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4 years ago

What is (4p-1) squared

Mathematics

1 answer:

ahrayia [7]4 years ago

5 0

(4p-1)(4p-1)

=16p^2 - 4p - 4p +1

=16p^2 -8p +1 (That's your answer)

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Which phrase describes the algebraic expression B2+7?

svp [43]

Answer:

180

Step-by-step explanation:

3 0

3 years ago

Mort bought his house in 2004 for $279,000. it was recently appraised at $186,000. What is the approximate percent of decrease i

Natalka [10]

Answer:

33.3%

Step-by-step explanation:

(279,000 - 186,000) / 279,000 = 0.33333333333

0.33333333333*100= 33.3333333333

Formula used:

$V_{2} -V_{1}$ / $V_{2}$ × 100

V2= 279,000

V1= 186,000

7 0

3 years ago

Use implicit differentiation to find the negative slope of a tangent to the circle x^2+y^2=16 at x=-2

SVETLANKA909090 [29]

Answer:

slope = - $\frac{\sqrt{3} }{3}$

Step-by-step explanation:

Differentiating implicitly with respect to x

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

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

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

$\frac{dy}{dx}$ is the measure of the slope of the tangent

rearrange equation to find corresponding y-coordinate of x = - 2

y² = 16 - 4 = 12 = 2 $\sqrt{3}$ ⇒ y = ± 2 $\sqrt{3}$

using x = - 2, y = - 2 $\sqrt{3}$ , then

$\frac{dy}{dx}$ = - $\frac{1}{\sqrt{3} }$ = - $\frac{\sqrt{3} }{3}$

3 0

3 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago

There is a bag filled with 5 blue, 6 red and 2 green marbles.

Kipish [7]

Answer:

the probability of getting 2 greens is 2/13

Step-by-step explanation:

6 0

3 years ago