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3 years ago

Serena hits a tennis ball downward from the top of the net at which the angle of

Mathematics

1 answer:

morpeh [17]3 years ago

8 0

Answer:

2.5 meter

Step-by-step explanation:

in a right triangle, tan of an angle = opposite side /adjacent side

tan 70° = x/ 0.9 , multiply both sides by 0.9

0.9 * tan 70° = x, solve on a calculator

x ≈ 2.5 m

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Which of the following statement is not true?

lorasvet [3.4K]

Answer:

integers are closed under division

Step-by-step explanation:

Integers are not closed under division.Let us consider two integers i and j.

Then $\frac{i}{j}$ need not necessarily be an integer. For example, 2 and 3 are integers but $\frac{2}{3}$ is not an integer. So the first option , namely, integers are closed under division is not true.

On the other hand, the remaining three options given are correct.

8 0

3 years ago

Find the equation of a line tangent to the circle x2+(y−3)2=34 at the point (5, 0).

salantis [7]

Answer:

Step-by-step explanation:

In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line. Let's begin by expanding through the parenthesis to get the standard form of the circle:

$x^2+y^2-6y+9=34$

Moving the 9 to the other side since the derivative of a constant is 0 gives us

$x^2+y^2-6y=25$

By implicit differentation, the derivative of that function is

$2x+2y\frac{dy}{dx}-6\frac{dy}{dx}=0$

To find the derivative, we have to solve for dy/dx:

$2y\frac{dy}{dx}-6\frac{dy}{dx}=-2x$

Factor out the dy/dx to get:

$\frac{dy}{dx}(2y-6)=-2x$

Now divide to get your slope formula (first derivative):

$\frac{dy}{dx}=\frac{-2x}{2y-6}$

Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:

$\frac{dy}{dx}=\frac{-2(5)}{2(0)-6}=\frac{-10}{-6}=\frac{5}{3}$

So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. The point-slop form of a line is:

y-y₁ = m(x-x₁)

Filling in we get:

y - 0 = 5/3(x - 5) so the equation of the tangent line is:

$y=\frac{5}{3}x-\frac{25}{3}$

Good luck in your calculus class!

3 0

3 years ago

How do you turn it into a percent

EastWind [94]

So what you do it you multiply that number by 100 because it is out of 100% so therefore it would be 140.6%. But I cannot tell you that that is correct without more information.

3 0

3 years ago

A circle has radius 50 cm. Which of these is closest to its area?

olga55 [171]

Answer:

7854 cm²

Step-by-step explanation:

3.14 x 50² = 7850

4 0

2 years ago

HELP !! a sandwich shop purchases a used pizza oven for $875. after 5 years, the oven will have to be discarded and replaced. wr

Sladkaya [172]

<h3>Answer: V = -175t + 875</h3>

==================================================

Explanation:

I'll use y in place of V for now. Also, I'll use x in place of t.

x = number of years

y = value of the oven

Initially, the oven's value is $875, so x = 0 and y = 875 pair up together. The point (0,875) is on the line.

The point (5, 0) is also on the line to indicate that x = 5 years later is when the value of the oven is y = 0 dollars.

We need to find the equation of the line through (0,875) and (5,0)

First we'll need the slope

m = (y2-y1)/(x2-x1)

m = (0-875)/(5-0)

m = -175

The negative slope means the oven is losing 175 dollars in value each year.

The y intercept is b = 875 as this is the initial value of the oven

Put together, y = mx+b turns into y = -175x+875

If we plugged x = 0 into this equation, we'd get y = 875

Similarly, plugging x = 5 into y = -175x+875 leads to y = 0. This helps check we have the right equation

Lastly, replace x with t and replace y with V to end up with V = -175t + 875 which is our final answer.

5 0

3 years ago