Type the expression that results from the following series of steps:<br> Start with t times by 5.

If 1900 square centimeters of material are available to make a box with a square base and an open top, find the largest possible

Evgen [1.6K]

Answer:

Volume = $7969$ cubic centimeter

Step-by-step explanation:

Let the length of each side of the base of the box be A and the height of the box be H.

Area of material required to make the box is equal to is $A^2 + 4*A*H.$

$A^2 + 4*A*H = 1900$

Rearranging the above equation, we get -

$`H = \frac{(1900 - A^2)}{(4*A)}$

Volume of box is equal to product of base area of box and the height of the box -

$V = A*A* H$

Substituting the given area we get -

$\frac{A^2*(1900 - A^2)}{4A} = \frac{(1900*A - A^3)}{4}$

For maximum volume

$\frac{dV}{dA} =0$

$\frac{ 1900}{4} - \frac{3*A^2}{4} = 0$

$A^2 = \frac{1900}{3}$

Volume of the box

= $\frac{\frac{1900}{3}*(1900 - \frac{1900}{3}) }{4 * \sqrt{\frac{1900}{3} } }$

= $7969$ cubic centimeter

3 0

2 years ago

Solve ln 2 + ln x = 5. Round to the nearest thousandth, if possible.

azamat

Answer:

The value of x nearest to thousandths is, 74.207

Step-by-step explanation:

Solve : $\ln 2 + \ln x = 5$

$\ln$ represents the logarithmic function with base e.

Using logarithmic properties:

$\ln (mn) = \ln m + \ln n$

$\ln x = a$ , then $x = e^a$

$\ln 2 + \ln x = 5$

Apply the logarithmic properties; we have

$\ln 2x = 5$

then;

$2x = e^5$

or

$2x=148.41315910258$

Divide both sides by 2 we get;

$x = 74.2065796$

Therefore, the value of x nearest to thousandths is, 74.207

3 0

3 years ago

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse. Using the two given measures, find th

almond37 [142]

I only could find part of the triangle sorry, but u1 is 2 radical 2

8 0

2 years ago

Please help! Explain as well since I need to know material for the test

Illusion [34]

3a)

<h3>Answer: The sum of a+b+c+d is equal to 220</h3>

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How I got this answer:

a+b+e = 180

c+d+f = 180

angles 'e' and 'f' are marked in the attached drawing below (see figure 1)

Add the two equations to get

(a+b+e)+(c+d+f) = 180+180

a+b+e+c+d+f = 180+180

a+b+e+c+d+f = 360

(a+b+c+d)+(e+f) = 360

(a+b+c+d)+(140) = 360 substutition (see below)

a+b+c+d = 360-140

a+b+c+d = 220

==========================================

3b)

The angles of the triangles add to 180 degrees each. The three angles e, f, and 40 add to 180 as well as they form a straight angle, so e+f+40 = 180 leading to e+f = 180-40 = 140. This will help us with the substitution rule I marked above

So the idea is you add up all the angles, and then take away the angles we don't want (e and f) so we end up with the sum of a+b+c+d

==========================================

4

<h3>Answer: 290</h3>

---------------------

Explanation:

Check out the attached image figure 2.

Angle DAE is given to be 30 degrees. Angle ADC is also equal to 30 because they are alternate interior angles.

Angle DCB is 40 degrees. The missing angle x of the triangle DCB is unknown for now, but we can solve for x

x+40+30 = 180

x+70 = 180

x = 180-70

x = 110

Therefore the purple angle marked in that diagram is 180-x = 180-110 = 70

The reflex angle to the 70 degree angle is 360-70 = 290

which is the shaded angle we want to determine

5 0

3 years ago

Step1. Formulate two real-life problems involving system of linear inequalities in

pav-90 [236]

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4 0

2 years ago

Type the expression that results from the following series of steps: Start with t times by 5.