Two sides of a triangle are equal in length. The third side of the triangle is 3 more than the equal sides. If the perimeter of the triangle is 48, what is the length of the longest side?

Show work

Answer:

a. 2in

b. [tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]

c. l'(3)=0.1938 in/hr

Step-by-step explanation:

a.

In part a, the problem is asking us to find how much snow will melt during the 6 hour period. In order to do so we need to take the M(t) function and integrate it in the given period of time, so we get:

[tex]\int\limits^6_0 {\frac{\pi}{6}sin(\frac{\pi}{12}t)} \, dt[/tex]

So now we solve:

[tex]\frac{\pi}{6}\int\limits^6_0 {sin(\frac{\pi}{12}t)} \, dt[/tex]

this is a known integral, so we get:

[tex]\frac{\pi}{6}[-\frac{12}{\pi}cos(\frac{\pi}{12}t)]^{6}_{0}[/tex]

we can simplify this so we get:

[tex]-2[cos(\frac{\pi}{12}t)]^{6}_{0}[\tex]

[tex]-2[cos(\frac{\pi}{12}(6))-cos(\frac{\pi}{12}(0))][/tex]

[tex]-2[cos(\frac{\pi}{2})-cos(0)][/tex]

[tex]-2[0-1][/tex]

2 in

b)

For part b they want us to write an expression for l(t), the total number of inches of snow at any time t.

in order to do so we need to find an expression for the rate of change of snow. A snowmaker is adding some snow while another amountn of snow is melting, so this rate of change is found by subtracting the two functions, so we get:

l'(t)=S(t)-M(t)

so:

[tex]l(t)=\int {(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))} \, dt[/tex]

so we integrate this to get:

[tex]l(t)=\frac{0.006}{3}t^{3}-\frac{0.12}{2}t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]

and we can simplify this:

[tex]l(t)=0.002t^{3}-0.006t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]

so now we need to find what C is equal to, we can use the fact that l(0)=40in so we get:

[tex]40=0.002(0)^{3}-0.006(0)^{2}+0.87(0)+2cos(\frac{\pi}{12}(0))+C[/tex]

which yields:

40=2+C

so

C=40-2

C=38

So the final function is:

[tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]

c)

for part c we need to find the rate of change of the total amount of snow at time t=3, so in this case we can use the equation we found previously:

l'(t)=S(t)-M(t)

[tex]l'(t)=(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))[/tex]

and substitute t=3

[tex]l'(3)=(0.006(3)^{2}-0.12(3)+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}(3)))[/tex]

which yields:

l'(t)=0.1938 in/hr

Answer:

3.66

Step-by-step explanation:

You have four numbers which sum equals 14.64. Now you divide 14.64 by 4 to get 3.66, or the mean/average

Simplify the expression.

− 52

Answer:

Solution in photo

Step-by-step explanation:

Answer:

Yes

Using SAS congruent property

Step-by-step explanation:

Answer:non

Step-by-step explanation:

Answer:

It's nonproportional

Answer:

(x - 5) (x - 4)

x(x - 4) - 5(x -4)

x^2 - 4x - 5x - 20

x^2 - 9x - 20

Expand: x (x - 4) - 5 (x - 4)

Simplify: x^2 - 9x - 20

Answer:

The ordered pair (15, 12) means that 15 pounds of beans cost $12.

Step-by-step explanation:

Ordered pairs are in the format of (x,y). The first number represents a point's position on the x-axis and the second represents a point's position on the y-axis. Also note that in this graph, the x-axis represents the weight of beans in pounds and the y-axis represents the cost of beans.

Knowing this, (15,12) means that 15 pounds of beans must cost $12.

Answer:

9 / 19

Step-by-step explanation:

Given that:

Number of slots on roulette wheel = 38

Number of red on wheel = 18

Number of black on wheel = 18

Number of green = 2

The probability that ball will land on red slot :

Recall: probability of event (A) = P(A)

P(A) = (number of required outcome / number of total possible outcomes)

Hence,

P(ball lands on red) = (Number of red slots / total number of slots)

P(ball lands on red) = 18 / 38

P(ball lands on red) = 9/ 19

Answer:

undefined

Step-by-step explanation:

when x has the same number is undefined

but when y has the same is zero

Answer:

A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new ... Roman Civilization began in 508 B.C. and ended in 476 A.D. How long did Roman Civilization last? 476-(-508) = 476+508 = 984 ...

Your income determines your credit score

False.

Your income can sometimes affect your credit score, but it's not based on it. Your credit score is based on your Payment history, Credit history, and debt.

Answer:

the values of N for which there will be no spectral leakage are;

N = Integers multiple by 8

Step-by-step explanation:

Given that;

discrete-time sinusoidal segment x[n] = 6.2cos(0.75πn + 1)

Using DFT to compute the spectrum

The spectral leakage will not be present in the spectrum if the product f₀Td is an integer.

Here, f₀ is sinusoid's frequency and Td is the segment duration

Now we calculate the period of the signal

2π/ω = 2π/0.75π

ω =  2 / 0.75

( × 4 )

ω =  8 / 3

Here, the numerator value is the period of the signal

T₀ = 8

The spectral leakage will not be present in the spectrum if N is  the Integer multiple of period T₀.

Therefore, the values of N for which there will be no spectral leakage are;

N = Integers multiple by 8

Option B since -7/15 equals -0.4666...

Hope it helps!

Answer:

54 groups of 1, 27 groups of 2, 18 groups of 3, 9 groups of 6, and repeat vice versa (6 groups of 9, etc).

Step-by-step explanation:

Total number of ways are 8 to arrange the balloon,

Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,

Given that,

Total number of balloon Sabrina has = 54,

The number of ways Sabrina can arrange the balloon are:

1 group of 54 balloons,

2 groups of 27 balloons,

3 groups of 18 balloons,

6 groups of 9 balloons,

9 groups of 6 balloons,

18 groups of 3 balloons,

27 groups of 2 balloons,

54 groups of 1 balloon,

There are total 8 different ways Sabrina can arrange the balloons.

To know more about Permutation and Combination on:

https://brainly.com/question/13387529

#SPJ2

Answer:

The orthocentre of the given vertices ( 2 , -3.5)

Step-by-step explanation:

Step(i):-

The orthocentre is the intersecting point for all the altitudes of the triangle.

The point where the altitudes of a triangle meet is known as the orthocentre.

Given Points are K (3.-3), L (2,1), M (4,-3)

The Altitudes are perpendicular line from one side of the triangle to the opposite vertex

The altitudes are  MN , KO , LP

step(ii):-

   Slope of the line  

                          [tex]KL = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{1-(-3)}{2-3} = -4[/tex]

The slope of MN =

The perpendicular slope of KL

                           = [tex]\frac{-1}{m} = \frac{-1}{-4} = \frac{1}{4}[/tex]

The equation of the altitude

                                 [tex]y - y_{1} = m( x-x_{1} )[/tex]

                                [tex]y - (-3) = \frac{1}{4} ( x-4 )[/tex]

                               4y +12 = x -4

                                x - 4 y -16 = 0 ...(i)

Step(iii):-

 Slope of the line  

                          [tex]LM = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{-3-1}{4-2} = -2[/tex]

The slope of KO =

The perpendicular slope of LM

                           = [tex]\frac{-1}{m} = \frac{-1}{-2} = \frac{1}{2}[/tex]

The equation of the altitude

                                 [tex]y - y_{1} = m( x-x_{1} )[/tex]

The equation of the line passing through the point K ( 3,-3) and slope

m = 1/2

                                [tex]y - (-3) = \frac{1}{2} ( x-3 )[/tex]

                                2y +6 = x -3

                             x - 2y -9 =0 ....(ii)    

Solving equation (i) and (ii) , we get

  subtracting equation (i) and (ii) , we get

                   x - 4y -16 -( x-2y-9) =0

                       - 2y -7 =0

                      -2y = 7

                        y = - 3.5

Substitute y = -3.5 in equation x -4y-16=0

               x - 4( -3.5) - 16 =0

               x +14-16 =0

                x -2 =0

                  x = 2

The orthocentre of the given vertices ( 2 , -3.5)

Answer:

4/x-1

Step-by-step explanation:

so divide by x

so 4/x

less 1

4/x-1

Answer:

12x + 3

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

6 + 4(3x - 2) + 5

Step 2: Simplify

Answer: Henrik grew 147 more potatoes than Derek

Step-by-step explanation:

Answer:

62.5 inches

Step-by-step explanation:

We would solve this using ratio

Width : Length = Width/Length

For the Original photo

5 inches : 7 inches = 5/7

For the enlarged phots

x : 87.5 inches = x/87.5

Equating both ratios together, we have:

5/7 = x /87.5

Cross Multiply

7x = 5 × 87.5

7x = 437.5

x = 437.5/7

x = 62.5 inches

Hence, the width of the enlarged photo is 62.5 inches

Answer:

3.5 hours

Step-by-step explanation:

if you multiply 6 and 2 by 3.5, then add them you get 28

Answer:

0.4245

Step-by-step explanation:

The probability that Z lies between -0.558 and 0.558 can be written as;

P(-0.558 < z < 0.558) = P(z < 0.558) - P(z < -0.558)

Using z - distribution table, we have;

P(z < 0.558) = 0.7122

P(z < -0.558) = 0.2877

Thus;

P(z < 0.558) - P(z < -0.558) = 0.7122 - 0.2877 = 0.4245

Answer:

Area = 1500 Sq m

Cost of grassing = ₹105000

Step-by-step explanation:

Area of the park = 50*30 = 1500 Sq m

Cost of grassing = 1500*70 =₹ 105000

Answer:

w = 3/2

Step-by-step explanation:

Area of a Rectangle

The 5-inch by 7-inch picture has a frame of width w surrounding all four sides.

a)

The total length of the framed picture is 7 + 2w

The total width of the framed picture is 5 + 2w

b)

The total area of the framed picture is:

At = (7 + 2w)(5 + 2w)

c) We know the total area is 80 square inches, thus:

(7 + 2w)(5 + 2w) = 80

Operating:

[tex]35 + 14w + 10w + 4w^2=80[/tex]

Simplifying:

[tex]4w^2 + 24w -45 =0[/tex]

We now write:

[tex]4w^2 + 30w - 6w -45 =0[/tex]

Factor out 2w from the first two terms and -3 from the last two terms:

[tex]2w(2w + 15) - 3(2w + 15) =0[/tex]

Factor out 2w+15

(2w + 15)(2w - 3)=0

The solutions are:

w = -15/2

w = 3/2

The only feasible solution is the positive value, thus

w = 3/2

Answer:

Between 80 and 160

Step-by-step explanation:

this is  such a bad graph i honestly could not give you an exact answer

Answer:

(0,0) and (1,1)

Step-by-step explanation: