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Artist 52 [7]
3 years ago
13

For the ratio 28 : 36, find an equivalent with both terms greater tan 6 less than 10

Mathematics
1 answer:
velikii [3]3 years ago
8 0
28:36
Divide both by 4 to get
7:9
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Calculus 2
FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

\displaystyle \int_1^47\sqrt{\ln(x)}\, dx

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

1)

The trapezoidal rule is given by:

\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}

Therefore, the trapezoidal approximation is:

\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)

Evaluate:

\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337

2)

The midpoint rule is given by:

\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x

Thus:

\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)

Simplify:

\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319

3)

Simpson's Rule is given by:

\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)

So:

\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)

Simplify:

\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834

6 0
3 years ago
Sfewrthewbtwebrhwebrthbweytbewhibthewghuelbtrueruhewbthujbrultbhrt
Tju [1.3M]
This fjzbwndjsjenskfkfnf I’m dababy
3 0
3 years ago
Write an helpful equation for 9% of 70
sweet [91]

Answer:

0.09(x)=70

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
mc015-1.jpg has coordinates of A(–6, –7), B(4, –2), and C(0, 7). Find the coordinates of its image after a dilation centered at
Tasya [4]
A (-12, -14)
B (8, -4)
C(0, 14)
4 0
3 years ago
If angle 1 is 110°, what would the other angle measures
lana66690 [7]

Answer:

Angle 2=   110 degrees

Angle 3 =  70 degrees

Angle 4 = 70 degrees

Step-by-step explanation:

<u>Finding angle 2</u>

In the figure attached below,the angles 1 and 2  Corresponding angles

When two lines are crossed by another line that is  called the Transversal, then, the angles in matching corners are called corresponding angles.

Corresponding angles are equal so

angle 2 = 110 degrees

<u>Finding angle 3</u>

Similarly 2 and 3 are consecutive angles and Consecutive angles are supplementary . That is the sum of the consecutive angles is 180 degree

then

angle 2  +angle 3 = 180

110  + angle 3 = 180

angle 3 = 180 -110

angle 3 = 70 degrees

<u>Finding angle 4</u>

Now angle 3 and angle 4 are alternate interior angle and they are equal

angle 3 = angle 4

so angle 4 is 70 degree

5 0
3 years ago
Read 2 more answers
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