Ask question

Ask question

All categories

3 years ago

15

The temperature in New Jersey is 85 degrees and climbing to 2 degrees per hour the temperature in Florida is a hundred and falli

ng 3 degrees per hour how many hours will it take for their temperature to be the same?

1 answer:

kompoz [17]3 years ago

4 0

Answer:

3

Step-by-step explanation:

i do maths lol

You might be interested in

The money used in Tonga is called the

monitta

Answer:14

Step-by-step explanation:

7*2=14

4 0

3 years ago

Help me with trigonometry

poizon [28]

Answer:

See below

Step-by-step explanation:

It has something to do with the<em> </em><u><em>Weierstrass substitution</em></u>, where we have

$\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$

First, consider the double angle formula for tangent:

$\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}$

Therefore,

$\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}$

Once the double angle identity for sine is

$\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}$

we know $\sin(x)=\dfrac{2t}{1+t^2}$ , but sure, we can derive this formula considering the double angle identity

$\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)$

Recall

$\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}$

Thus,

$\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}$

Similarly for cosine, consider the double angle identity

Thus,

$\cos(x)= \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}$

Hence, we showed $\sin(x) \text { and } \cos(x)$

======================================================

$5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]$

Solving

$5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3$

$\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies \dfrac{5-5t^2 -24t}{1+t^2}= 3$

$\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0$

$t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} = \dfrac{3\pm \sqrt{10}}{-2}$

$t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}$

Just note that

$\tan\left(\dfrac{x}{2}\right) = \dfrac{3\pm 8\sqrt{10}}{-2}$

and $\tan\left(\dfrac{x}{2}\right)$ is not defined for $x=k\pi , k\in\mathbb{Z}$

6 0

3 years ago

adelina 88 [10]

Answer:

28

Step-by-step explanation:

Let's set the ratio as

7x : 9x

If you add all the states that border an ocean and do not, you will get 48 states (because Alaska and Hawaii are not part of the continental US, as they do not touch the "main" part of the country)

So, we can write this equation.

7x + 9x = 48

Simplify.

16x = 48

Divide both sides by 16.

x = 4

Now, find how many states border an ocean. In our ratio, the number of states that border an ocean was 7x. Substitute x = 4 into 7x

7 * x = 7 * 4 = 28

The number of states that border an ocean is 28.

I hope this helps! Feel free to ask any questions!

7 0

3 years ago

One of ten different prizes was randomly put into each box of a cereal. If a family decided to buy this cereal until it obtained

Reptile [31]

Answer:

29.29

Step-by-step explanation:

The first trial among a distribution of independent trials with a constant success probability follows a geometric probability.

The expected value of a negative binomial is the reciprocal of its success probability <em>p.</em>

<em>E(X)=</em>1/<em>p</em>

At the first draw, we only selected one of the 10 prizes and so 1 draw gives a success

<em>E(X)=</em>1/<em>p</em>

<em>E(X1)</em>=1

After the first prize is drawn, we are interested in the first time (success), that we draw another prize that is different (<em>p</em>=9/10)

E(X2)=1/9÷10

E(X2)= 10/9

After the first prizes have being drawn, we now interested in the first time success that we draw a different prize from the first 2

E(X3)=1/8÷10

E(X3)=10/8

E(X3)=5/4

After the first three prizes have been drawn, we are now interested in the success of a first time draw for the 4th different prize

E(X4)=1/7÷10

E(X4)=10/7

Fifth different prize

E(X5)=1/6÷10

E(X5)=10/6

E(X5)=5/3

Sixth different prize

E(X6)=1/5÷10

E(X6)=10/5

E(X6)=2

Seventh different prize

E(X7)=1/4÷10

E(X7)=10/4

E(X7)=5/2

Eighth different prize

E(X8)=1/3÷10

E(X8)=10/3

Ninth different prize

E(X9)=1/2÷10

E(X9)=10/2

E(X9)=5

After the 9 different prizes have been drawn, we are interested in the first time we will draw the tenth different prize

E(X10)=1/1÷10

E(X10)=10

Add up all corresponding values;

<em>E(X)=</em>E(X1)+E(X2)+E(X3)+E(X4)+E(X5)+E(X6)+E(X7)+E(X8)+E(X9)+E(X10)

<em>E(X)=</em>1+10/9+5/4+10/7+5/3+2+5/2+10/3+5+10

<em>E(X)</em>= 29.29

Note: Those values in <em>E(X), </em>should be written the way it will in standard algebra ie they should be small.

4 0

3 years ago

Will give brainlest

Vilka [71]

Answer:

B. 1 5/6

Step-by-step explanation:

$\frac{5}{6}*2\frac{1}{5} = 1\frac{5}{6}$

5 0

3 years ago

Read 2 more answers