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4 years ago

What comes next? 1, 4, 7, ______

Mathematics

2 answers:

victus00 [196]4 years ago

7 0

Answer:

Step-by-step explanation:

1+3=4

4+3=7

7+3=10

zysi [14]4 years ago

6 0

Answer:

16, 22, 29

Step-by-step explanation:

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Which is the simplified form of the expression?

Anon25 [30]

Given:

Consider the given expression is:

$10n-\dfrac{1}{3}(9n-12)$

To find:

The simplified form of the given expression.

Solution:

We have,

$10n-\dfrac{1}{3}(9n-12)$

Using distributive property, it can be written as:

$=10n-\dfrac{1}{3}(9n)-\dfrac{1}{3}(-12)$

$=10n-3n+4$

$=7n+4$

Therefore, the correct option is A.

4 0

3 years ago

Karissa says that to represent the expression - 7 - (- 9) on number line, she should start at 7 and move units to the IN correct

Sholpan [36]

Answer:

Step-by-step explanation:

Should start at -7 and move 9 units towards right (in the positive direction).

Should stop at 2

8 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

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maw [93]

Step-by-step explanation: do fast

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8 0

3 years ago

Give the y intercept y=3/2x+3

morpeh [17]

Answer:

Y intercept: (0,3) or 3

Step-by-step explanation:

the b in y = mx + b is the y intercept.

3 0

3 years ago