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Finger [1]
3 years ago
7

Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75 with the ground. The height of the

kite from the ground is meters

Mathematics
2 answers:
GuDViN [60]3 years ago
6 0
You don't say if the answer needs to be rounded 
 the height is 77.27 meters ( not rounded)

 see attached picture for solution:

ANTONII [103]3 years ago
5 0
The height of the kite would be 77.27 m. This can be found using the law of sines. Assuming that the kite also makes a 90 degree angle with the ground, the proportion 80/sin90=h/sin75 can be used. Then, cross multiplication gets sin75x80=sin90xh. Divide both sides by sin90, and that results in 77.27 m. 
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The total resistance in a circuit with two parallel resistors is 2 ohms and R1 is 6 ohms. Using the equation for R2, in terms of
ivanzaharov [21]
<h2>Answer:</h2>

R_2  is 3 ohms

<h2>Step-by-step explanation:</h2>

In a circuit containing two resistors R_1 and R_2 connected together in parallel, the total resistance R_T is given by;

\frac{1}{R_T} = \frac{1}{R_1}  + \frac{1}{R_2}              ---------(i)

<em>Make </em>R_2<em> subject of the formula;</em>

=> \frac{1}{R_2} = \frac{1}{R_T}  - \frac{1}{R_1}  

=> \frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}

=>   {R_2} = \frac{R_TR_1}{R_1 - R_T}       ---------------(ii)

From the question,

R_1 = 6Ω

R_T = 2Ω

Substitute these values into equation (ii) as follows;

=> {R_2} = \frac{2*6}{6 - 2}

{R_2} = \frac{12}{4}

R_2 = 3Ω

Therefore, the value of R_2 = 3 ohms or R_2 = 3Ω

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Which of the following example is an improper fraction
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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your
Darina [25.2K]

Answer:

Given definite  integral as a limit of Riemann sums is:

\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Step-by-step explanation:

Given definite integral is:

\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}

Substituting (2) in above

f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Riemann sum is:

= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

4 0
3 years ago
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