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Lelu [443]
4 years ago
14

Justin is saving money for a new gaming console. He currently has $200 in a saving account and each week $10 to his balance. In

how many weeks will he have $500?
Mathematics
1 answer:
Nikitich [7]4 years ago
8 0

$500 - $200 = $300 dollars left.

$300 divided by $10 = 30 weeks.

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
ryzh [129]

First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

t=0\implies f(10,0)=155

t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299

t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
Write the standard form of the equation:<br> Slope= 3 y-intercept= -1
Amiraneli [1.4K]

Answer:

y=3x-1

Step-by-step explanation:

y=mx+b

y=3x+b

y=3x-1

7 0
3 years ago
Evaluate the expression 4•9+6/-3
kykrilka [37]
You have to multiplying first, then adding on 6 over negative 3 as a fraction. The parentheses it will be multiplying.

(4)(9)+6/-3 

= 34.

It will help you.

Have a great day!


-Charlie
8 0
3 years ago
Read 2 more answers
I'M GIVING BRAINLIEST TO WHOEVER ANSWERS ALL OF THE QUESTIONS CORRECTLY! PLEASE HURRY! :D
V125BC [204]

Answer:

Step-by-step explanation:

8. 7.5 Goes up by 2.5.

9. 7.3 Goes down by 2.1

10. 116/3

6 0
3 years ago
Read 2 more answers
Which of the following are characteristics of the graph of the quadratic parent function
stich3 [128]

Answer:

Answer – A and B

A. It is a parabola

B. It is in quadrants I and II

The most simple quadratic function is y = x^2. The graph drawn for this function, y = x^2) is known as the graph of the quadratic parent function OR the parent function for parabolas. This graph has some few characteristics:

- It is the simplest parabola (Generally, the graph of any quadratic function is a parabola).

- It passes through the origin (0,0).

- It is contained in Quadrants I and II.

hope this helps!

8 0
3 years ago
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