MATHEMATICS COLLEGE

A typical combine harvester sells for $500,000. If the value of the combine depreciates 5.52% each year, how many years will it take to lose half of it's value? Round your answer to the nearest whole number of years.

Answers

Answer 1

Answer:

To model the given problem, we use the following exponential function:

$V(t)=500,000(1-0.0552)^t.$

Now, we set the above equation to

$V(t)=(500,000)/(2)=250,000=500,000(1-0.0552)^t.$

Solving for t, we get:

$\begin{gathered} (250,000)/(500,000)=0.9448^(t,) \n tln(0.9448)=ln((1)/(2)), \n t=(ln((1)/(2)))/(ln(0.9448)). \end{gathered}$

Finally, we get:

$t\approx12\text{ years.}$

Answer:

$12\text{ years.}$

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A line with a slope of -1/2 passes thru the point (-4,3)...Which equation represents this line?

Which of the following expressions are equivalent to - -a/b

Answers

Answer:

B) $-(a)/(-b)$

Step-by-step explanation:

1. First, we have to know that two negatives equal positive.

2. Given the information above, $-(-a)/(b)$ can simplify to $(a)/(b)$ .

3. Let's go through each answer choice and see which one also simplifies to $(a)/(b)$ .

$(a)/(-b)$
$-(a)/(b)$

$-(a)/(-b)$
$(a)/(b)$

Therefore, the answer is B) $-(a)/(-b)$ .

Find the scale.

Model length: 40 cm

Actual length: 60 m

Answers

Answer:

2/3

Step-by-step explanation:

Given

Model length: 40 cm

Actual length: 60 m

Scale for any model is ratio of model length of object and actual length of object

Therefore scale for problem stated = Model length/Actual length

= 40/60 = 4/6 = 2/3

Need help
6n - 3(2n - 5)

SHOW ALL WORK!

Answers

6n - 3(2n-5)

mutiply the bracket by -3

(-3)(2n)= -6n

(-3)(-5)= 15

6n-6n+15

0+15

answer:

6n-3(2n-5)
6n-(6n-15)
6n-6n+15
(6n-6n)+15
=15

On a test, Avery lost 5points for each of the 6
questions she got wrong
but earned 10 points for
answering the bonus
question correctly. What
integer represents her
score in relation to a
perfect score of 100?

Answers

Answer:

bruhhhhhhhhhhhhhhhhhhhhhhhhhh

Estimate the average rate of change of the graphed function, over the interval 0 ≤ x ≤ 2.

Answers

Answer:

A) 2

Step-by-step explanation:

(0,3) and (2,7)

Use slope formula

(7-3)/(2-0) = 4/2 = 2

Answer:

A) 2

Step-by-step explanation:

Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answers

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² = $(n(n+1)(2n+1))/(6)$

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. : $(1* 2* 3)/(6)=(6)/(6)=1$

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

$1+4+9+...................+k^2=(k(k+1)(2k+1))/(6)$

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

$1+4+9+......................+(k+1)^2$

and R.H.S. becomes,

$((k+1)(k+2)(2k+3))/(6)$

Consider, L.H.S.,

$1+4+9+..+k^2+(k+1)^2\n\n=(k(k+1)(2k+1))/(6)+(k+1)^2\n\n=k+1[(k(2k+1))/(6)+(k+1)]\n\n=(k+1)[(2k^2+k+6k+6)/(6)]\n\n=(k+1)(2k^2+7k+6)/(6)]\n\n=(k+1)(2k^2+4k+3k+6)/(6)]\n\n=(k+1)[(2k(k+2)+3(k+2))/(6)]\n\n=((k+1)(2k+3)(k+2))/(6)$

So, L.H.S. = R.H.S.

Hence, P(n) is true for all integers n.

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