These are the four terms of the sequence 29,32,35,38. the question is write down the next term

Based on the table, which best predicts the end behavior of the graph of f(x)?

Yuki888 [10]

Answer: A. As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞.

6 0

3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

3 years ago

Shamir and Juliet are traveling at constant rates in their cars. If Shamir travels

snow_lady [41]

How much farther than Shamir will Juliet travel in one hour is : b. 3 miles.

<h3>Distance</h3>

1 hour= 60 minutes

Given:

Difference in 10 minutes=1/2 mile

Hence:

Difference in one hour=1/2×(60/10)

Difference in one hour=1/2× 6 mile

Difference in one hour=3 miles

Therefore how much farther than Shamir will Juliet travel in one hour is : b. 3 miles.

Learn more about distance here:brainly.com/question/2854969

#SPJ1

5 0

1 year ago

2x+6=76<br><br> Show your steps

Gennadij [26K]

Hola I’m Carribbean:)

Answer:

X = 35

Step-by-step explanation:

Subtract 6 from both sides.

2x+6−6=76−6

2x=70

Divide both sides by 2.

$\frac{2x}{2}$ ÷ $\frac{70}{2}$

= 35

8 0

2 years ago

Read 2 more answers

A plastic bin contains red yellow and green keychains out of 350 keychains 10% or yellow off the remaining keychains three sets

pantera1 [17]

Answer:

The question is not comprehensive, the comprehensive question is:

A plastic bin contains red, yellow, and green key chains. Out of 350 key chains, 10% percent are yellow. Of the remaining key chains, 3/5 are green. How many red key chains are inside the bin?

There are 126 red key chains in the plastic bin

Step-by-step explanation:

The plastic bin contains keychains of red, yellow and green colours.

According to the question, the total keychains in the bin are 350.

10% of this keychains are yellow i.e. 10/100 × 350 = 35

Thus, 35 keychains are yellow in colour.

This means, we have 350 - 35 = 315 keychains consisting of red and green colours left.

The question further says that 3/5 of the remaining keychains (315) are green i.e. 3/5 × 315 = 945/5 = 189

Thus, there are 189 green keychains in the bin.

To get the number of red keychains in the plastic bin, we add the number of yellow and green keychains, and subtract the sum from the total keychains (350).

We have 35 (yellow) + 189 (green) = 224 yellow and green keychains.

Hence, red keychains = 350 (total keychains) - 224 (yellow and green)

= 126 red keychains

There are 126 keychains in the plastic bin.

4 0

3 years ago

Read 2 more answers

These are the four terms of the sequence 29,32,35,38. the question is write down the next term​

These are the four terms of the sequence 29,32,35,38. the question is write down the next term