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2 years ago

12

A. y = -1 B. X = -1 C. y = 1 D. X = 1

1 answer:

Marizza181 [45]2 years ago

3 0

Answer- D X=1
The highest point in the number is X=1

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3 years ago

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3 years ago

Consider two functions f and g on [1, 8] such that integral^8_1 f(x) dx = 9, integral^8_1 g(x) dx = 5, integral^8_5 f(x) dx = 4,

Gelneren [198K]

I'll abbreviate the definite integral with the notation,

$I(f(x),a,b)=\int_a^bf(x)\,\mathrm dx$

We're given

$I(f,1,8)=9$
$I(g,1,8)=5$
$I(f,5,8)=4$
$I(g,1,5)=3$

Recall that the definite integral is additive on the interval $[a,b]$ , meaning for some $c\in[a,b]$ we have

$I(f,a,b)=I(f,a,c)+I(f,c,b)$

The definite integral is also linear in the sense that

$I(kf+\ell g,a,b)=kIf(a,b)+\ell I(g,a,b)$

for some constant scalars $k,\ell$ .

Also, if $a\ge b$ , then

$I(f,a,b)=-I(f,b,a)$

a. $I(2f,1,5)=2I(f,1,5)=2(I(f,1,8)-I(f,5,8))=2(9-4)=\boxed{10}$

b. $I(f-g,1,8)=I(f,1,8)-I(g,1,8)=9-5=\boxed{4}$

c. $I(f-g,1,5)=I(f,1,5)-I(g,1,5)=\dfrac{I(2f,1,5)}2-I(g,1,5)=10-3=\boxed{7}$

d. $I(g-f,5,8)=I(g,5,8)-I(f,5,8)=(I(g,1,8)-I(g,1,5))-I(f,5,8)=(5-3)-4=\boxed{-2}$

e. $I(7g,5,8)=7I(g,5,8)=7(5-3)=\boxed{14}$

f. $I(3f,5,1)=3I(f,5,1)=-3I(f,1,5)=-\dfrac32I(2f,1,5)=-\dfrac32(10)=\boxed{-15}$

4 0

2 years ago

A submarine elevation is -14 feet relative to sea level. A shark is swimming at elevation of -56 feet what is the difference in

likoan [24]

In order to solve this kind of problem, we must find the difference between two negative numbers describing elevation. Although when you have 2 negative numbers in a subtraction-elevation problem, the elevation difference won't be negative... It would be positive. -56 - (-14) would usually equal -42 feet but that would just describe a regular negative subtraction problem, so it becomes 42 feet. This answer is positive since it describe the distance between these integers.

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3 years ago

Is it True or False?

Pavlova-9 [17]

Answer:

true

Step-by-step explanation:

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