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marshall27 [118]
3 years ago
12

X + y = 3 4x + 4y = -12

Mathematics
1 answer:
Stolb23 [73]3 years ago
6 0

Answer:

oop

Step-by-step explanation:

4x+4y-4=-12-4

then you get the answer for x

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State the restrictions on the range for y=x^4+8x^3+k
sveticcg [70]
Answer: The range is y \ge k-432

The way to get this answer isn't completely obvious. What I did first was graph the function using GeoGebra allowing k to be a parameter. With k as a sliding parameter, the graph was able to be slid up and down the screen. The basic shape of the curve is a distorted W shape. The lowest point being the local minimum. Which is where the lower endpoint of the range would be.

Using the derivative, we can get
y = x^4 + 8x^3 + k
dy/dx = 4x^3 + 24x^2
set dy/dx equal to zero and solve for x
dy/dx = 0
4x^3 + 24x^2 = 0
4x^2(x + 6) = 0
4x^2 = 0 or x+6 = 0
x = 0 or x = -6

It turns out that x = 0 is a saddle point so we can ignore this value. Only x = -6 is where the local min is at. Plug this back into the original function

y = x^4+8x^3+k
y = (-6)^4+8(-6)^3+k
y = -432+k
y = k - 432

So when the input is x = -6, the output is k - 432 for some value k
In other words, the smallest y can get is k - 432. Otherwise it will be larger than this value

So that's why the range is y \ge k - 432

Note: if this calculus approach doesn't make much sense, then you can try various k values and use a calculator to find the lowest point. Making a table of k values with the corresponding lowest point would hopefully point you in the right direction. 
3 0
3 years ago
Me the answer to 2000 times blank equals 200,000
Blababa [14]
2000* 100= 200,000 is the answer

3 0
3 years ago
Read 2 more answers
How many solutions exist for the given equation?
irakobra [83]

Answer:

Its infinite solutions

Step-by-step explanation:

7 0
2 years ago
Question 4
Lana71 [14]

Answer:

$3.00

and haha funny number

6 0
3 years ago
Nate has an account that pays 2. 76% simple interest per year and wants to accumulate $3,090 in interest from it over the next 1
lana66690 [7]

We have given that,

interest rate = 2.76%

simple interest = 3,090

term = 15 years

<h3>What is the principle of simple interest?</h3>

Simple Interest = Principal * interest rate * term

3,090 = Principal * .0276 * 15\\3,090 = Principal * 0.414\\3,090 / 0.414  = Principal\\7,463.77 = Principal

Therefore,Nate should invest 7,463.77 to meet his goal.

To learn more about the simple  interest visit:

brainly.com/question/25793394

4 0
2 years ago
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