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stellarik [79]
3 years ago
13

Simplify square root

Mathematics
1 answer:
ivolga24 [154]3 years ago
3 0
It’s the second one, here’s how I got the answer to it.

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A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides
ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

                                                         =(15-2x)(10-2x)x cubic inches

                                                         =(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=12, b= -100 and c=15

x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}

\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}

\Rightarrow x=0.1528,8.18

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, V''|_{x=0.1528}=24(0.1528)-100

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

4 0
3 years ago
Find the exact value of secθ if cscθ=-4/3 and the terminal side of θ lies in Quadrant III.
Anton [14]
Quadrant is III so, sign would be negative for Sec.
Now, we know, csc = H / P
So, H = 4, P = 3
Calculate for B, 
B² = H² - P²
B² = 4² - 3²
B² = 16 - 9
B = √7

We know, sec Ф = H / B = 4 / √7
We can write it as: -4√7 / 7  [ -ve sign for 3rd quadrant ]

In short, Your Answer would be Option B

Hope this helps!
6 0
3 years ago
The perimeter of a rectangular slab of concrete is 24 meters. If the length of the
sergejj [24]

perimeter = 2L +2W

the problem states the length ( L) is 2 meters longer then width, so L = w+2

so perimeter =2(w+2) +2w

24 = 2(w+2) +2w

24 = 2w+4 +2w

24 = 4w+4

20=4w

w=20/4 = 5

3 0
3 years ago
From the set {20, 38, 47}, use substitution to determine which value of x makes the inequality true.
vredina [299]
One way is to solve (it's easier)

x-9>29
add 9
x+9-9>29+9
x+0>38
x>38
just pick the numbers bigger than 38 as answer


47 is only number (38>38 is false)



answer is A

7 0
3 years ago
Which of the following equations has
Tju [1.3M]
The One With Inifinetely Many Solutions is D. 3x-5=-5+3x are both the same.Meaning that no matter Which Value u Put For X u will get the same Answer On Both Side
7 0
2 years ago
Read 2 more answers
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