6. What multiplication sentence does<br> this array show?

The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. Wha

Xelga [282]

Answer:

The average value of $f$ over the interval $[-2,5]$ is $\frac{10}{7}$ .

Step-by-step explanation:

Let suppose that function $f$ is continuous and integrable in the given intervals, by integral definition of average we have that:

$\frac{1}{3-(-2)} \int\limits^{3}_{-2} {f(x)} \, dx = -6$ (1)

$\frac{1}{5-3} \int\limits^{5}_{3} {f(x)} \, dx = 20$ (2)

By Fundamental Theorems of Calculus we expand both expressions:

$\frac{F(3)-F(-2)}{3-(-2)} = -6$

$F(3) - F(-2) = -30$ (1b)

$\frac{F(5)-F(3)}{5-3} = 20$

$F(5) - F(3) = 40$ (2b)

We obtain the average value of $f$ over the interval $[-2, 5]$ by algebraic handling:

$F(5) - F(3) +[F(3)-F(-2)] = 40 + (-30)$

$F(5) - F(-2) = 10$

$\frac{F(5)-F(-2)}{5-(-2)} = \frac{10}{5-(-2)}$

$\bar f = \frac{10}{7}$

The average value of $f$ over the interval $[-2,5]$ is $\frac{10}{7}$ .

4 0

2 years ago

Hi ! please help !

tatuchka [14]

Hey there! I was looking at your question for a bit then realized you meant $i$ , the imaginary number, not "1" at the end of each number.

Complex numbers are numbers involving both real and imaginary numbers; thus, this question wouldn't make much sense without the imaginary number $i$

The expression we are given is:

$(3+4i)+(8+2i)$

Open parenthesis and combine like terms:

$=3+4i+8+2i$

$=11+6i$

This is answer choice B (assuming it's supposed to be an $i$ and not a "1" at the end)

Let me know if you need any clarifications, thanks!

~ Padoru

5 0

3 years ago

Read 2 more answers

What is the sign of the product (−4)(2)(−3)(6)?

lana [24]

Answer:

The sign would be positive.

The answer would be 144.

Step-by-step explanation:

Note that there are two negative numbers and two positive numbers:

positive x positive = positive answer.

negative x negative = positive answer.

Solve:

(-4) * (-3) = 12

2 * 6 = 12

12 * 12 = 144

144 would be your answer.

~

6 0

3 years ago

Read 2 more answers

I need help with this ASAP and can you explain so i can understand?!

Elanso [62]

Answer:

Adult tickets sold = 225

Student Tickets sold = 375

Step-by-step explanation:

Let:

Adult tickets sold = x

Student Tickets sold = y

Total tickets sold = 600

So, we can write: x+y = 600

Total money collected = 3037.50

Cost of 1 Adult ticket = $6.00

Cost of one Student ticket = $4.50

So, we can write: 6x+4.5y=3037.50

Now, we get a system of equations, that if solved we can find values of x and y

Let:

$x+y = 600--eq(1)\\6x+4.5y=3037.50--eq(2)$

We can solve using substitution method.

Finding value of x from eq(1) and putting it in eq(2)

$We\:have\\x+y=600\\x=600-y$

Put in eq(2)

$6x+4.5y=3037.50\\6(600-y)+4.5y=3037.50\\3600-6y+4.5y=3037.50\\-1.5y=3037.50-3600\\-1.5y=-562.5\\y=\frac{-562.5}{-1.5}\\y=375$

So, we get value of y = 375

Now put value of y in eq(1) to find value of x

$x+y=600\\Put\:y=375\\x+375=600\\x=600-375\\x=225$

So, we get value of x = 225

The Tickets sold will be:

Adult tickets sold = x = 225

Student Tickets sold = y = 375

3 0

2 years ago

Read 2 more answers

Solve 11 2/5 = q - 4 2/7 + 2 1/7

RideAnS [48]

I turn the mixed numbers into decimals before doing anything else.
11 2/5----> 57/5----> 11.4
4 2/7----> 30/7----> 4.29
2 1/7----> 15/7----> 2.14

11.4=q-4.29+2.14
11.4=q-2.15
13.55= q

13.55 converted to a fraction is 13 11⁄20
q=13 11⁄20

6 0

3 years ago

6. What multiplication sentence does this array show?