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liraira [26]
2 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]2 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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Travka [436]

Answer: Option D

D. 880 = 45d + 70; 18\ days

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call "d" the number of days that Barry attends school

So the cost was:

45d + 70 = 880

Now we solve the equation for the variable d

45d= 880-70

d= \frac{810}{45}

d= 18\ days

Therefore answer is the option D

8 0
3 years ago
School lunches cost ₱35.50 per week. about how much would 15.5 weeks of lunches cost?grade v​
Goryan [66]

Answer:

₱ 550.25

Step-by-step explanation:

₱ 35.50 * 15.5 weeks = ₱ 550.25

5 0
2 years ago
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Equation in slope y-intercept form and identify the slop and y-intercept of the line: 2x-5y=15
Dennis_Churaev [7]

Answer:

y=2/5x - 3

slope is 2/5

y intercept is -3

Step-by-step explanation:

6 0
2 years ago
The radius of a circle is 4.6 millimeters. Find the diameter.
kramer

Hi :)

Radius is half the diameter

4.6 mm (2) = 9.2 mm

The diameter of the circle is 9.2 mm.

4 0
3 years ago
A right triangle has an area of 2k^2-k-15 One of the legs has a length of k^2-9 What is the ratio of the area of a triangle to t
Darya [45]
<h3>Given</h3>

A = 2k² -k -15

L = k² -9

<h3>Find</h3>

A/L

<h3>Solution</h3>

\displaystyle\frac{A}{L}=\frac{2k^2-k-15}{k^2-9}=\frac{(k-3)(2k+5)}{(k-3)(k+3)}\\\\=\frac{2k+5}{k+3}

4 0
3 years ago
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