PLEASE HELP ASAP A student solved this system of equations.

You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?

lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

$V=\pi r^{2} h$

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

$V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\$

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro = 1000 cubic centimeters

$if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}$

1 cubic inch = 16.3870 cubic centimeters

$1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters$

Step 4

Finally, convert cubic centimeters into liters $1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters$

I can put 3.706 liters in the thermos

Have a good day

4 0

4 years ago

Find the measure of each marked angle (8x-8) (6x)

Elis [28]

Answer:

multiply 6x into 8x and -8 (hope this helps)

4 0

4 years ago

Solve for x.

Crank

The solutions to the given absolute value equation are:

x = −74 and x = 80

<h3>How to solve the given equation for x?</h3>

Here we want to solve the absolute value equation:

(1/7)*|x - 3| - 2 = 9

To solve this, we first need to isolate the absolute value part, so we get:

(1/7)*|x - 3| - 2 = 9

(1/7)*|x - 3| = 9 + 2

(1/7)*|x - 3| = 11

|x - 3| = 11*7

|x - 3| = 77

Now we can decompose the absolute value equation into two simpler ones, which are:

x - 3 = 77

x - 3 = -77

Solving those two equations we get:

x = 77 + 3 = 80

x = -77 + 3 = -74

Thus the solutions are:

x = -74 and x = 80, we conclude that the correct option is the last one.

If you want to learn more about absolute value equations:

brainly.com/question/5012769

#SPJ1

6 0

2 years ago

A study found that a driver’s reaction time A(x) to audio stimuli and his or her reaction time V(x) to visual stimuli (both in m

amid [387]

Answer:

The required inequality is $0.0001 x^2 - 0.089 x - 7$ .

Step-by-step explanation:

The given inequalities are

$A(x) = 0.0051x^2 - 0.319x + 15$

$V(x)= 0.005x^2 - 0.23x + 22$

where, x is the driver's age (in years), A(x) is driver’s reaction time to audio stimuli and V(x) is his or her reaction time to visual stimuli, 16 ≤ x ≤ 70.

We need to find an inequality that can be use to find the x-values for which A(x) is less than V(x).

$A(x)$

$0.0051x^2 - 0.319x + 15< 0.005x^2 - 0.23x + 22$

$0.0051x^2 - 0.319x + 15- 0.005x^2 + 0.23x- 22$

Combine like terms.

$0.0001 x^2 - 0.089 x - 7$

where, 16 ≤ x ≤ 70.

Therefore, the required inequality is $0.0001 x^2 - 0.089 x - 7$ .

5 0

4 years ago

Solve the inequality.<br>4(x – 7)>-8<br>

frez [133]

Answer:

x>5

Step-by-step explanation:

1. First, you do distributive property with 4(x-7), which is 4x-28

2. Add 28 to both sides

3. divide 4 on each side

4. 20 divided by 4 is 5

6. x>5

6 0

4 years ago