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3 years ago

(10x-20) (6x+8) what is x?

Mathematics

1 answer:

Lilit [14]3 years ago

7 0

X= 2 and x= -8/6 if you make it = 0
(10x-20)(6x+8)=0
10x-20=0
10x=20
x=2
6x+8=0
6x=-8
x=-8/6

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Please I need help step by step

zaharov [31]

To find the surface area, you need to do the following:
A side of the figure is a trapezoid, so you should do 13+5x7 (since there are 2 of the same sides there is no need to divide by two.) and it should equal 126. To find the area of the top of the figure, you need to do 5x2 which equals 10. The area of the bottom of the figure is 26 (13x2), then do 2x3x2 to get the sides on the left and right of the figure. After all of this, add them together. (126+10+26+12=174.)
The surface area should be 174mm.

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3 years ago

What is 0 to the -1,000

Tanya [424]

Answer:

Step-by-step explanation:

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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

Answer 1,2 and 3 and challenge thank you

Nadusha1986 [10]

NUMBER 2 is 240 because 6 times 4 times 10 is equal to 240. I am still working on the others

7 0

3 years ago

Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed.

OLEGan [10]

Answer: the value of population standard deviation is 3.87

Step-by-step explanation:

From the information given,

Number of sample, n = 8

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

Since confidence interval = 2.694,

It becomes

2.694 = 1.96 × standard deviation/√8

Dividing both sides of the equation by 1.96, it becomes

1.37 = standard deviation/√8

Standard deviation = 1.37 × √8

Standard deviation = 3.87

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3 years ago