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Aliun [14]
2 years ago
9

Question 1 of 10

Mathematics
1 answer:
Mnenie [13.5K]2 years ago
7 0

Answer: A

Step-by-step explanation:

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1. ) Consider the function f(x)=5−7x2,−5≤x≤1
Marat540 [252]
1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.

Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170


Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2

2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:

f'(c)= \frac{f(b)-f(a)}{b-a}

The differentiated form would be f'(x) = -2x. Then,

-2c =  \frac{(4- 0^{2} )-(4- (-1)^{2}) }{0--1}=1

c=- \frac{1}{2}

Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.
3 0
3 years ago
Town A and town B calculated the number of dogs in each town based on the average number of dogs per neighborhood. The graph bel
Inga [223]
Weetuoplkhgdaaxvmnvcdawrwtwvebrjtilpoolwnavaccaoqoqiyteqaddghjlknbczwdxdyvnuonl
5 0
3 years ago
4 2/3 + 1 3/4 give your answer as a mixed number
Anna71 [15]

Answer:

6 5/12

Step-by-step explanation:

Given the expression :

4 2/3 + 1 3/4

The sum of the numbers :

4 2/3 + 1 3/4

14/3 + 7/4

L.C.M of 3 and 4 = 12

(56 + 21) / 12

77 / 12

= 6 5/12

7 0
3 years ago
The top of a soup can has an area of 12.56 cm2. What is the radius of the can?
Wittaler [7]
Try to divide the diameter by two
6 0
3 years ago
The revenue for a vehicle rental store is $5460. There was 208 cars and 52 vans rented. A van rents for $10 more than a car.
Darya [45]
208c + 52v = 5460
v = c + 10

where c = the price for a car rental and v = the price for a van rental.
To solve this system, use substitution; the second equation says v is equal to c + 10, so plug in "c + 10" for v in the first equation and solve for c:

208c + 52(c + 10) = 5460
208c + 52c + 520 = 5460
260c + 520 = 5460
260c = 4940
c = 19

Now that we have c, we can plug it in to the second equation to find v:

v = (19) + 10
v = 29

So, c = 19 and v = 29, meaning that
The cost of a car rental is $19 and the cost of a van rental is $29.
7 0
3 years ago
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