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NARA [144]
3 years ago
5

you are lying 120 ft away from a tree that is 50 feet tall you look up at the top of the tree approxmaelty how far is your head

from the top of the tree in a straight line

Mathematics
1 answer:
Pepsi [2]3 years ago
5 0
Check the picture below.

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Number 8 please, I don't understand it
Nuetrik [128]
Lovin lemons sells 4 gallons for 24$ while sour co sells 4 gallons for 32 $ 

loving lemons is cheaper and ignore my grammer
7 0
3 years ago
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
A 12 inch candle and an 18 inch Candle are lit at 6 p.m. The 12 inch candle burns 0.5 inches every hour. The 18 inch candle burn
Stella [2.4K]
18 - 2H = 12 - .5H
Combine the variables
18 - 2H + .5H = 12 - .5H + .5H
18 - 1.5H = 12
Combine the whole numbers
18 - 18 - 1.5H = 12 - 18
-1.5H = -6
Divide by -1.5
-1.5H/-1.5 = -6 / -1.5
H = 4
The answer is 4 hours
7 0
3 years ago
H<br> nlaced inside a cylinder as shown. The radius of the cone is half the radius of the cylinder.
Sophie [7]

Answer:

umm what or we doing?

Step-by-step explanation:

5 0
3 years ago
Carrie has 300 marbles 25 of the marbles are green 15% of the marbles are red and the rest of the marbles are blue how many blue
Rus_ich [418]

Answer:

230.

Step-by-step explanation:

\:  \:  \:  \: 300 - 25 -  \frac{15}{100}  \times 300 =  \\  = 275 - 45 =  \\  = 230

Hope this helps!

4 0
3 years ago
Read 2 more answers
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