Yoshua borrowed $8,000 from his credit union over 9 months. He pays a simple interest of
9%. What is the total amount of money he will owe the bank?

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:

C = y=4x

Step-by-step explanation:

That answer because if you were to multiply on the way it will have the same graph

Answer:

The third option

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Opening the brackets, you get: 3x^2 - 2x + 5 - 2x^2 + 5x - 1

Simplifying, you get : x^2 + 3x + 4

Answer:

a

Step-by-step explanation:

3x^2 - 2x^2= x^2

-2x + 5x = 3x

5- 1 =5

Answer:

1 space to the right?

Step-by-step explanation:

Answer:

1 space to the left

Step-by-step explanation:

example 5.0 X 10% is the same as 5.0 x .10

5.0 x .10 = .50

Answer:I think you find the mean mode miden

Step-by-step explanation:

Answer:

the answer is 7 the problem is an easy one

Step-by-step explanation:

Answer: B is the correct answer

Step-by-step explanation: Lol its B

Answer:

2/9 of the high school students play string instruments.

Step-by-step explanation:

[tex] \frac{1}{3} \times \frac{2}{3} = \frac{2}{9} [/tex]

Answer:

nun of the 3 you gave use so the last one the 4th

Step-by-step explanation:

Answer:

Natalia's work is wrong.

Step-by-step explanation:

Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:

1) [tex]x = 6.2\times 12[/tex] Given.

2) [tex]x = \left(6+0.2\right)\times 12[/tex] Definition of addition.

3) [tex]x = 6\times 12 + 0.2\times 12[/tex] Distributive property.

4) [tex]x = 72 + \frac{2}{10}\times 12[/tex] Definitions of multiplication and decimal number.

5) [tex]x = 72 +[2\cdot (10)^{-1}]\cdot 12[/tex] Definition of division/Associative property.

6) [tex]x = 72 + [2\cdot 12]\cdot (10)^{-1}[/tex] Associative property.

7) [tex]x = 72 + 24\cdot 10^{-1}[/tex] Definition of multiplication.

8) [tex]x = 72 + \frac{24}{10}[/tex] Definition of divsion.

9) [tex]x = 72 + 2.4[/tex] Defintion of decimal number.

10) [tex]x = 74.4[/tex] Definition of addition/Result

Natalia's work is wrong.

Answer:

[tex]6 - 8x = 5x - 10x + 15 \\10x-8x-5x=15-6\\ - 3x = 9 \\ x = \frac{9}{ - 3} \\ x = - 3[/tex]

Answer:-3

the right answer  did ths on paper

Answer:

$135

Step-by-step explanation:

If each set cost $0.40 to make and sells for $1.75, the profit for each pack is $1.35.

To get 20% of this you do the following: 1.35×0.20

20% of $1.35 is $0.27.

If 500 sets of pencil are sold and the school gets $0.27 from each pack sold, you would multiply $0.27 by 500, which would give you the answer $135.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

11, 13, 15, 17, 19, ...

Determining the Recursive formula:

We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.

From the given sequence it is clear that every term can be obtained by adding two to the previous term.

i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2

so

aₙ₊₁ = aₙ+2, for n ≥1

Therefore, a recursive formula is:

Determining the Explicit formula:

Given the sequence

11, 13, 15, 17, 19, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

[tex]a_n=a_1+\left(n-1\right)d[/tex]

computing the differences of all the adjacent terms

[tex]3-11=2,\:\quad \:15-13=2,\:\quad \:17-15=2,\:\quad \:19-17=2[/tex]

The difference between all the adjacent terms is the same and equal to

[tex]d=2[/tex]

also

[tex]a_1=11[/tex]

so substituting [tex]d=2[/tex], [tex]a_1=11[/tex] in the nth terms

[tex]a_n=a_1+\left(n-1\right)d[/tex]

[tex]a_n=2\left(n-1\right)+11[/tex]

[tex]a_n=2n+9[/tex]

Therefore, the Explicit formula is:

[tex]a_n=2n+9[/tex]

Answer:

1234579

Step-by-step explanation:

first apply formula.then solved

Answer/Step-by-step explanation:

Parallelogram A:

Area = 5x + 20

Base = x + 4

Height = h = ?

Area of Parallelogram = base * height

Plug in the values

5x + 20 = (x + 4) * h

Divide both sides by x + 4

[tex] \frac{5x + 20}{x + 4} = h [/tex]

[tex] \frac{5(x + 4)}{x + 4} = h [/tex]

[tex] 5 = h [/tex]

Height = 5

Parallelogram B:

Area = 8x - 24

Base = b

Height = 8

Area of Parallelogram = base * height

Plug in the values

8x - 24 = b * 8

Divide both sides by 8

[tex] \frac{8x + 24}{8} = b [/tex]

[tex] \frac{8(x + 3)}{8} = b [/tex]

[tex] x + 3 = b [/tex]

Base = x + 3

Parallelogram C:

Area = 12x + 6y

Base = 6

Height = h = ?

Area of Parallelogram = base * height

Plug in the values

12x + 6y = 6 * h

Divide both sides by 6

[tex] \frac{12x + 6y}{6} = h [/tex]

[tex] \frac{6(2x + y)}{6} = h [/tex]

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

Height = 2x + y

Answer:

d.

Step-by-step explanation:

Given that:

In a school;

Population mean = 900

First student:

Sample size  = 100

Sample proportion = 0.17

Second student:

Sample size = 90

Sample proportion = 0.24

The difference between the two percentages is a result of the random error because numbers were not the same as a result of variability inherent in sampling.

Answer:

21 green cars

Step-by-step explanation:

Answer:

70 x 30/100 = 21

21 cars are green

Step-by-step explanation:

Answer:

2/3 chance

Step-by-step explanation:

You want to find numbers less than 5, so there are 4 numbers you can use. 4 out of 6 numbers possible is 4/6, or 2/3.

Answer:

C

Step-by-step explanation:

I think so im not sure sorry

Answer: the smallest initial velocity that is required to throw the stone is 56 ft/s

Step-by-step explanation:

We know that;

u = initial velocity  

v = final velocity  = 0

a = acceleration  = -g = -32,

s = distance travelled  = 49 feet

V² - u² = 2aS

we substitute

0² - u² = 2 × -32 × 49

0 - u² = -3136

u² = 3136

u = √3136

u = 56 ft/s

Therefore the smallest initial velocity that is required to throw the stone is 56 ft/s

Answer: Any number larger than 14.3; one possible value is 20

Note how 20 + (-14.3) = 20-14.3 = 5.7 which is positive.

If we picked something smaller than 14.3, like say 10, then

10+(-14.3) = 10-14.3 = -4.3 which is negative.

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

When adding a positive to a negative, you basically subtract the two values. Then whatever the largest value is, that's the sign of your result. For 20+(-14.3), the positive 20 is larger in absolute value so the overall result is positive. On the other hand, the -14.3 is larger in magnitude compared to the 10, which is why 10+(-14.3) has a negative result.

Answer:

It’s c

Step-by-step explanation:

The graph of the linear functions are solved and a = 4, b = -2 , c = -4

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution

On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.

Given data ,

Let the linear function be represented as A

Now , the value of A is

y = f ( x )

Now , the functions on the graph are above and below the y = f ( x )

So , the value of a = positive

And , a = 4

Now , the value of b = negative

And , y = f ( x + b ) is below f ( x )

So , b = -2

And , similarly c = -4

Hence , the linear functions are solved

To learn more about linear equations click :

https://brainly.com/question/10185505

#SPJ2

Answer:

the answer is B

Step-by-step explanation:

Got it correct on Edge 2020

Answer:

its 130000

Step-by-step explanation:

i had that as my exit ticket for mathcounts :) hope it helps