 210 / 275

275x = 210 × (115 + x)

275x = 24150 + 210x

275x - 210x = 24150

65x = 24150

x = 371. 54

Therefore, the distance across the river is 372 foot.

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he equations of two lines are given. determine whether the lines are parallel, perpendicular, or neither. y

Answers

By definition, perpendicular strains are strains intersecting at a proper attitude. The letters T and L are examples of perpendicular strains. By definition, parallel strains are strains at the equal aircraft that in no way intersect.

The letters N and Z include pairs of parallel linetwo non-vertical strains which are withinside the equal aircraft has the equal slope, then they may be stated to be parallel. Two parallel strains might not ever intersect. If non-vertical strains withinside the equal aircraft intersect at a proper attitude then they may be stated to be perpendicular.

We can decide from their equations whether or not strains are parallel with the aid of using evaluating their slopes. If the slopes are the equal and the y-intercepts are different, the strains are parallel. If the slopes are different, the strains aren't parallel. Unlike parallel strains, perpendicular strains do intersect.

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The table below gives values of a function g at selected values of x. x 0 1 3 7 g(x) 24 35 42 68
Which of the following statements, if true, would be sufficient to conclude that there exists a number c in the interval [0,7] such that g (c) = 50 ? I. g is defined for all in the interval (0,7). II. g is increasing for all in the interval (0,7]. III. g is continuous for all o in the interval 0,7). (A) II only (B) Ill only (C) I and Ill only (D) I, ll and III

Answers

g is continuous for all x in the interval [0,7] is correct statement that would be sufficient to conclude that there exists a number c in the interval [0,7] such that g (c) = 50.

Here the given function g(x) gives values for selected values of x.

Now we are to find a condition which will conclude that there exist a number 'c' in the interval [0,7] such that g(c)=50

If a function f : a, b [tex]\rightarrow[/tex] R be continuous on R with [tex]$\mathrm{f}(\mathrm{a}) \neq \mathrm{f}(\mathrm{b})$[/tex]  then the function f(x) attains every value between f(a) and f(b) at least once in the interval [a, b]

I. The option is false.

Because if the function is defined in the interval [0,7] then it is not necessary that there exist a point in this interval, where the function will attain the value 50.

II. The given option is false.

Because if the function is increasing in the interval [0,7] then it is not necessary that there exist a point in this interval, where the function will attain the value 50.

III. This option is correct.

Since g(0) = 24 and g(7) =  68 and 'g' is continuous on the interval [0,7] , so the function g(x) attains every value between 24 and 68 at least once in the interval [0,7].

That is there must be a point 'c' in the interval [0,7] such that g(c)=50.

Therefore option (B) is correct.

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