Listed below are the top 10 annual salaries (in millions of dollars) of TV

A shoreline is being washed away at the rate of 50 1/3 cm every year. A house is 30 1/5 more away from the shore. If the erosion

denis23 [38]

You can not work out it unless provided initial distance between the house and shoreline.

3 0

3 years ago

Please give the correct answer and explain im really trying to learn this so I need the explanation not just an answer. Thankyou

Maksim231197 [3]

Answer:

x = tan⁻¹(⅘)

Step-by-step explanation:

We can solve for x by using trigonometric ratios (sin, cos, and tan)

We need to apply the appropriate ratio that uses the two sides 8 and 10 from the perspective of x. See attached image for information about ratios. (Source: Math is Fun)

The tangent ratio is opposite divided by adjacent. It will relate x to the two sides. So we would write

tan(x) = ⁸⁄₁₀

Then we simplify and move the tan to the other side by multiplying both sides by the inverse of tan (since you cannot divide by tan)

tan(x) = ⅘

x = tan⁻¹(⅘)

Then we can use a calculator to evaluate x

If you want to find y, now that you have two angles of the triangle, you can find the sum of 90 + x and subtract that from 180 (since all angles of a triangle add up to 180) to find y.

6 0

3 years ago

56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site

tino4ka555 [31]

Answer:

Equation: 810= (90 + 24y)

y = 30 hours

Step-by-step explanation:

Given:

Site visit = $45 per site

cost per hour worked = $24

for <u>each </u>work site, the total amount of money earned

= site visit fee + cost for working

But the question mentions TWO sites, hence there will be two site visits. Therefore for TWO sites, we have to account for TWO site visit fee.

Therefore for TWO sites, the total amount of money earned

= site 1 visit fee + site 2 visit fee + cost for working

= (2 x site visit fee) + cost for working ------ Equation 1

We are further given that we worked y hours at the hourly work rate of $24 per hour.

Hence the cost for working

= y hours x hourly rate

= y x $24

= $24y (substituting this into equation 1 above)

for TWO sites, the total amount of money earned

= (2 x site visit fee) + cost for working

= (2 x $45) + $24y

= $90 + $24y

= $(90 + 24y)

We are also given that we have to earn $810 for two sites, hence

810 = 90 + 24y

810 - 90 = 24y

24y = 720

y = 720/24

y = 30 hours

8 0

3 years ago

An ant moves forward 18 1⁄2 inches in one hour. It turns around and crawls

zvonat [6]

Answer:

The ant moved 10.75 in after three hours

Step-by-step explanation:

18.5-13.5=5+5.75=10.75

46/8=5.75

7 0

2 years ago

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