All categories

3 years ago

In ΔPQR, the measure of ∠R=90°, QP = 29, RQ = 21, and PR = 20. What ratio represents the cosine of ∠P?

Mathematics

1 answer:

solniwko [45]3 years ago

6 0

Answer:

cos(P) = 20/29

Step-by-step explanation:

Given the following information:

∠R=90°,
QP = 29
RQ = 21
PR = 20

To ratio represents the cosine of ∠P we use the cosine law (please have a look at the attached photo)

$RQ^{2}$ = $QP^{2}$ + $PR^{2}$ − 2QP*PRcos(P)

<=> cos(P) = ( $QP^{2}$ + $PR^{2}$ - $RQ^{2}$ ) / 2QP*PR

<=> cos(P) =( $29^{2} + 20^{2} - 21^{2}$ ) /2*29*20

<=> cos(P) = 20/29

Hope it will find you well.

You might be interested in

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

What are the like terms in the expression?

Anarel [89]

Since none of the terms have the same variables the like terms would be (A) because they are both constants

5 0

3 years ago

Read 2 more answers

Witch expersson is equivalent to 4x-5?

barxatty [35]

Answer:

Uh where are the other expressions?

Step-by-step explanation:

7 0

3 years ago

A parabola can be drawn given a focus of (-4,10) and a directrix of y=-4 write the equation of the parabola in any form

sweet-ann [11.9K]

Answer:

$(x+4)^2=28(y-3)$

Step-by-step explanation:

The directrix of the parabola is the horizontal line with the eqaution $y=-4.$ The focus of the parabola is at point (-4,10), than the axis of symmetry of the parabola is the perpendicular line to the directrix passing through the focus. Its equation is $x=-4$

The distance between the directrix and the focus is $|10-(-4)|=14,$ so $p=14$ and the vertex is at point $\left(-4,10-\dfrac{14}{2}\right)\rightarrow (-4,3)$

Parabola goes in positive y-direction, hence its equation is

$(x-x_0)^2=2p(y-y_0),$

where $(x_0,y_0)$ is the vertex, so the equation of this parabola is

$(x+4)^2=28(y-3)$

8 0

3 years ago

Find the measure of angle y. Round your answer to the nearest hundredth. Right triangle

e-lub [12.9K]

<h3>The measure of angle y is 35.68 degrees</h3>

<em><u>Solution:</u></em>

Given that,

hypotenuse 12

Opposite 7

Find the measure of angle y

y is unknown and is between the hypotenuse and adjacent side

The figure is attached below

In a right triangle, the sine of the angle is the ratio of the side opposite to the angle to the hypotenuse

Therefore,

$sin\ y = \frac{opposite}{hypotenuse}\\\\sin\ y = \frac{7}{12}\\\\sin\ y = 0.5833\\\\y = sin^{-1}\ 0.5833\\\\Use\ arcsin\ calculator\\\\y = 35.6829 \\\\y \approx 35.68$

Thus measure of angle y is 35.68 degrees

7 0

3 years ago