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3 years ago

100% of my grade plz help

Mathematics

1 answer:

Montano1993 [528]3 years ago

3 0

Answer: for the box. x 5 / -2 / 2 / -1 / 0 / -3 / 3

y 9 / -5 / 0 / 5 / -1 / 9 / 7 / y

Step-by-step explanation:

I hope it helped

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Suppose a 50-foot ladder is leaning against a wall. Which statements about the base of the ladder are true?

Liula [17]

Answer and Step-by-step explanation:

These are the statements that make the question complete:

A. If the base is 24 feet from the wall, the ladder reaches 45 feet up the wall.

B. If the base is 30 feet from the wall, the ladder reaches 40 feet up the wall.

C. If the base is 27 feet from the wall, the ladder reaches 44 feet up the wall.

D. If the base is 14 feet from the wall, the ladder reaches 48 feet up the wall.

Since the ladder leans against a wall, a right angle triangle is formed. Since the ladder is now slant, then it's length becomes the hypothenuse.

The correct statements can be gotten through Pythagoras theorem which says:

A² + B² = C² where C is the hypothenuse and A and B are the other two sides.

Since the hypothenuse is 50, we can test each statement by taking the square of the two sides and add them up, if they are equal to 50² = 2500, then the statement is true.

A. 24² + 45² = 576 + 2025 = 2601 ≠ 2500, therefore it is false.

B. 30² + 40² = 900 + 1600 = 2500, therefore it is true.

C. 27² + 44² = 729 + 1936 = 2665 ≠ 2500, therefore it is false

D. 14² + 48² = 196 + 2304 = 2500, therefore it is true.

From here, statements B and D are true while the rest are all false.

7 0

3 years ago

Solve for x (2x-8) (9x-10)

mars1129 [50]

Answer

x+3=17

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

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

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