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2 years ago

Find the tangent of ∠I.

Mathematics

1 answer:

snow_tiger [21]2 years ago

8 0

The simplified, rationalized form is tan I = √70/5

<h3>SOH CAH TOA identity</h3>

From the given diagram, we are given the following parameters

Adjacent to m<I = IG
Hypotenuse = √95

According to the SOH CAH TOA identity;

tan m<I = opp/adj

tanm<I = Determine the opposite side using the pythagoras theorem:

GH² = (√95)² - 5²

GH² = 95 - 25

GH² = 70

GH = √70

Determine the value of tanm<I

tan I = √70/5

Hence the simplified, rationalized form is tan I = √70/5

Learn more on SOH CAH TOA here: brainly.com/question/20734777

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find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6

taurus [48]

Answer:

$f(x) = \frac{6}{x^2} -8$ or $f(x) = -\frac{6}{x^2} + 4$

Step-by-step explanation:

Given

$(x,y) = (1,-2)$ --- Point

$\int\limits^6_2 {(1 + 144x^{-6})} \, dx$

The arc length of a function on interval [a,b]: $\int\limits^b_a {(1 + f'(x^2))} \, dx$

By comparison:

$f'(x)^2 = 144x^{-6}$

$f'(x)^2 = \frac{144}{x^6}$

Take square root of both sides

$f'(x) =\± \sqrt{\frac{144}{x^6}}$

$f'(x) = \±\frac{12}{x^3}$

Split:

$f'(x) = \frac{12}{x^3}$ or $f'(x) = -\frac{12}{x^3}$

To solve fo f(x), we make use of:

$f(x) = \int {f'(x) } \, dx$

For: $f'(x) = \frac{12}{x^3}$

$f(x) = \int {\frac{12}{x^3} } \, dx$

Integrate:

$f(x) = \frac{12}{2x^2} + c$

$f(x) = \frac{6}{x^2} + c$

We understand that it passes through $(x,y) = (1,-2)$ .

So, we have:

$-2 = \frac{6}{1^2} + c$

$-2 = \frac{6}{1} + c$

$-2 = 6 + c$

Make c the subject

$c = -2-6$

$c = -8$

$f(x) = \frac{6}{x^2} + c$ becomes

$f(x) = \frac{6}{x^2} -8$

For: $f'(x) = -\frac{12}{x^3}$

$f(x) = \int {-\frac{12}{x^3} } \, dx$

Integrate:

$f(x) = -\frac{12}{2x^2} + c$

$f(x) = -\frac{6}{x^2} + c$

We understand that it passes through $(x,y) = (1,-2)$ .

So, we have:

$-2 = -\frac{6}{1^2} + c$

$-2 = -\frac{6}{1} + c$

$-2 = -6 + c$

Make c the subject

$c = -2+6$

$c = 4$

$f(x) = -\frac{6}{x^2} + c$ becomes

$f(x) = -\frac{6}{x^2} + 4$

3 0

3 years ago

Jessica lost some of her money.She found 3/6 of it.What fraction of her money is still missing?

Cloud [144]

3/6 is the answer because,
3/6+3/6= 6/6 or 1

5 0

3 years ago

Christian just lit a new candle and then let it burn all the way down to nothing. The length of the candle remaining unburned, i

AVprozaik [17]

Given:

The length of the candle remaining unburned, in inches, can be modeled by the equation

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To find:

The slope and its interpretation in the context of the problem.

Solution:

Slope intercept form of a linear function is

$y=mx+b$

where, m is slope and b is y-intercept or initial value.

We have,

$L=6-t$

It can be written as

$L=6+(-1)t$

The coefficient of t is -1. So, using slope intercept form the slope of this equation is -1.

Here, -1 means length of the candle remaining unburned is decreasing at the rate of 1 inch per hour.

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3 years ago

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EastWind [94]

Answer:

11 seconds

Step-by-step explanation:

If the height h(t) of the sunglasses after t seconds is given by the polynomial function

h(t)=-16t²+1936

The sunglasses will hit the ground when the height h(t)=0

h(t)=-16t²+1936=0

-16t²+1936=0

-16t²=-1936

t²=1936/16=121

t=√121=11 seconds

The Sunglasses will hit the ground 11 seconds after it is dropped by the pilot.

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