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3 years ago

. The value of a lottery prize doubles

Mathematics

1 answer:

inna [77]3 years ago

8 0

Answer: P(t) = $1000*2^t

Step-by-step explanation:

Ok, we know that in the week 1 the price is: p = $1000

After one week, the price doubles, so here we have: p = 2*$1000

After another week, the price doubles again, here the price is:

p = 2*(2*$1000) = $1000*2^2

Here we already can see the relation, for each week, we multiply the previous price by two, which will increase the exponent in the two by 1 unit.

Then, for week number t, the price will be:

P(t) = $1000*2^t

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What graph represents the inequality y≥2−2x?

babunello [35]

$y\geq2-2x\\\\\text{Let's the line}\ y=2-2x\\\\for\ x=0\to y=2-2(0)=2\to(0,\ 2)\\for\ x=1\to y=2-2(1)=0\to(1,\ 0)$

$\text{draw a line and shade above the line}\\\\\text{Look at the picture}$

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2 years ago

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Use separation of variables to solve dy dx − tan x = y2 tan x with y(0) = √3. Find the value of c in radians, not degrees

a_sh-v [17]

Answer:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

Step-by-step explanation:

Rewrite the equation as:

$\frac{dy(x)}{dx}-tan(x)=y(x)^{2} *tan(x)$

Isolating $\frac{dy}{dx}$

$\frac{dy}{dx} =tan(x)+tan(x)*y^{2}$

Factor:

$\frac{dy}{dx} =tan(x)*(1+y^{2} )$

Dividing both sides by $(1+y^{2} )$ and multiplying them by $dx$

$\frac{dy}{1+y^{2} } =tan(x)dx$

Integrate both sides:

$\int\ \frac{dy}{1+y^{2} } = \int\ tan(x) dx$

Evaluate the integrals:

$arctan(y)=-log(cos(x))+C_1$

Solving for y:

$y(x)=tan(-log(cos(x))+C_1)$

Evaluating the initial condition:

$y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)$

$\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1$

Converting 60 degrees to radians:

$60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}$

Replacing $C_1$ in the diferential equation solution:

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2 years ago

Can someone help me with this one? Thank you.

Andreas93 [3]

Step-by-step explanation:

I haven't used distance formula or Pythagoras theorem, not sure why that's given at the bottom of your question. check the image. that is how I solved it

4 0

3 years ago

Tanya bought a bunch of bananas that weighed 2 pounds 14 ounces. How much is this. A) 30 ounces B)46 ounces C)16 ounces D)38 oun

koban [17]

Answer:

B) 46 ounces

Step-by-step explanation:

1 pound is 16 ounces, so 16*2 = 32 + 14 = 46!

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2 years ago

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makvit [3.9K]

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