Which two values of x are roots of the polynomial below? 4x2-6x+1

. Explain how trigonometry can be used to determine the height of a cell phone tower. Be sure to list the tools required and how

Pachacha [2.7K]

Well a cellphone tower has angles and it has a distance so it is possible to use trigonometry to determine its height. tools to be used are maybe a calculator, measuring tape, paper, and a pencil or pen

7 0

2 years ago

Read 2 more answers

Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)

Ksju [112]

Well, here's one way to do it at least...

For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). 

Let P=(4,0) be the projection of B onto the x-axis. 
Let Q=(-3,0) be the projection of C onto the x-axis. 

Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). 

Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). 

Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. 

||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) 
||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) 

Using the Law of Cosines... 
||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) 
||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) 
||a||^2 = 86 - 36 
||a||^2 = 50 
||a|| = sqrt(50) 

Now apply the Law of Sines to find the other two angles. 

||b|| / sin(B) = ||a|| / sin(A) 
sqrt(41) / sin(B) = sqrt(50) / .9080 
(.9080)sqrt(41) / sqrt(50) = sin(B) 
.8222 = sin(B) 
asin(.8222) = B 
55.305 = B 

Two down, one to go... 

||c|| / sin(C) = ||a|| / sin(A) 
sqrt(45) / sin(C) = sqrt(50) / .9080 
(.9080)sqrt(45) / sqrt(50) = sin(C) 
.8614 = sin(C) 
asin(.8614) = C 
59.470 = C 

So your three angles are: 

A = 65.225 
B = 55.305 
C = 59.470

8 0

1 year ago

The smiths want to replace the stairway that leads from their porch to their sidewalk with a ramp. The porch is 3 feet off the g

Elis [28]

Use the pythagorean therom. 12 squared + 3 squared = x squared
So the answer is 12.4 feet

7 0

2 years ago

Which shows a recursive and an explicit formula for a sequence whose initial term is 14 and whose common difference is −4? A. A(

liberstina [14]

Answer: A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4)

Step-by-step explanation:

Arithmetic sequence is a sequence that is identified by their common difference. Let a be the first term, n be the number of terms and d be the common difference.

For an arithmetic sequence, common difference 'd' is added to the preceding term to get its succeeding term. For example if a is the first term of a sequence, second term will be a+d, third term will give a+d+d and so on to generate sequence of the form,

a, a+d, a+3d, a+4d...

Notice that each new term keep increasing by a common difference 'd'

The nth term of the sequence Tn will therefore give Tn = a+(n-1)d

If the initial (first) term is 14 and common difference is -4, the nth of the sequence will be gotten by substituting a = 14 and d = -4 in the general formula to give;

Tn = 14+(n-1)-4 (which gives the required answer)

Tn = 14-4n+4

Tn = 18-4n

5 0

1 year ago

Read 2 more answers

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

2 years ago