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3 years ago

Explain weather 14t-3t is equivalent to 3t-14t. Support your sender by evaluating the expression for t=2.

Mathematics

1 answer:

m_a_m_a [10]3 years ago

6 0

Answer:

Solving 14t-3t we get 22 and 3t-14t we get -22

So, 14t-3t is not equivalent to 3t-14t.

Step-by-step explanation:

We need to explain weather 14t-3t is equivalent to 3t-14t. Support your sender by evaluating the expression for t=2.

Equivalent expressions are those that have same values for any value of variable substituted.

Now, We check if our expressions are equivalent, by evaluating the expression for t=2.

If they are equivalent, they would have same result after evaluation.

First, put t=2 into 14t-3t

$14t-3t\\Put\:t=2\\=14(2)-3(2)\\=28-6\\=22$

Now put t=2, into 3t-14t

$3t-14t\\Put\:t=2\\=3(2)-14(2)\\=6-28\\=-22\\$

For solving 14t-3t we get 22 and 3t-14t we get -22

So, 14t-3t is not equivalent to 3t-14t.

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

Optimizing With Derivatives

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

Grace rides her bike 21 km in 1 1/6 hours. What is her average speed in kilometers per hour?

aleksandrvk [35]

126 because 20 X 6 and 6 x 1

4 0

2 years ago

On a map, 2 inches represents 300 miles. How many inches would there be between two cities that are 1,200 miles apart?

solniwko [45]

Answer:

Step-by-step Explanation:

Step 1. Divide 1200 by 300:

1200 ÷ 300 = 4

Step 2. Multiply 4 by 2:

4 * 2 = 8

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3 years ago

Can one fifth be simplified

Svetradugi [14.3K]

No, and never, cus there ain't any numbers that are greater than 1 that can go into both of them.
so basically if the numerator is 1, you can't simplify it anymore. Is Impossible.

3 0

3 years ago

When Theresa got her puppy, it weighed 6 ponds less than 2/3 of its weight now. If the puppy weighed 4 pounds when she first rec

sesenic [268]

Answer:

15 lb

Step-by-step explanation:

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