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Vadim26 [7]
3 years ago
14

Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = −sin x, [0,

π] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
Mathematics
1 answer:
deff fn [24]3 years ago
7 0

Answer with Step-by-step explanation:

We are given that

f(x)=-sin x

[0,\infty]]

Average value of the function is given gy

f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx=\frac{1}{\pi-0}\int_{0}^{\pi}-sinx dx

f_{avg}=\frac{1}{\pi}[cosx]^{\pi}_{0}

Using the formula

\int sin xdx=-cos x

f_{avg}=\frac{1}{\pi}(cos\pi-cos0)

f_{avg}=\frac{1}{\pi}(-1-1)=-\frac{2}{\pi}

f(x)=f_{avg}

-sinx=-\frac{2}{\pi}

sinx=\frac{2}{\pi}

x=sin^{-1}(\frac{2}{\pi})=0.69radian

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Find the lateral area of this cone.
Fiesta28 [93]

Answer:

65π

Step-by-step explanation:

Slant height, l = √r² + h²

l = √5² + 12²

l = √25 + 144

l = √169

l = 13

Lateral area = πrl

Lateral area = π5*13

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4 0
3 years ago
Which of the following equations shows the correct way to apply the Commutative Property of Addition?
o-na [289]

Answer:

Commutative Property of Addition: a + b = b + a

Step-by-step explanation:

The Commutative Property of Addition implies that even on changing the order of addition the final result (i.e. the sum) remains the same.

  • Consider the addition of two numbers, say <em>a</em> and <em>b</em>:

a + b = b + a

Suppose <em>a</em> = 5 and <em>b</em> = 6, then:

<em>a</em> + <em>b</em> = 5 + 6 = 11

<em>b</em> + <em>a</em> = 6 + 5 = 11.

Thus, a + b = b + a.

  • Consider the addition of three numbers, say <em>a, b</em> and <em>c</em>:

a + b + c= a + c + b = b + a + c = c + a + b

Suppose <em>a</em> = 4, <em>b</em> = 3 and <em>c</em> = 6, then:

a + b + c = 4 + 3 + 6 = 13

a + c + b = 4 + 6 + 3 = 13

b + a + c = 3 + 4 + 6 = 13

c + a + b = 6 + 4 + 3 = 13.

Thus, a + b + c= a + c + b = b + a + c = c + a + b.

4 0
3 years ago
Whats 1.5 divided by 1.5​
yawa3891 [41]

Answer:

1

hope this helped

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
How do you substract two digits for example 60-4 only by the operator plus(+)? only digets &gt;=0 are allowed​
Olegator [25]

Answer:

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtraction is signified by the minus sign (−). For example, in the adjacent picture, there are 5 − 2 apples—meaning 5 apples with 2 taken away, which is a total of 3 apples. Therefore, the difference of 5 and 2 is 3, that is, 5 − 2 = 3. Subtraction represents removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.

Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer. It is also not associative, meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Because 0 is the additive identity, subtraction of it does not change a number. Subtraction also obeys predictable rules concerning related operations such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.

Performing subtraction is one of the simplest numerical tasks. Subtraction of very small numbers is accessible to young children. In primary education, students are taught to subtract numbers in the decimal system, starting with single digits and progressively tackling more difficult problems.

In advanced algebra and in computer algebra, an expression involving subtraction like A − B is generally treated as a shorthand notation for the addition A + (−B). Thus, A − B contains two terms, namely A and −B. This allows an easier use of associativity and commutativity.

5 0
3 years ago
I can’t figure this out
Neporo4naja [7]

Answer:d

Step-by-step explanation:it is d -2 2/3 is the lowest

5 0
3 years ago
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