How does the exponent of each power of ten correspond with placing a decimal

Solve: 3.6 (5x4) divided 3+5.0=

zavuch27 [327]

The value of the expression will be 9.

Explanation

Given expression is : $\frac{3.6(5*4)}{3+5.0}$

First we will simplify both numerator and denominator separately using order of operations. So....

$3.6(5*4)=3.6(20)=72\\\\ and\\\\ 3+5.0=8$

Thus the expression....

$\frac{3.6(5*4)}{3+5.0}=\frac{72}{8}=9$

7 0

2 years ago

The table shows the gallons of water in a pool over time.

Luda [366]

Answer:

- 6 gallons per minute.

Step-by-step explanation:

Let the function that models the quantities of water, Q (in gallons) in a pool over time, t (in minutes), is

Q = a + bt ........... (1)

Now, Q(t = 0) is given to be 50 gallons.

So, a = 50 and b denotes the rate at which the quantity of water in the pool is decreasing and it is given by the slope of equation (1).

Now, two points on the graph are (0,50) and (1,44).

So, the slope = b = $\frac{50 - 44}{0 - 1}$ = - 6 gallons per minute.

Therefore, the equation of this situation is given by Q = 50 - 6t, where the slope is equal to - 6 gallons per minute. (Answer)

4 0

2 years ago

Read 2 more answers

If the screws that are 4/8 of an inch are laid end to end touching each other how far would the row extend?

Irina18 [472]

Idk because you did not say yes you did how many sides there were

8 0

2 years ago

Read 2 more answers

Mr. Phillips is mixing paint for his art class. How many 6-ounce bottles can he fill with the quantities of paint shown at the r

Delvig [45]

Is there any images?

7 0

2 years ago

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At x = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at x = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at x = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago