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vlabodo [156]
3 years ago
11

Expression is not equivalent to (1 − sin2(x)) tan(-x).

Mathematics
1 answer:
Hitman42 [59]3 years ago
7 0
Are You trying to find out the equivalent expression? or...
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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by
a_sh-v [17]

Answer:

Dimension of the box is 16.1\times 7.1\times 2.45

The volume of the box is 280.05 in³.

Step-by-step explanation:          

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is L=21-2h

The width of the box is W=12-2h

The volume of the box is V=L\times W\times H

V=(21-2h)\times (12-2h)\times h

V=(21-2h)\times (12h-2h^2)

V=252h-42h^2-24h^2+4h^3

V=4h^3-66h^2+252h

To maximize the volume we find derivative of volume and put it to zero.

V'=12h^2-132h+252

0=12h^2-132h+252

Solving by quadratic formula,

h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}

h=\frac{132\pm72.99}{24}

h=2.45,8.54

Now, substitute the value of h in the volume,

V=4h^3-66h^2+252h

When, h=2.45

V=4(2.45)^3-66(2.45)^2+252(2.45)

V\approx 280.05

When, h=8.54

V=4(8.54)^3-66(8.54)^2+252(8.54)

V\approx -170.06

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is L=21-2(2.45)=16.1

The width of the box is W=12-2(2.45)=7.1

So, Dimension of the box is 16.1\times 7.1\times 2.45

6 0
3 years ago
there are 4 aces and 4 kings in a standard deck of 52 cards. you picking card random. what is the probability of selecting an ac
Mkey [24]
Probability of an Ace= 4/52
Probability of a King = 4/52

Probability of an Ace or a King = P(Ace) + P(King)
=4/52 +4/52
=8/52
=2/13

8 0
3 years ago
Please what is the answer for <br> 2:3q+1:4q=20
zhuklara [117]

Answer: Q=240/11

Step-by-step explanation:

3 0
3 years ago
please help me it is URGENT pls the first one is solve and the 2nd one is simplify I will give u lots of points thank you
klasskru [66]
I.) (5x+3)/4-(2x-4)/3=5
Clear fractions:
3·((5x+3)/4)=15x+9
4·((2x-4)/3)=8x-16
15x+9-(8x-16)=5
15x+9-8x+16=5
Combine like terms:
7x+25=5
7x=-20
x=-20/7

II.) (3/11)·(5/6)-(9/12)·(4/3)+(5/13)·(6/15)
Remember PEMDAS
So first multiply:
3/11·5/6=15/66
9/12·4/3=3/3·1/1=3/3=1
5/13·6/15=1/13·6/3=6/39=2/13
(15/66)-1+(2/13)
Combine:
15/66-1/1=15/66-66/66=-51/66
-51/66+2/3=-51/66+44/66=-7/66
Answer: -7/66 :)
7 0
3 years ago
Read 2 more answers
spencer surveyed five of his friends to find out how many pets they have his results are shown in the table lara has 3 cody has
Phantasy [73]
The mean is the average.
Add all the number of pets and divide by how many people there were.
3+5+2+4+1
15/number of people
15/5
=3

Hope this helps :)
4 0
3 years ago
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