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tangare [24]
2 years ago
13

Show that the equation x^3+7x-4=0 has a solution between x=0 and x=1

Mathematics
1 answer:
Aleksandr [31]2 years ago
3 0

Step-by-step explanation:

Using the Intermediate Value Theorem, the following is applied:

"If f(x) is a continuous on interval [a,b] and we have two points f(a) and f(b) then there must be some value c such that f(a)<f(c)<f(b).

So here there must be a c such that

f(0) < f(c) < f(1)

Note: F(c)=0, the questions that the function have a solution between 0 and 1, so that means we must have some value, c such that f(c)=0 that exists

Next, plug in the x values into the function

f(0)  =  - 4

f(1) =  {1}^{3}  + 7(1) - 4 = 4

Since cubic functions are continuous and -4<0<4, then there is a solution c that lies between f(0) and f(1)

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DENIUS [597]

Answer:

-0.825

Step-by-step explanation:

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3 years ago
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The length of a flower garden is 529 cm what is the length in meters
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1. Express the product of 2x2 + 7x – 10 and x + 5 in standard form.
Vladimir79 [104]
Step 1: Start with the following:
(a + b + c)(d + e)

Step 2: Distribute (d + e) to each of the term in the first parenthesis
a(d + e) + b(d + e) + c(d + e)

Step 3: Distribute d and e to each term:
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An equation that is equal to -3(x + 2)=-7
Lapatulllka [165]
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7 0
4 years ago
A cafeteria manager needs to know how many apple and bananas to order. She asked students to choose either an apple or a banana
lilavasa [31]

Answer:

  48

Step-by-step explanation:

The fraction who picked apples is the rest of the students:

  1 - 5/8 = 3/8

of them.

So the number who picked apples relative to the number who picked bananas is ...

  apples/bananas = (3/8)/(5/8) = 3/5

Multiplying this by the number who picked bananas gives the number who picked apples:

  apples = bananas · 3/5 = 80·3/5 = 48

48 students picked apples.

____

<em>Alternate solution</em>

Let "a" represent the number who picked apples. The ratio of banana choosers to the total is 5/8, and there were 80 who chose bananas. That gives rise to the equation ...

  80/(80 +a) = 5/8

  640 = 400 +5a . . . . . . multiply by 8(80+a) and simplify

  240 = 5a . . . . . . . . . . . subtract 400

  240/5 = a = 48 . . . . . . divide by 5

48 students picked apples.

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3 years ago
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