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liraira [26]
3 years ago
12

Determine, using the intermediate value theorem, if the function F(x)=x^3+2x-1 has a zero on the interval [0,1]. Justify your an

swer and find the indicated zero, if it exists.
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
7 0

Plug x = 0 into the function

f(x) = x^3 + 2x - 1

f(0) = 0^3 + 2(0) - 1

f(0) = -1

Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.

Repeat for x = 1

f(x) = x^3 + 2x - 1

f(1) = 1^3 + 2(1) - 1

f(1) = 2

This result is positive.

---------------------------

We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.

To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515

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svp [43]
6.3c-2(1.5c+4.1)=6.3c-3c-8.2=3.3c-8.2 :))))

7 0
3 years ago
∠5 ​ and​ ​ ∠6 ​ ​are complementary angles.<br><br> m∠5=13°<br><br> What is the measure of ​ ∠6 ​?
loris [4]

Answer:

the measure of <6 is 77 degrees

x + 13 = 90

x = 77

Step-by-step explanation:

4 0
2 years ago
If g(x)= 3x-1 solve for x when g(x)=-20.
Nadya [2.5K]

Good evening

Answer:

x=\frac{-19}{3}

Step-by-step explanation:

g(x) = -20

⇔

3x-1 = -20

⇔

3x = -20 + 1

⇔

3x = -19

⇔

x = -19/3

____________________

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3 0
3 years ago
Find m∠IUV if m∠IUV=x+49, m∠TUI=x+63, and m∠TUV=106∘.?<br> I'll mark you brainliest!
8090 [49]

Answer:

46

Step-by-step explanation:

You have to do IVU+TUI=TUV

so... x+49+x+63=106

5 0
2 years ago
Consider the following system of equations. -10x2-10y2=-300 5x2+5y2=150 Which statement describes why the system has infinite so
scoundrel [369]

Answer:

The equations represent circles that result in the same graph.

Step-by-step explanation:

we have

-10x^{2}-10y^{2}=-300

Divide by -10 both sides

x^{2}+y^{2}=30 -----> equation A

This is the equation of a circle centered at origin with radius r=\sqrt{30} \ units

and

5x^{2}+5y^{2}=150

Divide by 5 both sides

x^{2}+y^{2}=30 -----> equation B

This is the equation of a circle centered at origin with radius r=\sqrt{30} \ units

equation A and equation B are equal

therefore

The system has infinite solutions, because the equations represent circles that result in the same graph.

4 0
3 years ago
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