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2 years ago

BRAINLIESTTTT ASAP! please answer

Mathematics

1 answer:

romanna [79]2 years ago

8 0

Simply add $b^{2}$ to both sides of the equation:

$a^{2} =c^{2} + b^{2}$

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At a price of $p the demand x per month (in multiples of 100) for a new piece of software is given by x 2 + 2xp + 4p 2 = 5200. B

WINSTONCH [101]

Answer:

The rate of decrease in demand for the software when the software costs $10 is -100

Step-by-step explanation:

Given the function of price $p the demand x per month as,

$x^{2}+2xp+4p^{2}=5200$

Also given that, the price is increasing at the rate of 70 dollar per month.

$\therefore \dfrac{dp}{dt}=70$ .

To find rate of decrease in demand, differentiate the given function with respect to t as follows,

$\dfrac{d}{dt}\left(x^2+2xp+4p^2\right)=\dfrac{d}{dt}\left(5200\right)$

Applying sum rule and constant rule of derivative,

$\dfrac{d}{dt}\left(x^2\right)+\dfrac{d}{dt}\left(2xp\right)+\dfrac{d}{dt}\left(4p^2\right)=0$

Applying constant multiple rule of derivative,

$\dfrac{d}{dt}\left(x^2\right)+2\dfrac{d}{dt}\left(xp\right)+4\dfrac{d}{dt}\left(p^2\right)=0$

Applying power rule and product rule of derivative,

$2x^{2-1}\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+4\left(2p^{2-1}\right)\dfrac{dp}{dt}=0$

Simplifying,

$2x\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+8p\dfrac{dp}{dt}=0$

Now to find the value of x, substitute the value of p=$10 in given equation.

$x^{2}+2x\left(10\right)+4\left(10\right)^{2}=5200$

$x^{2}+20x+400=5200$

Subtracting 5200 from both sides,

$x^{2}+20x+400-5200=0$

$x^{2}+20x-4800=0$

To find the value of x, split the middle terms such that product of two number is 4800 and whose difference is 20.

Therefore the numbers are 80 and -60.

$x^{2}+80x-60x-4800=0$

Now factor out x from $x^{2}+80x$ and 60 from $60x-4800$

$x\left(x+80\right)-60\left(x+80\right)=0$

Factor out common term x+80,

$\left(x+80\right)\left(x-60\right)=0$

By using zero factor principle,

$\left(x+80\right)=0$ and $\left(x-60\right)=0$

$x=-80$ and $x=60$

Since demand x can never be negative, so x = 60.

Now,

$2x\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+8p\dfrac{dp}{dt}=0$

Substituting the value.

$2\left(60\right)\dfrac{dx}{dt}+2\left(60\left(70\right)+10\dfrac{dx}{dt}\right)+8\left(10\right)\left(70\right)=0$

Simplifying,

$120\dfrac{dx}{dt}+2\left(4200+10\dfrac{dx}{dt}\right)+5600=0$

$120\dfrac{dx}{dt}+8400+20\dfrac{dx}{dt}+5600=0$

Combining common term,

$140\dfrac{dx}{dt}+14000=0$

Subtracting 14000 from both sides,

$140\dfrac{dx}{dt}=-14000$

Dividing 140 from both sides,

$\dfrac{dx}{dt}=-\dfrac{14000}{140}$

$\dfrac{dx}{dt}=-100$

Negative sign indicates that rate is decreasing.

Therefore, the rate of decrease in demand of software is -100

6 0

2 years ago

Find cosθ, cscθ, and tanθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.

NNADVOKAT [17]

Answer:

see explanation

Step-by-step explanation:

To find cscθ we require to find the third side of the triangle.

let 3rd side be x and using Pythagoras' identity

x² + 8² = 9²

x² + 64 = 81 ( subtract 64 from both sides )

x² = 17 ( take square root of both sides )

x = $\sqrt{17}$

Then

cosθ = $\frac{adjacent }{hypotenuse}$ = $\frac{8}{9}$

cscθ = $\frac{hypotenuse}{opposite}$ = $\frac{9}{\sqrt{17} }$

tanθ = $\frac{opposite}{adjacent}$ = $\frac{\sqrt{17} }{8}$

3 0

2 years ago

PLEASE HELP ME!!<br>PLACE THEM IN ORDER FROM LEAST TO GREATEST

Naya [18.7K]

7
_ 0.61 0.95.
8
my 5th grader answered it he needs some help with his math and we saw this question and he wanted to help. So if it's not right I'm sorry it was out of kindness

3 0

2 years ago

If 6 candy bars cost a total of $12, then $2 is the ___________ of the candy bars. *

den301095 [7]

$2 can get you one candy bar. So if you want 6 it would cost $12

8 0

2 years ago

Do you think a negative number raised to an even power will be positive or negative? Explain.

Tanya [424]

Answer:

A negative number taken to an even power gives a positive result (because the pairs of negatives cancel), and a negative number taken to an odd power gives a negative result (because, after cancelling, there will be one minus sign left over).

Step-by-step explanation:

4 0

2 years ago