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MaRussiya [10]
3 years ago
10

The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x

units.
Which expression represents the volume of the prism, in cubic units?

x3 + 9
x3 + 3x2
x3 + 3x + 3
x3 + 6x2 + 9x
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
5 0

Answer:

B. x^3 + 3x^2

Step-by-step explanation:

Volume of a rectangular prism=width * length * height

V=w*l*h

h=3 greater than the length of the base

h=x+3

Length of the base=x

Width=x

Substituting values into the formula

V=w*l*h

=(x)*(x)*(x+3)

Multiplying

=(x^2)(x+3)

=x^3 + 3x^2

Option B is the correct answer

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A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude ​
I am Lyosha [343]

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

We are given three sides of a triangle, Let the sides be :

  • ( a ) = 35 cm

  • ( b ) = 54 cm

  • ( c ) = 61 cm

We can find the area of the triangle with its three sides using Heron's Formula

  • <u>Heron's </u><u>Formula</u>

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

\sf{   \pmb { \longrightarrow \:  \sqrt{s(s - a)(s - b)(s - c)} }}

where ( s ) :

\sf \longrightarrow s = \dfrac{a + b + c}{2}

Therefore, for the given triangle first we will calculate ( s )

\begin {aligned}\quad & \quad \longmapsto  \sf  s =  \dfrac{a + b + c}{2}  \\  & \quad \longmapsto  \sf s =  \dfrac{35 + 54 + 61}{2}  \\ & \quad \longmapsto  \sf s =  \dfrac{150}{2}  \\ & \quad \longmapsto  \sf s  = 75cm \end{aligned}

Now, Area of triangle will be:

\begin{aligned}&:\implies \sf\quad \sf \:  A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \:  A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)}   \\&:\implies \sf\quad \sf \:  A = \sqrt{75 \times 40 \times 21 \times 14}  \\ &:\implies \sf\quad \sf \:  A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5}  \\ &:\implies \sf\quad \sf \:  A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5}  \\ &:\implies \sf\quad \sf \:  A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf   A =939.15 {cm}^{2} }} \end{aligned}

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

\begin{aligned}&:\implies \sf\quad \sf \:  Area =939.15 \\ &:\implies \sf\quad \sf \:   \dfrac{1}{2}  \times b \times h =939.15 \\ &:\implies \sf\quad \sf \:   \dfrac{1}{2} \times 61 \times h  = 939.15 \\&:\implies \sf\quad \sf \:  h =939.15 \times  \dfrac{2}{61}   \\&:\implies \sf\quad \sf \:  h = \dfrac{1818.3}{61}  \\ &:\implies \sf\quad  \boxed{ \pmb{\sf \:  h =30.79 \: (approx)}} \end{aligned}

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2 years ago
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The perimeter of triangle ABC is given by the expression 3x2 - 7x + 2.
VladimirAG [237]

Answer:

<em>Perimeter of ABC = AB + BC+AC. Replace letters with equations.</em>

<em>3x^2-7x+2</em><em> = </em><u><em>2x^2-10x+6 + x^2-x-4 + AC</em></u><em> = </em><em>3x^2-11x+2 + AC</em><em>.</em>

<em>AC = 4x;</em>

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astraxan [27]
2x^3(x+7)(x-7)
Thats the answer for your question!
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Compare the values of the underline digits. 2,402 and 64,513   the value of 4 in _______________ is _______ times the values of
Ludmilka [50]
64,513; 10; 2,402. The 4 in 64,513 is essentially 4,000 whereas the 4 in 2,402 is only 400. 400(10)=4000.
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3 years ago
Length width height equals to 62, what is the maximum volume
joja [24]
Assuming that the given shape is a cuboid, 

volume=l×w×h

v=s³ (since cuboids have same length, they have same side length) 

62=s³
∛62=s 
s=3.957 ≈ 4 units 


Hope I helped :) 
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