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3 years ago

Solve for f. h = f² + 2g

Mathematics

2 answers:

SIZIF [17.4K]3 years ago

3 0

F^2=h-2g
f=√h-2g
hope it helps

jekas [21]3 years ago

3 0

Answer:

$f=\sqrt{h-2g}\text{ or }f=-\sqrt{h-2g}$ .

Step-by-step explanation:

We have been given an equation $h=f^2+2g$ . We are asked to solve for f.

First of all, we will subtract $2g$ from both sides of our equation.

$h-2g=f^2+2g-2g$

$h-2g=f^2$

$f^2=h-2g$

Now, we will take square root of both sides of our equation.

$f=\pm\sqrt{h-2g}$

Therefore, the values of f are $f=\sqrt{h-2g}\text{ or }f=-\sqrt{h-2g}$ .

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Flauer [41]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

An arch over a doorway is an arc that is 90 centimeters wide and 30 centimeters high. You are curious about the size of the enti

krek1111 [17]

Answer:

The length of the arc = $114.66\,cm$

And the length of the full circle: $306.3\, cm$

Step-by-step explanation:

To solve this problem we will be analyzing aright angle triangle that is formed when drawing the appropriate radius associated with the arc and the chord of a segment of circumference as depicted by the triangle shaded in yellow in the attached image.

Notice that the information given in this problem can be represented by:

1) the 90 cm width of the arc with the value of 2x (drawn in orange) in the drawing

2) the 30 cm of the arc's height with the value of y (drawn in green) in the drawing

In order to use the Pythagorean theorem in the little yellow triangle, notice that the hypotenuse is given by the radius R of the circle, and the two legs of the right angle triangle are given by "x" and "R-y"

So the Pythagoras theorem becomes:

$R^2=x^2+(R-y)^2\\R^2=x^2+R^2-2Ry+y^2\\0=x^2-2Ry+y^2\\2Ry=x^2+y^2\\R=\frac{x^2+y^2}{2y}$

Therefore, in our case, where x=45 cm, and y=30 cm, we have:

$R=\frac{x^2+y^2}{2y} \\R=\frac{45^2+30^2}{60}\,cm \\R=48.75\, cm$

Now, with the radius, we can calculate the length of the arc of circle if we know the subtended angle in radians:

length of arc = $R \,\theta$

The angle $\theta$ subtended by the arc can be obtained by doubling the angle with vertex at the circle's center in our yellow right angle triangle. This is done via the sine function:

$\theta=2\,arcsin(x/R)\\\theta=2\,arcsin(45/48.75)\\\theta=2.352\,radians$

Therefore, length of the arc = $R \,\theta=48.75\,cm\,*\,2.352=114.66\,cm$

And the length of the full circle: $2\,\pi \, R =2\,\pi\,48.75\,cm = 306.3\, cm$

3 0

3 years ago

Which one does it simplify to? please

9966 [12]

Answer:

$1 + { \sin} \theta$

Step-by-step explanation:

$\frac{ { \cos}^{2} \theta}{1 - \sin \theta} \\ \\ = \frac{ { \cos}^{2} \theta}{(1 - \sin \theta)} \times \frac{(1 + \sin \theta)}{(1 + \sin \theta)} \\ \\ = \frac{{ \cos}^{2} \theta(1 + { \sin} \theta)}{(1 - { \sin}^{2} \theta)} \\ \\ = \frac{{ \cancel{ \cos}^{2} \theta}(1 + { \sin} \theta)}{ \cancel{{ \cos}^{2} \theta}} \\ \\ = 1 + { \sin} \theta$