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scoundrel [369]

3 years ago

12

Assume a and b are non zero rational numbers and c is an irrational number. For each of the following expressions determine dete

rmine wether the result is irrational rational or both justify your answers?

1 answer:

rodikova [14]3 years ago

4 0

Part A is irrational, but Parts B and C are both rational.

We know that Part A is irrational because an irrational number added to a rational number is still irrational. Also, an irrational number multiplied by a rational number is still irrational.

With Part B, we have an irrational number in the square root of 7. However, it is then squared to give us 7. This leaves us with 7 times a^2 which is rational. Two rational numbers multiplied still give us a rational number.

Finally, Part C only involves adding and multiplying rational numbers. Since that can only yield rational numbers, it must be rational.

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Write in slope intercept form given two points (1,2) and (-2,5)

Anvisha [2.4K]

I’m pretty sure it’s -1
How you solve this is y2-y1/x2-x1
So 5-2/-3-1 which would be -1

4 0

2 years ago

An airplane flies 2700 miles in 3 hours and 45 minutes. What is its average speed in miles per hour?

fenix001 [56]

Answer:

720 MPH

Step-by-step explanation:

2700 miles / 3.75 hours = 720 MPH

6 0

3 years ago

Read 2 more answers

"Define a variable write an inequality and solve each problem".A number +1 is greater than -5 less than three.

Brrunno [24]

Answer: -5 < x + 1 < 3

Step-by-step explanation:

Let x be the number.

-5 < x + 1 < 3

4 0

2 years ago

when full the gas tank of a car holds 15 gallons. it now contains 12 gallons. what percent represents how full the tank is?

Masteriza [31]

Hello!

to find the percent of a whole, use this equation here:

(remaining) / (total) = X

X * 100 = %

in this case:

12 / 15 = 0.8

0.8 * 100 = 80

your answer is 80%

I hope this helps, and have a nice day!

5 0

2 years ago

A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the

kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

Area of one side face= $l\times b=xy$

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box= $V=lbh=x^2y$

Total cost= $9(x^2)+5x^2+4(4xy)=14x^2+16xy$

$204=14x^2+16xy$

$204-14x^2=16xy$

$y=\frac{204-14x^2}{16x}=\frac{102-7x^2}{8x}$

Substitute the values of y

$V(x)=x^2\times \frac{102-7x^2}{8x}=\frac{1}{8}(102x-7x^3)$

Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

$x=\sqrt{4.85}=2.2$

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

$V''(2.2)=-\frac{42}{8}(2.2)=-11.55$

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

5 0

3 years ago