The area of a rectangle is 8x^2 +14x + 3. the width is 2x +3. What is the length?

Melinda paints 7/8 of a wall in 1 1/6 hours. what part of a wall does Melinda paint in 1 minute

marissa [1.9K]

1 1/6 hours is equal to 60 minutes add 10 minutes = 70 minutes
7/8 takes 70 minutes
To find out what can be done in 10 minutes, divide both numbers by 7
7/8 / 7 = 1/8
1/8 takes 10 minutes
To find out how much is painted in 1 minute, divide both by 10
1/8 / 10 = 1/80

1/80 takes 1 minute

8 0

2 years ago

The ratio of the radii of two similar cylinders is 3:5. The volume of the smaller cylinder is 54pi cubic centimeters. Find the v

8090 [49]

5/3 = 1.66667

1.666666^3=4.6296 (Volume is measured in cubic units)
54x4.6396=250
250 x pi = 250Pi.

8 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

Total employment for sheet metal workers in 2016 is projected to be 201,000. if this is a 6.3% increase from 2006, approximately

fomenos

Answer:

Option d.

Step-by-step explanation:

Total employment for sheet metal workers in 2016 is projected to be = 201,000

This is a 6.3% increase from 2006.

Let the number of workers in 2006 be n

n + (6.3% of n) = 201,000

n + ( 0.063n) = 201,000

1.063n = 201,000

n = $\frac{201,000}{1.063}$

n = 189,087. 4882 ≈ 189,000

the total employment in 2006 was approximately 189,000

Option d is the answer.

8 0

2 years ago

Bill launched a model rocket, and estimated its height h, In feet, after 1 seconds. His results are shown in the table

gizmo_the_mogwai [7]

Answer:

Bill launched a model rocket, and estimated its height h, In feet, after 1 seconds. His results are shown in the table

Time, 1 0 1 2 3 4

Height, h 0 110 190 240 255

Bill's data can be modeled by the function h(t) = -1612 + 128.

Which value is the best prediction for the height of the rocket after 5.5 seconds?

A 150 ft

B. 180 ft

C. 220 ft

D. 250 ft

E 260 ft

0 1

2 years ago