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bulgar [2K]
3 years ago
13

leonard is flying kite he is holding the end of the string at distance of 1.2 m above the ground. if the string is 15 m how long

and makes an angle of 40 degrees with the horizontal, how high is the kite above the ground?​
Mathematics
1 answer:
larisa86 [58]3 years ago
7 0

Answer:

The kite is 10.8 m above the ground.

Step-by-step explanation:

Here we can make a triangle rectangle like the one shown in the graph below, where we want to find the value of the cathetus X, and that plus 1.2m will be the distance between the kite and the ground.

Notice that X is the opposite cathetus to the 40° angle, then:

We can use the relation:

Sin(θ) = (opposite cathetus)/(hypotenuse)

where, in our case, we have:

θ = 40°

hypotenuse = 15m

opposite cathetus = X

Replacing these in the equation, we get:

Sin(40°) = X/15m

Now we can solve this for X.

Sin(40°)*15m = X = 9.6m

And the actual height of the kite is X + 1.2m

Then:

H = 9.6m + 1.2m = 10.8m

The kite is 10.8 m above the ground.

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xxMikexx [17]

Answer:

654.16-2.02\frac{165.23}{\sqrt{42}}=602.66    

654.16+2.02\frac{165.23}{\sqrt{42}}=705.66    

So on this case the 95% confidence interval would be given by (602.66;705.66)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=654.16 represent the sample mean

\mu population mean (variable of interest)

s=165.23 represent the sample standard deviation

n=42 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=42-1=41

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that t_{\alpha/2}=2.02

Now we have everything in order to replace into formula (1):

654.16-2.02\frac{165.23}{\sqrt{42}}=602.66    

654.16+2.02\frac{165.23}{\sqrt{42}}=705.66    

So on this case the 95% confidence interval would be given by (602.66;705.66)    

7 0
3 years ago
6 - 2x = 6x = 10 + 6
Natalija [7]

Answer:Simplifying

6 + -2x = 6x + -10x + 6

Reorder the terms:

6 + -2x = 6 + 6x + -10x

Combine like terms: 6x + -10x = -4x

6 + -2x = 6 + -4x

Add '-6' to each side of the equation.

6 + -6 + -2x = 6 + -6 + -4x

Combine like terms: 6 + -6 = 0

0 + -2x = 6 + -6 + -4x

-2x = 6 + -6 + -4x

Combine like terms: 6 + -6 = 0

-2x = 0 + -4x

-2x = -4x

Solving

-2x = -4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4x' to each side of the equation.

-2x + 4x = -4x + 4x

Combine like terms: -2x + 4x = 2x

2x = -4x + 4x

Combine like terms: -4x + 4x = 0

2x = 0

Divide each side by '2'.

x = 0

Simplifying

x = 0

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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