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2 years ago

Find the focus of the parabola y = –1/4(x + 3)^2 + 2.

Mathematics

1 answer:

DIA [1.3K]2 years ago

6 0

I think the answer is b or d I hop is helping you

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Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

Dvinal [7]

Answer:

1.692 m/min

Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

$x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta$

$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

$\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}$

4 0

2 years ago

We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote the my net winning

TEA [102]

Answer:

The probability mass of X is 0.03

Step-by-step explanation:

If we set the winning requirement of your heads and my tails then the occurring possibility of both is 1/2 or 0.5.

Hence let us make a graph and use the figures to calculate the all the probabilities of you getting a heads.

Where X represents the number of dollars won during the flip of the coin, probability of heads represent the chances of occurrence of the value and of winning the dollars.

The probability of winning start to drop as the winning amount increases.

X 0 1 2 3 4 5

Probability of Heads 0 0.50 0.25 0.13 0.06 0.03

8 0

2 years ago

Worth 80 points!! It's alot for me to understand and i wanna get it right someone help?

Mandarinka [93]

Add all the new budget amounts:

510 + 254 + 295 + 51 + 0 + 100 + 100+ 0 + 100 = 1410

Her monthly total is 1410, which is less than her income of 1700

1700 - 1410 = 290

She has $290 extra each month.

So she can divide that amount by 2 to put an equal amount in each blank category, or add what ever amount less than that into each one.

4 0

2 years ago

Could someone help me please

Ymorist [56]

Jupiter has greatest mass.

7 0

2 years ago

Read 2 more answers

What is the value of 7P7? A. 1 B. 14 C. 49 D. 5040

sp2606 [1]

The answer is
D. 5040

3 0

2 years ago