All categories

3 years ago

decide if the following change is an increase or decrease. then determine the percent of change. 48 inches to 30 inches

1 answer:

3 0

48 inches to 30 inches is a decrease.
percent decrease = change/original value x 100%
= (48 - 30)/48 x 100%
= 18/48 x 100%
= 37.5% decrease

You might be interested in

Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere

Ket [755]

Answer:

$e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...$

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

Step-by-step explanation:

Taylor series expansions of f(x) at the point x = a

$\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...$

This expansion is valid only if $\text{f}\:^{(n)}(a)$ exists and is finite for all $n \in \mathbb{N}$ , and for values of x for which the infinite series converges.

$\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1$

$\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...$

$\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}$

$\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4$

$\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4$

$\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4$

Substituting the values in the series expansion gives:

$e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...$

Factoring out e⁴:

$e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]$

Taylor Series summation notation:

$\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n$

Therefore:

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

7 0

1 year ago

What is the least common multiple of all numbers 1-12

Otrada [13]

The LCM is: 2,7,7,2,0.

8 0

3 years ago

If you roll two fair six-sided dice, what is the probability that both dice show an odd number?

OLEGan [10]

Answer:

1/4

Step-by-step explanation:

Both dice have odd numbers 1, 3, 5. The chances of getting an odd number on each number is 3/6

The probability of getting odd numbers on both is:

3/6 ⋅ 3/6 = 9/36 = 1/4

5 0

3 years ago

Read 2 more answers

Evaluate 7w-14 for w=9.

sashaice [31]

That's the answer and how you do it.

(i love to eat)

5 0

3 years ago

A car bought for $13,000 depreciates at a rate of 15% per year. Use an exponential function to find the value of the car after 5

anygoal [31]

Answer:

$ 11093

Explanation:

Recall that the formula for compound interest is:

A = P ( 1 + r/ n ) n ( t )

−−−−−−−−−−−−−−−−−−−−−−

where:

A = future value

P = principal (starting) amount

r = annual interest rate, expressed as a decimal

n = number of times the interest is compounded in a year

t = number of years compound interest occurs for

1 . Start by substituting your known values into the formula. Note that the annual interest rate is − 0.15 since the car depreciates (becomes lower in value) each year.

A = 25000 ( 1 + − 0.15 1 ) 1 ( 5 )

2 . Solve for A .

A = 25000 ( 0.85 ) )5

A = 11092.63

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

A ≈ $ 11093 a

−−−−−−−−−−−−−−−

3 0

2 years ago

Read 2 more answers