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2 years ago

Work out the Perimeter of the Triangle For 100 Points

Mathematics

1 answer:

WINSTONCH [101]2 years ago

5 0

Answer:

P = 4x + 14

Step-by-step explanation:

$P=(3x-5)+(19-x)+(2x)=(3x-x+2x)+(-5+19)=4x+14$

Hope this helps

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John spent half of his weekly allowance

Citrus2011 [14]

Answer:

Step-by-step explanation:

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3 years ago

PLZ HELP!! ILL GIVE BRAINLIESTT

Nadya [2.5K]

Answer:i am not sure about this

Given Statement:

Angela is very tired after working outside all day.

Conditional Statement:

If she was working outside all day, then angela is very tired.

Converse Statement:

If angela is very tired, then she was working outside all day.

Inverse Statement:

If angela did not work outside all day then she will not be tired

Contrapositive Statement:

If angela is not tired then she did not work outside all day

Biconditional Statement:

Angela is very tired if and only if she worked outside all day

Step-by-step explanation:

6 0

3 years ago

Marta wants to purchase charms for her necklace. Each charm cost $1.59. She wants to spend no more than $20 for the charms. Whic

Svetllana [295]

Which inequality represents this situation ?

1.59×n < 20

How many charms can Marta purchase ?

20 : 1.59 = 12 (+$0.92)

5 0

3 years ago

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:

<u>Optimizing With Derivatives </u>

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

The dimensions of a triangular prism are shown below what is the volume of the prism in cubic feet

Yuliya22 [10]

Answer:

B. 192.5 ft³

Step-by-step explanation:

To find the volume of a triangle prism, multiply the base, height, and length together, and then divide it by 2 (or multiply that by 0.5).

(5 * 7 * 11)/2

Multiply 5 by 7 to get 35.

(35 * 11)/2

Multiply 35 by 11 to get 385.

385/2

192.5 ft³ is the volume of this triangluar prism.

8 0

3 years ago