Use trigonometric ratios to solve the right triangle.
The length of leg DF is WARRAND -
The length of leg DE is

Answer:

4185

Step-by-step explanation:

A culture of bacteria grows exponentially according to the following general exponential growth function;

[tex]P_{t}=P_{0}e^{kt}[/tex]

where;

p(t) is the population at any given time t.

p(0) is the initial population

k is the growth constant

From the information given we have;

p(0) = 1500

at t = 5, p(t) = 2300; p(5) = 2300

We shall use this information to determine the value of k;

[tex]2300=1500e^{5k}[/tex]

Divide both sides by 1500;

[tex]\frac{23}{15}=e^{5k}\\\\ln(\frac{23}{15})=5k\\\\k=0.08549[/tex]

Therefore, the population of the bacteria at any time t is given by;

[tex]P_{t}=1500e^{0.08549t}\\\\P(12)=1500e^{0.08549(12)}=4184.3[/tex]

Answer:

  C. -4n + 8

Step-by-step explanation:

Try the formulas and see which works.

__

The common difference is -4, so the coefficient of n in the explicit formula is -4. Every term is divisible by 4, so there won't be 3 anywhere in the formula.

__

-4·1 +8 = 4

-4·2 +8 = 0

-4·3 +8 = -4

-4·4 +8 = -8

The formula -4n+8 reproduces the sequence exactly.

As near as I can tell, you're given the vector field

[tex]\vec F(x,y,z)=\langle y,-x,14\rangle[/tex]

and that [tex]S[/tex] is the part of the upper half of the sphere with equation

[tex]x^2+y^2+z^2=4[/tex]

with boundary [tex]C[/tex] the circle in the plane [tex]z=0[/tex].

Parameterize [tex]C[/tex] by

[tex]\vec r(t)=\langle2\cos t,2\sin t,0\rangle[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\vec F(x,y,z)[/tex] along [tex]C[/tex] is

[tex]\displaystyle\int_C\vec F(x,y,z)\cdot\mathrm d\vec r=\int_0^{2\pi}\langle2\sin t,-2\cos t,14\rangle\cdot\langle-2\sin t,2\cos t,0\rangle\,\mathrm dt[/tex]

[tex]=\displaystyle-4\int_0^{2\pi}(\sin^2t+\cos^2t)\,\mathrm dt=\boxed{-8\pi}[/tex]

Parameterize [tex]S[/tex] by

[tex]\vec s(u,v)=\langle2\cos u\sin v,2\sin u\sin v,2\cos v\rangle[/tex]

with [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le\dfrac\pi2[/tex]. We have

[tex]\nabla\times\vec F(x,y,z)=\langle0,0,-2\rangle[/tex]

Take the normal vector to [tex]S[/tex] to be

[tex]\vec s_v\times\vec s_u=\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle[/tex]

Then the surface integral of the curl of [tex]\vec F(x,y,z)[/tex] across [tex]S[/tex] is

[tex]\displaystyle\iint_S(\nabla\times\vec F(x,y,z))\cdot\mathrm d\vec S=\iint_S(\nabla\times\vec F(x(u,v),y(u,v),z(u,v)))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}\langle0,0,-2\rangle\cdot\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle-4\int_0^{\pi/2}\int_0^{2\pi}\sin2v\,\mathrm du\,\mathrm dv=\boxed{-8\pi}[/tex]

Based on the pattern table, the value of a is 1/64.

Given:

Find:

Solution:

The negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.

So, [tex]2^{-6} = \frac{1}{2^{6} } = \frac{1}{64}[/tex]

As, [tex]2^{6} = 64[/tex].

So, a = 1/64

Hence, the value of a is 1/64

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Answer:

  16 1/4 years

Step-by-step explanation:

Assuming interest is compounded annually, the account balance (A) after t years will be ...

  A = P(1 +r)^t

  3200 = 1700·1.0397^t

  log(3200) = log(1700) +t·log(1.0397)

  t = (log(3200) -log(1700))/log(1.0397) ≈ 16.247

The account will reach a balance of $3200 after about 16 1/4 years.

___

You may be asked to round your answer to the nearest integer or tenth. We leave that exercise to the student.

Answer:

In the year 2010, the population of the city was 175,000

Step-by-step explanation:

If we rewrote this as a linear expression in standard form (it is linear, btw), it would look like this:

[tex]P(t)=\frac{11}{2}t+175[/tex]

The rate of change, the slope of this line, is 11/2.  If the year 2010 is our time zero (in other words, we start the clock at that year), then 0 time has gone by in the year 2010.  In the year 2011, t = 1 (one year goes by from 2010 to 2011); in the year 2012, t = 2 (two years have gone by from 2010 to 2012), etc.  If we plug in a 0 for t we get that y = 175,000.  That is our y-intercept, which also serves to give us the starting amount of something time-related when NO time has gone by.

a)

[tex]x^2+y^2-2x+2y-1=0[/tex]

It could be expressed as:

[tex](x-1)^2-1+(y+1)^2-1-1=0\\\\\\i.e.\\\\\\(x-1)^2+(y+1)^2=3\\\\\\i.e.\\\\\\(x-1)^2+(y+1)^2=(\sqrt{3})^2[/tex]

Hence, the radius of circle is: √3≈1.732 units

b)

[tex]x^2+y^2-4x+4y-10=0[/tex]

It is represented as:

[tex](x-2)^2-4+(y+2)^2-4-10=0\\\\\\i.e.\\\\\\(x-2)^2+(y+2)^2=18\\\\\\(x-2)^2+(y+2)^2=(3\sqrt{2})^2[/tex]

Hence, the radius of circle is: 3√2≈4.242 units

c)

[tex]x^2+y^2-8x-6y-20=0[/tex]

on converting to standard form

[tex](x-4)^2+(y-3)^2=(3\sqrt{5})^2[/tex]

Hence, the radius of circle is: 3√5≈6.708 units

d)

[tex]4x^2+4y^2+16x+24y-40=0[/tex]

on dividing both side by 4 we obtain:

[tex]x^2+y^2+4x+6y-10=0\\\\\\(x+2)^2+(y+3)^2=(\sqrt{23})^2[/tex]

Hence, radius of circle is: √23=4.796 units

e)

[tex]5x^2+5y^2-20x+30y+40=0[/tex]

on dividing both side by 5 we obtain:

[tex]x^2+y^2-4x+6y+8=0[/tex]

[tex](x-2)^2+(y+3)^2=(\sqrt{5})^2[/tex]

Hence, radius of circle is: √5=2.236 units

f)

[tex]2x^2+2y^2-28x-32y-8=0[/tex]

which could also be represented as follows:

[tex]x^2+y^2-14x-16y-4=0\\\\\\(x-7)^2+(y-8)^2=(\sqrt{117})^2[/tex]

Hence, the radius of circle is: [tex]\sqrt{117}[/tex]≈ 10.817 units

g)

[tex]x^2+y^2+12x-2y-9=0[/tex]

It could also be written as:

 [tex](x+6)^2+(y-1)^2=(\sqrt{46})^2[/tex]

Hence, the radius of circle is: [tex]\sqrt{46}[/tex]≈ 6.782 units

            The ascending order is:

        a → e → b → d → c → g → f

The radius of a circle can be found from its equation in general form, which can be rearranged into the format (x-h)² + (y-k)² = r². From there, the radii of all the circles can be determined, and the circles arranged in ascending order by these lengths.

To arrange the circles in ascending order of their radii, we need to understand the general equation of a circle which is in the format "(x-h)² + (y-k)² = r²". Here, (h,k) are the coordinates of the center of the circle, and 'r' is the radius of the circle. The given equations of the circles usually can be rewritten into this format.

To ascertain the radius of a circle from its equation, identify the constant term on the right hand side of the equation, which is the square of the radius (r²). The square root of this term will give you the 'r' - radius of the circle.

Once you know the radii of all the circles, arrange the equations in ascending order of these radii value. Remember, the smaller the r, the smaller the circle's circumference and area.

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Use Slide method for some of them, some are perfect squares:

Watch this video and try it a few times, pay attention to the signs when you are seeing which one will be negative when you multiply it out, in picture is me working out all problems requested.

Ask your brother for further help!

Answer:

c=6.30 units

Step-by-step explanation:

we know that

Applying the law of sines

a/sin(A)=c/sin(C)

Solve for c

c=a*sin(C)/sin(A)

substitute the values

c=21*sin(17°)/sin(103°)=6.30 units

Answer:

365

Step-by-step explanation:

Answer: 24, 44, and 66 [tex]cm^{2}[/tex]

Step-by-step explanation:

Check all of the possible combinations of the faces:

6 × 4 = 24

11 × 4 = 44

11 × 6 = 66

So the answers are 24, 44, and 66 [tex]cm^{2}[/tex]

Answer:

option B 24 cm² option C 44 cm² and option E 66 cm² are the correct options

Step-by-step explanation:

A rectangular prism has 6 faces, in which opposite faces are always similar.

So a rectangular prism has 3 different faces

(1) From the figure given

for face (1)  Area = 11 × 4

                           = 44 cm²

For face (2) Area = 4 × 6

                            = 24 cm²

For face (3) Area = 11 × 6

                             =66 cm²

Now we can say that option B 24 cm² option C 44 cm² and option E 66 cm² are the correct options

Answer:

(4,7)

Step-by-step explanation:

3x+x+3=19

4x=16

x=4

so y=7

c. (4,7)

Answer:

  about 2.33

Step-by-step explanation:

The value can be found from a probability table, any of several web sites, your graphing calculator, most spreadsheet programs, or any of several phone or tablet apps.

A web site result is shown below. (I have had trouble in the past reconciling its results with other sources.) One of my phone apps gives the z-value as about ...

  2.26347874

which is in agreement with my graphing calculator.

Answer:

[tex]Z = 2.325[/tex].

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.

This is the value of Z when X has a pvalue of 0.99. This is between 2.32 and 2.33, so the answer is [tex]Z = 2.325[/tex].

Try this:

if x=13 it means 'one solution'; the only point;

if 0=13 it means 'no solution'; wrong equation = no points;

if 0=0 it means 'many solutions'; no variable in the equation = much points.

Finally:

System #1 - one solution;

System #2 - no solution;

System #3 - many solutions.

Answer:

20,309 people more people per sq mile.

Step-by-step explanation:

First step is to calculate the population density of both cities, then we'll be able to answer the question.

We're looking for a number of people per sq mile... so we'll divide the population by the area.

New York City: 8.54 million people on 302.6 sq miles

DensityNYC = 8,540,000 / 302.6 =  28,222 persons/sq mile

Los Angeles: 3.98 million people on 503 sq miles

DensityLA = 3,980,000 / 503 = 7,913 persons/sq mile

Then we do the difference...  28,222 - 7,913 = 20,309 people more people per sq mile.

If we were to make the ratio, we'd get 3.57, 3.57 more people in NYC per sq mile compare to LA.

Final answer:

New York City has approximately 20,309 more people per square mile than Los Angeles when rounded to the nearest person, based on their population densities.

Explanation:

To calculate how many more people per square mile live in New York City versus Los Angeles, we need to find the population density for each city and then subtract Los Angeles's density from New York City's density.

New York City's population density: 8.54 million people ÷ 302.6 square miles = approximately 28,220 people per square mile.

Los Angeles's population density: 3.98 million people ÷ 503 square miles = approximately 7,911 people per square mile.

The difference in population density: 28,220 people per square mile (NYC) - 7,911 people per square mile (LA) = approximately 20,309 people per square mile.Therefore, about 20,309 more people per square mile live in New York City than in Los Angeles, when rounded to the nearest person.

1 < x < 3 because

( x < 3 ) intersecting ( x > 1)

For this case we must find the intersection of the following inequations:

[tex]x + 1 <4\\x-8> -7[/tex]

So:

[tex]x + 1 <4\\x <4-1\\x <3[/tex]

All values of "x" less than 3.

[tex]x-8> -7\\x> -7 + 8\\x> 1[/tex]

All values of "x" greater than 1.

Thus, the intersection of the equations will be given by the values of "x" greater than 1 and less than 3.

[tex](1 <x <3)[/tex]

ANswer:[tex](1 <x <3)[/tex]

Set up an equation based on the information given

[tex]89 + 89 + x + x = 328[/tex]

Combine like terms

[tex]89 + 89 = 178[/tex]

[tex]x + x = 2x[/tex]

[tex]2x + 178 = 328[/tex]

Solve

[tex]2x + 178 = 328[/tex]

[tex]328 - 178 = 150[/tex]

[tex]2x = 150[/tex]

[tex]x = 75[/tex]

Answer

The width of the rectangular field is 75 yards.

Answer:

[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big)[/tex]

Step 2: Evaluate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

3:45 PM

Step-by-step explanation:

The least common multiple of 3, 5, and 6 is 30, so the next occurrence will be 30 minutes after 3:15 PM, at 3:45 PM.

Answer:  The next time at which the three sounds will happen simultaneously at 3 : 45 PM.

Step-by-step explanation:  Given that Max sneezes every 5 minutes, Lina coughs every 6 minutes and their dog barks every 3 minutes.

We are to find the time at which these three sounds will happen simultaneously if there was sneezing, barking, and coughing at 3:15 PM.

We have

the sneezing, barking and coughing happen simultaneously at an interval that is equal to the L.C.M. of 5, 6 and 3 minutes.

Now,

L.C.M. (5, 6, 3) = 30.

Therefore, the sneezing, barking and coughing happen simultaneously at an interval of 30 minutes.

Since there was sneezing, barking, and coughing at 3:15 PM, so the next time at which the three sounds will happen simultaneously is

3 : 15 PM + 30 min = 3 : 45 PM.

Thus, the next time at which the three sounds will happen simultaneously is 3 : 45 PM.

Answer:

=> 6s

Step-by-step explanation:

Given terms

24s^3  ,12s^4  and 18s

GCF consists of the common factors from all the terms whose GCF has to be found.

In order to find GCF, factors of each term has to be made:

The factors of 24s^3:

24s^3=2*2*2*3*s*s*s

The factors of 12s^4:

12s^4=2*2*3*s*s*s*s

The factors of 18s:

18s=2*3*3*s

The common factors are(written in bold):

GCF=2*3*s

=6s

So the GCF is 6s ..  

Answer:

6s

Step-by-step explanation:

I'm unsure about this answer, but I got 108 people. I just did a simple proportion of 6/1500 = x/27000 and solved for x.

Answer:

108 people

Step-by-step explanation:

We can write a proportion to solve this problem.  Take the number of people over the living space

6 people           x people

------------    = ------------------

1500 ft^2            27000 ft^2

Using cross products

6 * 27000  = 1500 x

Divide each side by 1500

6 * 27000/1500 = 1500x/1500

108 = x

108 people  can be reasonably accommodated

Answer:

10 hours

Step-by-step explanation:

If I have $50 in my bank account, and I want to have a total of $130 in my account. It means that I need to work enough hours to make $130 - $50 = $80.

If I make $8 per hour, and I need to make $80, then I just have to work 10 hours. ($80/8 = 10)

Answer:

  see below

Step-by-step explanation:

Each point moves to twice its original distance from (-4, -3). The point (-4, -3) remains unmoved.

Answer: (-4,1) ; (2,-3) ; (-4,-3)

Answer:

Membership decreased by an average of 6,600 people per year from Year 3 to Year 5

Step-by-step explanation:

The average rate of change from Year 3 to Year 5 will be given by the slope of the line joining the points;

(3, 96.8) and (5, 83.6)

The slope of a line given two points is calculated as;

( change in y)/( change in x)

In this case y is the number of members for a given year x.

average rate of change = (83.6-96.8)/(5-3)

                                        = -6.6

Since the number of members is given in thousands, we have;

-6,600

The negative sign implies a decrease in the number of members. Therefore, membership decreased by an average of 6,600 people per year from Year 3 to Year 5

Answer:

No real solution

Step-by-step explanation:

Work is on another question for this. You have asked it multiple times

For this case we must find the solution of the following quadratic equation:

[tex]50-x ^ 2 = 0[/tex]

Subtracting 50 from both sides of the equation:

[tex]-x ^ 2 = -50[/tex]

Multiplying by -1 on both sides of the equation:

[tex]x ^ 2 = 50[/tex]

We apply square root on both sides to eliminate the exponent:

[tex]x = \sqrt {50}\\x = \pm \sqrt {25 * 2}\\x = \pm \sqrt {5 ^ 2 * 2}\\x = \pm5 \sqrt {2}[/tex]

ANswer:

[tex]x = \pm5 \sqrt {2}[/tex]

Answer:

The dimensions that will minimize cost are 3.42 cm and 6.84 cm

Step-by-step explanation:

* Lets explain how to solve this problem

- We have a storage box with a square base

- The volume of the box is 80 cm³

* From the information above we can find relation between the two

 dimensions of the box

∵ The base of the box is a square with side length L cm

∵ The height of the box is H cm

∵ The volume of the box = area of its base × its height

- The base is a square and area the square = L² cm²

∴ The volume of the box = L² × H

∵ The volume of the box = 80 cm³

∴ L² × H = 80

- Lets find H in terms of L by divide both sides by L²

∴ H = 80/L² ⇒ (1)

- The cost of the top and bottom is $0.20 per cm²

- We can find the cost of top and bottom by multiplying the area of

  them by the cost per cm²

∵ The top and the bottom are squares with side length L cm

∴ The area of them = 2 × L² = 2L² cm²

∵ The cost per cm² is $0.20

∴ The cost of top and bottom = 2L² × 0.20 = 0.40L² ⇒ (2)

- Now we can find the cost of the lateral area (area of the 4 side faces)

 by multiplying the area of them by the cost per cm²

∵ The lateral area = the perimeter of its base × its height

∵ The base is a square with side length L cm

∴ The perimeter of the base = 4 × L = 4L cm

∵ The height of the box is H cm

∴ The lateral area = 4L × H

- Now lets replace H by L using equation (1)

∴ The lateral area = 4L × 80/L²

- To simplify it : 4 × 80 = 320 and L/L² = 1/L

∴ The lateral area = 320/L cm²

∵ The cost of the sides is $0.10 per cm²

∴ The cost of the lateral area = 320/L × 0.10 = 32/L ⇒ (3)

- Now lets find the total cost of the box by adding (2) and (3)

∴ The total cost (C) = 0.40L² + 32/L

* For the minimize cost we will differentiate the equation of the

  cost C with respect to the dimension L (dC/dL) and equate it

  by 0 to find the value of L which makes the cost minimum

- In differentiation we multiply the coefficient of L by its power and

 subtract 1 from the power

∵ C = 0.40L² + 32/L

- Lets change 32/L to 32L^(-1) ⇒ (we change the sign of the power by

 reciprocal it)

∴ C = 0.40L² + 32L^(-1)

-  Lets differentiate

∴ dC/dL = (0.40 × 2)L^(2 - 1) + (32 × -1)L^(-1 - 1)

∴ dC/dL = 0.80L - 32L^(-2)

- For the minimum cost put dC/dL = 0

∴ 0.80L - 32L^(-2) = 0 ⇒ add 32L^(-1) to both sides

∴ 0.80L = 32L^(-2)

- Change 32L^(-2) to 32/L² (we change the sign of the power by

 reciprocal it)

∴ 0.80L = 32/L² ⇒ use cross multiplication to solve it

∴ L³ = 32/0.80 = 40 ⇒ take ∛ for both sides

∴ L = ∛40 = 3.41995 ≅ 3.42 cm ⇒ to the nearest 2 decimal place

- Substitute this value of L in equation (1) to find H

∵ H = 80/L²

∴ H = 80/(∛40)² = 6.8399 ≅ 6.84 cm ⇒ to the nearest 2 decimal place

* The dimensions that will minimize cost are 3.42 cm and 6.84 cm

Answer:

  see below

Step-by-step explanation:

The slopes of parallel lines are the same. The slopes of perpendicular lines are negative reciprocals of each other, hence their product is -1.

___

For the most part, the concept of adding slopes of lines does not relate to parallel or perpendicular lines in any way.

Answer:

c

Step-by-step explanation:

Answer:

7 cents/mile

Step-by-step explanation:

You are looking for a unit rate of cents per mile.

Change the dollar amount to cents, and divide by the number of miles.

$13.08 * (100 cents)/$ = 1308 cents

(1308 cents)/(183 miles) = 7.001 cents/mile

Answer:

The amount of water left in the tank is approximately 58.1 cubic meters

Step-by-step explanation:

step 1

Find the volume of the a cube shape tank

The volume is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=4.6\ m[/tex]

substitute

[tex]V=4.6^{3}=97.336\ m^{3}[/tex]

step 2

Find the volume of cone

The volume is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=2.5\ m[/tex]

[tex]h=6\ m[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(2.5)^{2}(6)[/tex]

[tex]V=39.25\ m^{3}[/tex]

step 3

Find the difference of the volumes

[tex]97.336\ m^{3}-39.25\ m^{3}=58.1\ m^{3}[/tex]

Answer:

  D. slope = 3 and y-intercept = -3

Step-by-step explanation:

The equation can be rearranged by adding the opposite of the term with parentheses:

  y = 3(x -1)

Expanding this to slope-intercept form gives ...

  y = 3x -3 . . . . . . . . slope = 3, y-intercept = -3

_____

Slope-intercept form is ...

  y = mx +b . . . . . . . . slope = m, y-intercept = b