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3 years ago

The thing is in the picture

Mathematics

1 answer:

vitfil [10]3 years ago

6 0

The answer should be C 20

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Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integr

prisoha [69]

Split up the interval [0, 2] into 4 subintervals, so that

$[0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right]$

Each subinterval has width $\dfrac{2-0}4=\dfrac12$ . The area of the trapezoid constructed on each subinterval is $\dfrac{f(x_i)+f(x_{i+1})}4$ , i.e. the average of the values of $x^2$ at both endpoints of the subinterval times 1/2 over each subinterval $[x_i,x_{i+1}]$ .

So,

$\displaystyle\int_0^2x^2\,\mathrm dx\approx\dfrac{0^2+\left(\frac12\right)^2}4+\dfrac{\left(\frac12\right)^2+1^2}4+\dfrac{1^2+\left(\frac32\right)^2}4+\dfrac{\left(\frac32\right)^2+2^2}4$

$=\displaystyle\sum_{i=1}^4\frac{\left(\frac{i-1}2\right)^2+\left(\frac i2\right)^2}4=\frac{11}4$

4 0

3 years ago

Kwame bought a car for $25,000. The value of the car is decreasing at a rate of 6.5% each year. Write a function that represents

sweet-ann [11.9K]

<h3>The function that represents the price P of the car after x years is:</h3>

$P = 25000(0.935)^x$

Solution:

The decreasing function is given as:

$y = a(1 - r)^t$

Where,

y is future value

a is initial value

r is decreasing rate in decimal

t is time period

From given,

a = 25000

$r = 6.5 \% = \frac{6.5}{100} = 0.065$

number of years = x

future value = P

Therefore,

$P = 25000(1 - 0.065)^x\\\\P = 25000(0.935)^x$

Thus the function is found

8 0

4 years ago

*the problem is in the pic that is uploaded

Alex787 [66]

Hmm,
ok,
complete square ok
wait wat

he went from
(x-3)²=16 to
x-3=16
?????
he square rooted the left side only
he has to do it to both sides

he should have done
(x-3)²=16
x-3=+/-4
x=3+/-4
x=7 or -1

8 0

3 years ago

What is a good anime to watch

DaniilM [7]

Answer:

My hero acadamia. I didnt spell that right. Its on hulu.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Oliver has music lessons in Monday Wednesday and Friday.Each lesson is 3/4 of an hour Oliver says he will have lessons for three

Hoochie [10]

Oliver is incorrect because if he were correct he would learn for 2 hours and 15 minutes because, 45 minutes * 3= 2:15 minutes.

4 0

3 years ago

The thing is in the picture​

The thing is in the picture