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podryga [215]
3 years ago
5

Brandon buys a radio for $43.99 in a state where the sales tax is 7% what is the total Brandon pays for the radio?

Mathematics
1 answer:
babymother [125]3 years ago
7 0
An increase by a percentage equal 1+percentage value multiplied by the original value.
7%=0.07
1+0.07=1.07
$43.99(1.07)=$47.0693
Round that to two decimal spaces.
$47.07
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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
Which expression is equivalent to (-3y - x) - (5y - 8x)?
Vinil7 [7]

Answer:

b

Step-by-step explanation:

plz mark brainliest

4 0
3 years ago
Can someone please tell me how to solve this?: -27 , exponent 2/3<br><br><br><br> -27^2/3
Vlada [557]
So this is asking the cube root of -27 then squared.
Cube root of -27=-3
And -3^2=9

So I believe your answer is 9
4 0
3 years ago
Answer the question and answer it down below
Sergio039 [100]

Answer:

4:24 p.m.

Step-by-step explanation:

Figure out how often the buses leave at the same time. This is the same as the least common multiple (LCM) of how often they leave the stadium.

The LCM is found by multiplying the maximum number of each prime factor found in any of the numbers.

The prime factors of a number are found by dividing it by whole numbers until the factors are all prime. Prime numbers only have the factors 1 and itself.

6 = 2 X 3

8 = 2 X 2 X 2

The greatest times 2 repeats is three times.

The greatest times 3 repeats is one time.

2 X 2 X 2 X 3 = 24

The LCM is 24, and the buses have the same leaving times every 24 minutes.

Find 24 minutes after 4:00 p.m. Change the minutes only, which are the numbers right of the colon : .

The buses will next leave together at 4:24 p.m.

5 0
3 years ago
Find the range of the function<br> F(x) = (x-2)2 +2
viktelen [127]
(x - 2)^2 will always be positive and will have a minimum value of  0 

so f(x) will have minimum of 2

Range is [2,∞)
8 0
3 years ago
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