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Elza [17]
1 year ago
6

Under his cell phone plan, Alexander pays a flat cost of $69.50 per month and $5 per gigabyte. He wants to keep his bill under $

85 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Alexander can use while staying within his budget.
I don't know how to write inequality

69.50 dollars + 5 dollars is 74.50 dollars add 5 dollars 79.50 add 5 dollars again and 84.50
Mathematics
2 answers:
dedylja [7]1 year ago
6 0
69.50+5x>_85
69.50+5(3)>_85
84.50>_85
astraxan [27]1 year ago
4 0

Answer- 5g+ 69.50= 85  ; 3.1 (3)

An inequality is an equation with letters and number that sum to ONE whole.

In this case we have a flat cost, which is standalone and 5 dollars per gigabyte which is not standalone. Let G stand for each gigabyte.

This means our equation is 5g(five dollars times each gigabyte used) +69.50 that is gives. He has to keep his entire month under 85 dollars, which means our equation must equal 85. Now our equation will look like this.

Inequality- 5g+ 69.50= 85.

In order to solve how many gigabytes will be used we solve our equation backwards. We subtract 69.50 from 85,because we know that must has already been spent. This gives us 15.50. This means we will have to divided 15.50 into five dollars to see how many gigabytes are spent. 15.50 divided into five is 3.1 gigabytes.

This means Alexander will have to use 3.1 (or 3 if you have to round) gigabytes in order to spend 85 dollars or less per month.

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Aloiza [94]

The ball's maximum height is 30.25 feet.

<h3>What is quadratic equation?</h3>

A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, b, are the coefficients, c is the constant term, and x is the variable.

Given:

h= -16t²+36t+10

Differentiate w.r.t. 't',

h' = -32t+36

When h=0, that will be the maximum height

32t= 36

t= 9/8

t= 1.125 sec.

So, The maximum height is

h(1.123)= -16(1.125)² + 36*1.125+10

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5 0
1 year ago
Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).
Firdavs [7]

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y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))

C) The most general solution is

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

Step-by-step explanation:

Given non homogeneous ODE is

y''+4y'+5y=10x+e^{-x}---(1)

To find homogeneous solution:

D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)

To find particular solution:

y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\

Substituting y_{p},y'_{p},y''_{p} in (1)

y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\

Equating the coefficients

5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\

The general solution is

y=y_{h}+y_{p}

from (2) ad (3)

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

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2 years ago
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Lilit [14]
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Answer:

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sweet-ann [11.9K]

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