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wariber [46]
2 years ago
11

Devon's uncle built for him a cube-shaped toy box. The box has a volume of 25 cubic feet. Devon wants to place the toy box again

st a wall and under a shelf that is 36 inches above the ground. Will the toy box fit? Explain your reasoning.
Mathematics
1 answer:
Tcecarenko [31]2 years ago
3 0

Answer:

a

Step-by-step explanation:

a)

(b)

(c)

Step-by-step explanation:

we are given

length is x+1

width is x+3

height is x-3

(a)

we can use volume formula

now, we can plug it

now, we can simplify it

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

now, we can factor it

(b)

we are given volume

so, we can set

and then we can solve for x

now, we can factor it

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Find the length of the following​ two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16
andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)}     dt

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)}     dt

Doing the operations inside of the brackets the derivatives are:

1 ) (\frac{d((1/2)t^2)}{dt} )^2= t^2

2) \frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1

Entering these values of the integral is

r(t)= \int\limits^{16}_{0}  \sqrt{t^2 +2t+1}     dt

It is possible to factorize the quadratic function and the integral can reduced as,

r(t)= \int\limits^{16}_{0} (t+1)  dt= \frac{t^2}{2} + t

Thus, evaluate from 0 to 16

\frac{16^2}{2} + 16

The value is r= 144 units

5 0
3 years ago
Which rational number equals 0.5 ?
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1/2 is equal to 0.5.

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3 years ago
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5(1)= 5; identity property of multiplication
(3+5)+0=(3+5); identity property of addition
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3+5=5+3; commutative property of addition
3+(5+7)=(3+5)+7; associative property for addition

hope this helps :)
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2 years ago
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