Ask question

Ask question

All categories

4 years ago

9

in a given rectangular prism, the length is represented by x + 1, the width is represented by x +4 and the height is 7. express

the volume of the rectangular prism in terms of x.

1 answer:

Karo-lina-s [1.5K]4 years ago

3 0

Base = x^2 + 5x + 4

volume = base × height
volume = ( x^2 + 5x + 4 ) × 7
volume = 7x^2 + 35x + 28

You might be interested in

Please please help!!

shepuryov [24]

Answer:

$\large\boxed{x=0\ and\ x=\pi}$

Step-by-step explanation:

$\tan^2x\sec^2x+2\sec^2x-\tan^2x=2\\\\\text{Use}\ \tan x=\dfrac{\sin x}{\cos x},\ \sec x=\dfrac{1}{\cos x}:\\\\\left(\dfrac{\sin x}{\cos x}\right)^2\left(\dfrac{1}{\cos x}\right)^2+2\left(\dfrac{1}{\cos x}\right)^2-\left(\dfrac{\sin x}{\cos x}\right)^2=2\\\\\left(\dfrac{\sin^2x}{\cos^2x}\right)\left(\dfrac{1}{\cos^2x}\right)+\dfrac{2}{\cos^2x}-\dfrac{\sin^2x}{\cos^2x}=2$

$\dfrac{\sin^2x}{(\cos^2x)^2}+\dfrac{2-\sin^2x}{\cos^2x}=2\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-(1-\cos^2x)}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-1+\cos^2x}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{1+\cos^2x}{\cos^2x}=2$

$\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{(1+\cos^2x)(\cos^2x)}{(\cos^2x)^2}=2\qquad\text{Use the distributive property}\\\\\dfrac{1-\cos^2x+\cos^2x+\cos^4x}{\cos^4x}=2\\\\\dfrac{1+\cos^4x}{\cos^4x}=2\qquad\text{multiply both sides by}\ \cos^4x\neq0\\\\1+\cos^4x=2\cos^4x\qquad\text{subtract}\ \cos^4x\ \text{from both sides}\\\\1=\cos^4x\iff \cos x=\pm\sqrt1\to\cos x=\pm1\\\\ x=k\pi\ for\ k\in\mathbb{Z}\\\\\text{On the interval}\ 0\leq x$

4 0

3 years ago

HELP PLEASE!! VERY MUCH APPRECIATED!!

SOVA2 [1]

Answer:

1.3445367773335334434333233332

3 0

3 years ago

Here is a rectangle.

NISA [10]

Step-by-step explanation:

Let the area of rectangle with given points are as follows :

A(-3,3)

B(3,2)

C(4,-1) = C( x1,y1)

D(-2,-3) = D( x2, y2)

Now,

The distance of CD = root under

(x2-x)^2 +( y2 - y1)^2

= root under (-2-4)^2 + ( -3+1)^2

= root under (-6)^2 + (-2)^2

= root under 36 + 4

= root under 40

= 2root 10

Therefore; the unit number if CD is 2 root 10.

6 0

2 years ago

Compare <img src="https://tex.z-dn.net/?f=5%5E%7B149%7D" id="TexFormula1" title="5^{149}" alt="5^{149}" align="absmiddle" class=

maxonik [38]

A = 5¹⁴⁹
B = 11⁹⁹

Case 1: A>B
Result: True

Case 2: A=B
Result: False

Case 3: AResult: False

8 0

4 years ago

Anthony has a bag that contains 4 blue candies, 6 green candies, and 10 yellow candies. * Without looking, he pulls out a piece

BigorU [14]

Answer:

0.03

Step-by-step explanation:

6 0

3 years ago