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2 years ago

Geometry Solve for x. Round to the nearest tenth of a degree, if necessary.

Mathematics

1 answer:

zvonat [6]2 years ago

3 0

Answer:

13. x = 52.8°

14. 663.65 ft

15. 30.7 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and trig functions of the acute angles.

The sides adjacent and opposite the angle are marked. The relevant trig relation is ...

Tan = Opposite/Adjacent

tan(x°) = 2.5/1.9

The angle is found using the inverse tangent function:

x° = arctan(2.5/1.9) ≈ 52.8°

Again, the tangent relation comes into play. The given values are the side opposite and the angle, and we are asked for the side adjacent.

Tan = Opposite/Adjacent

tan(11°) = (129 ft)/(distance to shore)

distance to shore = (129 ft)/tan(11°)

distance to shore ≈ 663.65 ft

In this scenario, the given angle is opposite the given side of the triangle. The measure of the hypotenuse is needed.

Sin = Opposite/Hypotenuse

sin(71°) = (29 ft)/(ladder length) . . . . substitute given information

ladder length = (29 ft)/sin(71°) . . . . . . solve for ladder length

ladder length ≈ 30.7 ft

You might be interested in

Four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x.

Aleksandr [31]

4(x + 15) > = 120
4x + 60 > = 120
4x > = 120 - 60
4x > = 60
x > = 60/4
x > = 15...........so ur answer is 15 or more

4 0

2 years ago

A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s2 = 16 for scores on a college placement test in mat

Helen [10]

Answer:

The 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =16$ represent the sample variance

s=4 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=98% or 0.98

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 mean or variance 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.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.01,19)" "=CHISQ.INV(0.99,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=36.191$

$\chi^2_{1- \alpha/2}=7.633$

And replacing into the formula for the interval we got:

$\frac{(19)(16)}{36.191} \leq \sigma^2 \leq \frac{(19)(16)}{7.633}$

$8.400 \leq \sigma^2 \leq 39.827$

So the 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

7 0

3 years ago

How do you solve this??? I need it fast please help with steps.<br> (x+3)(x+1)^2(x−4)>0

scZoUnD [109]

Answer:

x < -3 or x > 4

Step-by-step explanation:

The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).

The factors tell you the following about the zeros:

x = -3 . . . sign change from + to -

x = -1 . . . graph touches, but no sign change. - on either side of x=-1

x = 4 . . . sign change from - to +

The function will be positive for x < -3 and for x > +4.

_____

<em>Additional comments</em>

The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.

However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.

The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).