Volume = are base*height
32 = x^2*h --> h = 32/x^2
surface area = 4x(32/x^2) + x^2
SA = 128/x + x^2
SA' = -128/x^2 + 2x = 0
2x = 128/x^2
2x^3 = 128
x^3 = 64
x = 4
surface area minimized when length of base is 4 in.
hope this help
Answer:
D
Step-by-step explanation:
($20/hr) is the hourly rental rate, and x is the number of hours for which the bike is rented.
In f(x) = 10 + 20x letting x = 10 results in the total rental cost of the bike for 10 hours (Answer D)
a. Using the vertical angles theorem, m∠7 = 47°.
b. Based on the definition of linear pair, the equation that can be used to solve for x is: 2x - 5 + 47 = 180.
c. x = 69
<h3>What is a Linear Pair?</h3>
A linear pair is two angles whose sum equals 180°.
Given the image, where:
m∠5 = 47°
a. ∠5 and ∠7 are vertical angles. Since verticl angles are congurent, therefore:
m∠7 = m∠5 = 47°
m∠7 = 47°
b. m∠6 = (2x - 5)°
m∠6 + m∠5 = 180° (linear pair)
Substitute
2x - 5 + 47 = 180 (equation that can be used to solve x)
c. 2x - 5 + 47 = 180
2x + 42 = 180
2x = 180 - 42
2x = 138
x = 138/2
x = 69
Learn more about linear pair on:
brainly.com/question/3768841
The volume of a cuboid is given in terms of length, width, and height by ...
... V = LWH
Filling in the given numbers, we can solve for the height.
... 8100 in³ = (30 in)(15 in)H
Dividing by the coefficient of H, we have ...
... (8100 in³)/(450 in²) = H = 18 in
The chest will be 18 inches tall.
The meaning of a quadrilateral inscribed in a circle is that the angles on the opposite vertices are supplementary or in other words equals to 180 degrees.
In this exercise it is asked you to find the measure in degrees of angle A. First of all, you have to find the value of x. To do this you have to select two angles on this case angles A and C.
m<A+m<C=180 Substitute the values of angles A and C
2x+9+3x+1=180 Combine like terms
5x+10=180 Subtract in both sides by 10
5x=170 Divide in both sides by 5 to isolate x
x= 34
Now that the value of x is known, you can substitute it into the expression representing angle A.
m<A=2x+9
m<A=2(34)+9
m<A=77
The measure of angle A is 77 degrees.