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2 years ago

If 5 is an element in the domain of f(x)= 8x-21/5, what is the corresponding element in the range?

Mathematics

1 answer:

Delvig [45]2 years ago

6 0

Answer:

The corresponding element in the range when 5 is an element in the domain is $f(5)=\frac{179}{5}$

Step-by-step explanation:

Given that the 5 is an element in the domain of f(x)

The function f is defined by $f(x)=8x-\frac{21}{5}$

To find the corresponding element in the range:

That is put x=5 in the given function f(x)

Therfore f(x) becomes

$f(5)=8(5)-\frac{21}{5}$

$=40-\frac{21}{5}$

$=\frac{200-21}{5}$

$f(5)=\frac{179}{5}$

Therefore corresponding element in the range when 5 is an element in the domain is $f(5)=\frac{179}{5}$

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If a fire is burning a building and it takes 2 hours to put it out using 2000 gal./min., what minimum diameter cylindrical tank

strojnjashka [21]

Answer:

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

Step-by-step explanation:

A gallon equals 0.134 cubic feet. First, we determine the amount of water ( $Q$ ), measured in cubic feet, needed to put out the fire under the assumption that water is consumed at constant rate:

$Q = \dot Q \cdot \Delta t$ (1)

Where:

$\dot Q$ - Volume rate, measured in feet per minute.

$\Delta t$ - Time, measured in minutes.

If we know that $\dot Q = 2000\,\frac{gal}{min}$ and $\Delta t = 120\,min$ , then the amount of water is:

$Q = \left(2000\,\frac{gal}{min} \right)\cdot (120\,min) \cdot \left(0.134\,\frac{ft^{3}}{gal} \right)$

$Q = 32160\,ft^{3}$

And the diameter of the cylindrical tank based on the capacity found above is determined by volume formula for a cylinder:

$Q = \frac{\pi}{4}\cdot D^{2}\cdot h$ (2)

Where:

$D$ - Diameter, measured in feet.

$h$ - Height, measured in feet.

If we know that $Q = 32160\,ft^{3}$ and $h = 12\,ft$ , then the minimum diameter is:

$D^{2} = \frac{4\cdot Q}{\pi\cdot h}$

$D = 2\cdot \sqrt{\frac{Q}{\pi\cdot h} }$

$D = 2\cdot \sqrt{\frac{32160\,ft^{3}}{\pi\cdot (12\,ft)} }$

$D \approx 58.415\,ft$

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

8 0

2 years ago

Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of

11111nata11111 [884]

SOLUTION

Given the question on the question tab;

$From\text{ the graph; we will trace from x=1 upward to meet the curve, then trace to the y-axis.}$

The trace on the graph is given below;

$The\text{ value of y when x=1 is 15.}$

Final answer:

The volume of the box when x=1 is 15 cubic inches.

7 0

1 year ago

anzhelika [568]

The answer is D as said above

8 0

3 years ago

Please help me asap

Sonja [21]

Step-by-step explanation:

4/sin45=

$4 \sqrt{2}$

6 0

2 years ago

Six times a number is 45 greater than the product of the number and -3. Find the number.

LiRa [457]

Answer:

Step-by-step explanation:

6a = (a*-3) + 45

then:

6a = -3a + 45

6a + 3a = 45

9a = 45

a = 45/9

a = 5

Check:

6*5 = (5*-3) + 45

30 = -15 + 45

8 0

3 years ago