Miss Kito is building a rectangular pen for her lea.She will use the side of her house for one wall of the pen;therefore she will not need any fencing on that side.On the other three sides, she will use special fencing that costs $12 per foot . She wants the entire enclosed area to be 2400 square feet. Lastly,she needs four corner that costs $5 each ?

Let x represent the length of each side of the pen perpendicular to the house and let y represent the length of the side of the pen parallel to the house.Write a function c(x) for the cost of the materials for the llama pen in terms of x. Simplify

Please explain and thank you

Answer and Step-by-step explanation: There are a number of ways of calculating an area under a curve. The more precise way is to use Definite Integral:

The function is [tex]2x\sqrt{x^{2}+1}[/tex], then the area under, with interval between 0 and 6 is:

[tex]\int\limits^6_0 {(2x\sqrt{x^{2}+1}) } \, dx[/tex]

To solve this integration, use substitution method, in which:

[tex]u=x^{2}+1[/tex]

[tex]\frac{du}{dx}=2x[/tex]

du = 2xdx

Replacing into the integral:

[tex]\int\limits^a_b {\sqrt{u} } \, du[/tex]

Solving:

[tex]\int\limits^a_b {\sqrt{u} } \, du=\frac{2}{3} \sqrt{u^{3}}[/tex]

Replacing it back to x:

[tex]\int\limits^6_0 {2x\sqrt{x^{2}+1} } \, dx =\frac{2}{3}\sqrt{(x^{2}+1)}[/tex]

Substituing limits between 0 and 6:

[tex]= \frac{2}{3}[\sqrt{(6^{2}+1)^{3}}-\sqrt{(0^{2}+1)^{3}} ][/tex]

= 149.37

Area under the curve using Integration is 149.37 square units

Another way of calculating area under the curve is dividing the area into a number of small rectangles and then adding the area of each one. This method is called Riemann Sums and it is an approximation of the area.

The method is done by the following relation:

in which

i is the n, the number of subintervals the area is dividing into

Δx is width of each subintervals.

For the function f(x) = [tex]2x\sqrt{x^{2}+1}[/tex], interval between 0 and 6:

[tex]\Delta x=\frac{6-0}{12}[/tex]

[tex]\Delta x=[/tex] 0.5

[tex]A=\Sigma f(x_{i}).\Delta x[/tex]

[tex]A = f(0)*0.5+f(0.5)*0.5+f(1)*0.5+f(1.5)*0.5+f(2)*0.5+f(2.5)*0.5+f(3)*0.5+f(3.5)*0.5+f(4)*0.5+f(4.5)*0.5+f(5)*0.5+f(5.5)*0.5[/tex]

[tex]A=0+1.12*0.5+2.83*0.5+...+50.99*0.5+61.49*0.5[/tex]

A = 131.575 square units

[tex]\Delta x=\frac{6-0}{5}[/tex]

Δx = 1.2

[tex]A=f(0)*1.2+f(1.2)*1.2+f(2.4)*1.2+f(3.6)*1.2+f(4.8)*1.2[/tex]

[tex]A=0*1.2+3.75*1.2+12.48*1.2+26.90*1.2+47.07*1.2[/tex]

A = 108.24 square units

Comparing results, notice that with less subintervals, the area is far from the exact measure. It occurs because Riemann Sums is an approximation method. So, if there are more subintervals, more approximate is the area, therefore, more precise it will be.

Answer:

The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Step-by-step explanation:

Let us use these facts above to solve the question

∵ The quadratic function f(x) = y has a vertex point (-4, -5)

∵ g(x) = f(x + 2) + 3

→ By using the two facts above

∴ f(x) is translated 2 units to the left

∴ f(x) is translated 3 units up

→ That means the vertex point must move 2 units left and 3 units up

∵ The rule of translation is T (x, y) → (x - 2, y + 3)

∵ The coordinates of the vertex point of f(x) are (-4, -5)

∴ Its image is (-4 - 2, -5 + 3)

∴ Its image is (-6, -2)

∴ The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Answer:

$57.38

Step-by-step explanation:

The total bill is $45.90.

They decided to tip the waiter 25%.

Therefore, the total amount they leave will be the total bill plus the amount they will tip.

They amount they tipped is 25% of the total bill. Therefore, the tip is 0.25(45.9) or approximately $11.48 (rounded up).

So, the amount they will leave is the original amount plus the tip. So, in total, they left:

$45.90+$11.48 or $57.38

Answer:

57.38

Step-by-step explanation:

percent means per one hundred, or 1/100.

25%=25/100

45.90 times 25/100= 11.475

Since money doesn't have a thousandthes digit, I just rounded it up to 11.48.

11.48+45.90=57.38

Another way you could do it would be to just mutiply 45.90 by 125/100 to get 57.375, which rounds to 57.38.

Answer:hi how’s it going

Step-by-step explanation:

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer:

119.76

8 days

0.5217

93

Step-by-step explanation:

Given that:

1)

Kim's time = 135.46 seconds

Tyron's time is 15.7s faster ;

Tyron's time = 135.46 - 15.7 = 119.76

Janna takes her medicine 3 times a day. How many days will a 60 ml medicine last if 2 1/2ml is taken each time?

(2 1/2 * 3) = 7.5 mL per day

60 mL / 7.5 = 8 days

3. May bought 23 of a kilo of meat. She cooked 12 of it. How much did she cook?

Total bought = 23 of a kilo of meat

Amount cooked = 12 /23= 0.5217 kilo

4. Arjay bought 8.75 meters of cloth for ₱813.75. Find the cost price per meter.

Cost per meter :

813.75 / 8.75 = 93 per meter

5. Jay will divide his P112,000 among his 3 brothers. His elder brother will receive of the amount while the remaining amount is to be equally divided among the two younger brother. How much will each of the younger brothers receive?

Question 5 is Incomplete

Answer:

x=[tex]\frac{13}{30}+i\frac{\sqrt{251}}{30}[/tex]

Step-by-step explanation:

Answer:

I do not fully understand this question so I will try to answer it the best I can.

25x^2-10x^2-13x=-7

15x^2-13x=-7

That is the question simplified. The part that you need to do from here is to figure out what x is. A way you can do that is by plugging in different solutions of what x could be until you find a solution that fits into the equation. I can't help that much but I hope that my solution helps.

Answer:

X=8

Step-by-step explanation:

Hope this helps

Answer:

169

Step-by-step explanation:

Answer:

The cost would be $0.10. You would figure this out because 10 cents is a 10th of a dollar

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of the ball (spherical in nature) Vb = 4/3πrb³

Volume of the hole Vh = 4/3πrh³

rb is the radius of the ball

rh is the radius of the hole

If a ball of radius 17 has a round hole of radius 7 drilled through its center, the volume of the resulting solid will be expressed as:

V = Vb - Vh

V = 4/3πrb³ - 4/3πrh³

factor out the like terms;

V = 4/3π(rb³-rh³)

Given

rb = 17

rh = 7

V = 4/3π(17³-7³)

V = 4/3π(4913-343)

V = 4/3π(4570)

V = (4π*4570)/3

V = 57,399.2/3

V = 19,133.067

Hence the volume of the resulting solid is 19,133.067

Answer:

150 cubic centimeters

Step-by-step explanation:

1/6×X+95=4/5×X

Subtract X from both sides of the equation

Multiply/Combine like terms

95=19/30×X

Multiply by 30/19 and simply

30/19*95=X

Solve for X to get 150

1/6×150=25

4/5×150=120

Answer:

150 cubic centimeters

Step-by-step explanation:

1/6*x+95=4/5*x

Move stuff around

95=1/6+4/5*x

Multiply/Combine like terms  

95=19/30*x

Multiply by 30/19 and then simplify

30/19*95=x

Solve for x

1/6*150=25

4/5*150=120

Answer:

B) 5 hours

Step-by-step explanation:

First, find the amount of mph between 60 and 80:

80 - 60

= 20 mph

Since the speed increases 4 mph per hour, we can find how long it will take to get to 80 mph by dividing 20 by 4:

20/4

= 5

So, the correct answer is B, 5 hours

Answer:

The answer is 6 6/12

Step-by-step explanation:

Answer:

a) 0.0977

b) 0.3507

c) No it is not unusual for a broiler to weigh more than 1610 grams

Step-by-step explanation:

Mean = 1395 grams

Standard deviation = 200 grams. Use the TI-84 Plus calculator to answer the following.

We solve using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

(a) What proportion of broilers weigh between 1160 and 1250 grams?

For x = 1160

z = 1160 - 1395/300

= -0.78333

Probability value from Z-Table:

P(x = 1160) = 0.21672

For x = 1250 grams

z = 1250 - 1395/300

z = -0.48333

Probability value from Z-Table:

P(x = 1250) = 0.31443

The proportion of broilers weigh between 1160 and 1250 grams is

0.31443 - 0.21672

= 0.09771

≈ 0.0977

(b) What is the probability that a randomly selected broiler weighs more than 1510 grams?

For x = 1510

= z = 1510 - 1395/300

z = 0.38333

Probability value from Z-Table:

P(x<1510) = 0.64926

P(x>1510) = 1 - P(x<1510) = 0.35074

Approximately = 0.3507

(c) Is it unusual for a broiler to weigh more than 1610 grams?

For x = 1610

= z = 1610 - 1395/300

z = 0.71667

Probability value from Z-Table:

P(x<1610) = 0.76321

P(x>1610) = 1 - P(x<1610) = 0.23679

No it is not unusual for a broiler to weigh more than 1610 grams

Answer:

c

Step-by-step explanation:

Answer:

8 4/5

Step-by-step explanation:

Answer:

this is the answer i hope it helps you 3 33/40

Answer:

Step-by-step explanation: 1,872

Answer: 1,872

Step-by-step explanation:

Answer:

The dimension of the triangle is 4.144 m and the dimension of the square is 2.392 m

Step-by-step explanation:

let a side of the equilateral triangle = x

let a side of square = y

3x + 4y = 22

4y = 22 - 3x

[tex]y = \frac{11}{2} -\frac{3x}{4}[/tex]

subjective function, the total area is given by;

[tex]f(x,y) = \frac{x^2\sqrt{3} }{4} +y^2[/tex]

[tex]f(x) = \frac{x^2\sqrt{3} }{4} + (\frac{11}{2} -\frac{3x}{4})^2\\\\f(x) = \frac{x^2\sqrt{3} }{4} +\frac{121}{4} -\frac{33x}{4} +\frac{9x^2}{16} \\\\f(x)' = \frac{x\sqrt{3} }{2} -\frac{33}{4} +\frac{9x}{8} \\\\\frac{x\sqrt{3} }{2} -\frac{33}{4} +\frac{9x}{8}=0\\\\\frac{x\sqrt{3} }{2} + \frac{9x}{8} =\frac{33}{4}\\\\\frac{4x\sqrt{3} +9x}{8} = \frac{33}{4}\\\\4x\sqrt{3} +9x = 66\\\\x(4\sqrt{3} +9) = 66\\\\x(15.928) = 66\\\\x = \frac{66}{15.928}\\\\x = 4.144 \ m[/tex]

solve for y

[tex]y = \frac{11}{2} -\frac{3x}{4}\\\\y = \frac{11}{2} -\frac{3*4.144}{4}\\\\y = 5.5-3.108\\\\y = 2.392 \ m[/tex]

Therefore, the dimension of the triangle is 4.144 m and the dimension of the square is 2.392 m

9514 1404 393

Answer:

  0 ft

Step-by-step explanation:

The line hangs down 15 feet from the top of each pole, so the distance between them must be zero if the total line length is 30 feet.

Answer: -22

Step-by-step explanation:

first let's plug in -10 to the f(x) function.

F(-10) = 3(-10) + 10 = -30 +10 = -20

Now we plug in -20 into the g(x) function

g(-20) = -20 -2 = -22

Answer:

If g(x) = x - 2, then g(f(x)) = f(x) - 2. So the whole equation would be: 3x + 10 × x - 2. Simplified: g(f(x)) = 13x - 2

UwU

Answer:

3 /4 I think

Step-by-step explanation:

Answer:

p

Step-by-step explanation:

Answer:

the perimeter is 25.

Step-by-step explanation:

have a nice day!

Answer:

1. -8 feet= 8 feet

-2 feet= 2 feet

2.  Jordin’s balance is a debt of MORE than 27$

3. Dinah had the greatest DECREASE in weight, with losing 1.4 pounds.

Hope this helps hun! Good Luck!

Answer:

4

Step-by-step explanation:

Answer:

119.6

Step-by-step explanation:

52 × 230  over 100 = 119.6

Answer:

90°

Step-by-step explanation:

Measure of angle 3 is,

⇒ ∠3 = 90 degree

We have to given that,

A kite is shown in image.

Since, We know that,

If two sides of  triangle are equal then its corresponding angles are also equal in a triangle.

Now, By given figure, we have;

64 x 2 + x + x = 180

128 + 2x = 180

2x = 180 - 128

2x = 52

x = 26

So, We get;

Measure or angle 1 is,

∠ 1 + 64 + 26 = 180

∠1 = 180 - 90

∠1 = 90 degree

Hence, By definition of vertically opposite angle,

⇒ ∠1 = ∠3 = 90 degree

Learn more about the angle visit:;

https://brainly.com/question/25716982

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