Suppose you deposit $2,000 in a saving account that pays interest at an annual rate of 4% with interest compounded monthly. Answer the
following questions:

(a)Write a function that represents the amount of money in the account after t years

(b) How much money is going to be in the account after 5 years.

(c) How many years will it take for the account to go over $2,500?

From the definition, we have

[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{f(x) - f(10)}{x - 10}[/tex]

With [tex]f(x)=\sqrt{x-1}[/tex], we get [tex]f(10)=\sqrt{10-1}=\sqrt9=3[/tex]. So the limit we want to compute is

[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{\sqrt{x-1} - 3}{x - 10}[/tex]

Rationalize the numerator by multiplying by its conjugate:

[tex]\displaystyle \frac{\sqrt{x-1} - 3}{x - 10} \times \frac{\sqrt{x-1}+3}{\sqrt{x-1}+3} = \frac{\left(\sqrt{x-1}\right)^2-3^2}{(x-10)\left(\sqrt{x-1}+3\right)} = \frac{x-10}{(x-10)\left(\sqrt{x-1}+3\right)}[/tex]

x is approaching 10, which is to say x ≠ 10, so we can cancel the factors of x - 10 and remove the discontinuity.

Then we're left with

[tex]\displaystyle f'(10) = \lim_{x\to0} \frac1{\sqrt{x-1}+3} = \frac1{\sqrt{10-1}+3} = \frac1{\sqrt9+3} = \frac1{3+3} = \boxed{\frac16}[/tex]

evaluated by direct substitution, which we can do since the limand is continuous.

Answer:

A

Hope This Helps! :)

Answer:

B. 4 inches

Step-by-step explanation:

(24)(1) / 6 = 4

Answer:

a. (53, 12)

b. I couldn't find this without making a graph myself, hopefully someone will find it or you can figure it out for yourself using the answer I did provide.

Answer:

Describe a set of transformations that would map triangle FGH onto F'G'H

Step-by-step explanation:

Answer:

$19,260

Step-by-step explanation:

1 year = 12 months

5 × 12 = 60

5 years = 60 months

$321 × 60 = $19,260

1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:

[tex]\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}[/tex]

Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.

2. f(x) is continuous at x = -1, so the limit can be computed directly again:

[tex]\displaystyle \lim_{x\to-1} f(x) = \lim_{x\to-1}(x-2) = -1-2=\boxed{-3}[/tex]

3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So

[tex]\displaystyle \lim_{x\to-2}f(x) = \boxed{-1}[/tex]

4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.

5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case

[tex]\displaystyle \lim_{x\to2^+}f(x) = \boxed{0}[/tex]

When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.

6. It should be rather clear from the plot that

[tex]\displaystyle \lim_{x\to0}f(x) = \lim_{x\to0}(\sin(x)+3) = \sin(0) + 3 = \boxed{3}[/tex]

because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.

For 7-8, divide through each term by the largest power of x in the expression:

7. Divide through by x². Every remaining rational term will converge to 0.

[tex]\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}[/tex]

8. Divide through by x² again:

[tex]\displaystyle \lim_{x\to-\infty}\frac{x+3}{x^2+x-12} = \lim_{x\to-\infty}\frac{\frac1x+\frac3{x^2}}{1+\frac1x-\frac{12}{x^2}} = \frac01 = \boxed{0}[/tex]

9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:

[tex]\displaystyle \lim_{x\to6}\frac{2x^2-12x}{x^2-4x-12}=\lim_{x\to6}\frac{2x(x-6)}{(x+2)(x-6)} = \lim_{x\to6}\frac{2x}{x+2} = \frac{2\times6}{6+2}=\boxed{\frac32}[/tex]

10. Factorize the numerator and simplify:

[tex]\dfrac{-2x^2+2}{x+1} = -2 \times \dfrac{x^2-1}{x+1} = -2 \times \dfrac{(x+1)(x-1)}{x+1} = -2(x-1) = -2x+2[/tex]

where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is

[tex]\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}[/tex]

Answer:

The answer is B

Step-by-step explanation:

Btw if its wrong im sorry

Answer:

20

Step-by-step explanation:

Answer:

B. 486,732

__________________________________________________________

To solve digit problems, multiply the value of the digit example: tens place, hundreds place by 10 to get to the next digit, and then you will have your answer.

[tex]600 * 10 = 6,000~-- > ~thousands~place[/tex]

Therefore, the answer would be B. because it has a 6 in the thousands place.

__________________________________________________________

Ask in comments.

486,732 is the number in which the  digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691. Option B is correct.

To find the number in which the digit 6 has a value that is 10 times as great as the value of the digit 6 in 283,691, we need to compare the place values of the digit 6 in both numbers.

In the number 283,691:

The 6 is in the hundreds place.

Now let us multiply this place with 10.

100×10 = 1000.

Find the number in which the digit is in 1000 place.

In the number 486732, the 6 is in 1000 place.

Hence, Option B is correct. 486,732 is the number in which the  digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691.

To learn more on Number system click:

https://brainly.com/question/1763119

#SPJ3

Length is not given or any diagram hasn't been attached.

Length to be taken as x

Now

Volume:-

Answer:

D=3h+5

Step-by-step explanation:

Given: The rate of increasing speed  = 3 miles per hour

The distance she traveled before stopping = 5 miles

Let h represents the number of additional hours for hiking.

Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-

D=3h+5

Answer:

D = 3h + 5

Step-by-step explanation:

Answer:

$39

Step-by-step explanation:

[tex]12(.75 + 2.50) = 12(3.25) = 12(3) + 12(.25) = 36 + 3 = 39[/tex]

Answer:

90

Step-by-step explanation:

x/15=66/11

x/15=6

multiply by 15 on both sides to get the variable by itself

x=90

Answer:

Step-by-step explanation:

from Cyrus' to Jane's ,  the distance is  D= [tex]\sqrt{8^{2} +21^{2} }[/tex] = 22.47 mi

from Adriana's to Madisyn's , the dist. is D =[tex]\sqrt{21^{2} +14^{2} }[/tex] = 25.24 mi

Answer:

1.a) 90 1.b) 32

Step-by-step explanation:

1.) 1^2 + 2^3 + 3^4

Squared means how much times to multiply the same number.

So, 1^2= 1x1=1

2^3=2x2x2=8

3^4=3x3x3x3=81.

So, 81+8+1=90

2. 4^2=4x4=16+2^4=2x2x2x2=16

16+16=32

Please mark me brainliest :)

Answer:

4 the answer is 4

Step by step explanatin:

Answer:

D. y=40x + 50

y=35x + 75

Step-by-step explanation:

x is per hr

it's 40 and 35 dollars per hr

Answer:

30yd²

Step-by-step explanation:

A = a*b/2 = 5yd * 12 yd / 2 = 60 yd² / 2 = 30 yd²

Answer: 30 yd²

Step-by-step explanation:

Let's start by flipping the triangle over to become a standard right-angled triangle so that the side measuring 5 yards becomes the bottom and 12 yards becomes the height.

The area of any triangle is

Area = 1/2 x breadth x height

Area = 1/2 x 5yd x 12yd = 5 x 12/2 = 60/2 = 30yd²

Answer:

Mean - 12

Median - 9

Mean - Median = 3

Step-by-step explanation:

math

Answer:

AB = 23, BC = 13

Step-by-step explanation:

[tex]5x - 7 = 23[/tex]

[tex]5x = 30[/tex]

[tex]x = 6[/tex]

AB = 23, BC = 3(6) - 5 = 18 - 5 = 13

Answer:

1962.5 m^2

Step-by-step explanation:

area of the entire circle = pi (50^2)

subtract the large area

pi 50^2 -   4.71 /2pi   pi 50^2 =

Answer:

76 squared cm

Step-by-step explanation

the equation is (b+b*h/2) so u just take 7 plus 12 times 8 divided by 2 and you get 76

Answer:

D) 140 degrees

Step-by-step explanation:

Radius is perpendicular to tangent line

Draw DA, construction

DA is an angle bisector, m<BAD = 20,

Now, DBA and DCA are congruent right triangles

This is due to LA congruency

90 + 20 + x = 180

x = 70

BDA = CDA

so 70 + 70 = 140

D) 140 degrees

(I'm not that good at geo, so :( )

Anwer o.5

Step-by-step explanation:

because 0.5 x 1 = 0.5

Answer:

(x = 0, y = 0) and (x = 3, y = 0)

Step-by-step explanation:

Let's test out each pair by substituting the values into the inequalities.

Case 1: x = 0, y = 0

0 <= 6

0 < 6

It works!

Case 2: x = -5, y = -15

-15 <= 10 + 6 = 16

-5 + 15 = 10 < 6

It doesn't work.

Case 3: x = 4, y = -2

-2 <= -8 + 6 = -2

4 + 2 = 6 < 6

It doesn't work.

Case 4: x = 3, y = 0

0 <= -6 + 6 = 0

3 < 6

It works!

Case 5: x = 10, y = 0

0 <= -20 + 6 = -14

From here we can already see that it doesn't work

Case 1 and 4 work!

Answer:

5.

Step-by-step explanation:

Have you heard of something called reading?

Answer:

95.45%

Step-by-step explanation:

Honestly I looked it up I hope it helps though and best of luck! : )

Answer:

47.5% I just took it