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3 years ago

What is the area of this composite figure? 12ft2 80 ft2 88 ft2 100 ft2

Mathematics

2 answers:

Julli [10]3 years ago

6 0

Answer:

Step-by-step explanation:

just took the test.

iVinArrow [24]3 years ago

5 0

Look at the picture.

$x=10ft-2ft=8tf\\\\A_1=10ft\cdot8ft=80ft^2\\\\y=10ft-6ft=4ft\\\\A_2=4ft\cdot2ft=8ft^2\\\\A_F=A_1+A_2\to A_F=80ft^2+8ft^2=88ft^2$

$Answer:\ \boxed{88ft^2}$

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Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Otrada [13]

I guess the "5" is supposed to represent the integral sign?

$I=\displaystyle\int_1^4\ln t\,\mathrm dt$

With $n=10$ subintervals, we split up the domain of integration as

[1, 13/10], [13/10, 8/5], [8/5, 19/10], ... , [37/10, 4]

For each rule, it will help to have a sequence that determines the end points of each subinterval. This is easily, since they form arithmetic sequences. Left endpoints are generated according to

$\ell_i=1+\dfrac{3(i-1)}{10}$

and right endpoints are given by

$r_i=1+\dfrac{3i}{10}$

where $1\le i\le10$ .

a. For the trapezoidal rule, we approximate the area under the curve over each subinterval with the area of a trapezoid with "height" equal to the length of each subinterval, $\dfrac{4-1}{10}=\dfrac3{10}$ , and "bases" equal to the values of $\ln t$ at both endpoints of each subinterval. The area of the trapezoid over the $i$ -th subinterval is

$\dfrac{\ln\ell_i+\ln r_i}2\dfrac3{10}=\dfrac3{20}\ln(ell_ir_i)$

Then the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{20}\ln(\ell_ir_i)\approx\boxed{2.540}$

b. For the midpoint rule, we take the rectangle over each subinterval with base length equal to the length of each subinterval and height equal to the value of $\ln t$ at the average of the subinterval's endpoints, $\dfrac{\ell_i+r_i}2$ . The area of the rectangle over the $i$ -th subinterval is then

$\ln\left(\dfrac{\ell_i+r_i}2\right)\dfrac3{10}$

so the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{10}\ln\left(\dfrac{\ell_i+r_i}2\right)\approx\boxed{2.548}$

c. For Simpson's rule, we find a quadratic interpolation of $\ln t$ over each subinterval given by

$P(t_i)=\ln\ell_i\dfrac{(t-m_i)(t-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+\ln m_i\dfrac{(t-\ell_i)(t-r_i)}{(m_i-\ell_i)(m_i-r_i)}+\ln r_i\dfrac{(t-\ell_i)(t-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

where $m_i$ is the midpoint of the $i$ -th subinterval,

$m_i=\dfrac{\ell_i+r_i}2$

Then the integral $I$ is equal to the sum of the integrals of each interpolation over the corresponding $i$ -th subinterval.

$I\approx\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt$

It's easy to show that

$\displaystyle\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt=\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)$

so that the value of the overall integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)\approx\boxed{2.545}$

4 0

3 years ago

The window is 60 inches wide. What is the width of the window in feet.

blsea [12.9K]

Answer:

5feet

Step-by-step explanation:

1 foot= 12 inches

1 inches = 1/12 feet

60 inches= 60x1/12= 5 feet

8 0

3 years ago

Twelve less than 5 times a number is greater than or equal to 6 more than twice the number. Each inequality and number line repr

jenyasd209 [6]

Answer: x ≥ 6

Step-by-step explanation:

12 less than 5 times a number ≥ 6 more than twice the number

5x - 12 ≥ 2x + 6

Note: the word "than" switches the order of the terms.

5x - 12 ≥ 2x + 6

-2x +12 -2x +12

3x ≥ 18

÷3 ÷3

x ≥ 6

Graph: 6 -----------→ the dot is closed (filled in) since it is "equal to"

3 0

3 years ago

Please respond as soon as you can, I will give brainliest answer!

spin [16.1K]

Answer: Non-Linear Function line

Step-by-step explanation:

The reason is if it was a linear one then it would be a straight line and since this is not a straight line then it is a Non-Linear Function because you can't just look at it and see what the increase and decrease was for a certain time period.

4 0

3 years ago

Mary is 5 years older than bob. If the sum of their ages is 39 write and solve an equation to find ages. Please help me with a c

nikdorinn [45]

5x=39 x stands for the age of bob so 39/5 =7.8 which is rounded up to 8 and if you multiply 8 by 5 you get 40 but if you multiply 7.8 by 5 you get 39 so his age would be 7.8 years old.

4 0

3 years ago

Read 2 more answers