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Anarel [89]

2 years ago

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Mathematics

1 answer:

Arte-miy333 [17]2 years ago

8 0

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

Question : 1

weight of microbe in a test tube is 0.001 g,

weight of 456 such test tubes :

$456 \times 0.001$

$456 \times \dfrac{1}{1000}$

$\dfrac{456}{1000}$

$0.456$

weight of microbes in 456 such test tubes is :

456 g

Question : 2

One crate weights 32.5 kg

the, 100 crates weight :

$32.5 \times 100$

$3250 \: kg$

Question : 3

3. Push ups in one day - 53

push ups in 10 days :

$53 \times 10$

$530 \: \: push \: \: ups$

Question : 4

1 metal ball weights 5727 kg,

so, 100 metal balls weight :

$100 \times 5727$

$572700 \: \: kg$

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Find the roots for the above given quadratic equation. Please show the working too.

Mars2501 [29]

Step-by-step explanation:

$9x^{2} - 9 (a + b)x + 2a^{2} + 5ab + 2b^{2} = 0\\9x^{2} - 3[(3a + 3b)]x + 2a^{2} + 4ab +ab + 2b^{2} = 0\\9x^{2} - 3[(a + 2b) + (2a + b)]x + 2a[a + 2b] + b [a + 2b] = 0\\9x^{2} - 3(a + 2b)x - 3 (2a + b) + (a + 2b)(2a + b) = 0\\3x [3x - (a + 2b)] -(2a + b)[3x - (a + 2b)]=0\\\:\: [3x - (a + 2b)] - [3x - (2a + b)] = 0\\\\\\\\\circ\:3x - (2a + b) = 0\\\boxed{\underline{x = \frac{2a + b}{3} }}\\\\\\\\\circ\:3x - (2a + b) = 0\\\boxed{\underline{x = \frac{a + 2b}{3} }}$

So, the roots are:

1) x = 2a + b/3

2) x = a + 2b/3

_________

Hope it helps!

◇ Please refer to the attachment if the latex code shows some error.

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6 0

2 years ago

Read 2 more answers

A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

goldfiish [28.3K]

Answer:

wire for square to maximize total area = 23 m

Wire to minimize total area = 2.019 m

Step-by-step explanation:

For the square, let's say the total length of the square is "y" m.

Thus, length of one side is = y/4

And area of the square = (y/4) = y²/16

Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.

Thus, length of one side of equilateral triangle = (23 - y)/3

Using trigonometric ratio, we can find the height of the triangle and thus area.

Area of triangle = (√3)/4) × ((23 - y)/3)²

Area of triangle = (√3)/36)(23 - y)²

So, total area of square and triangle is;

A_total = (y²/16) + (√3)/36)(23 - y)²

Now, extremizing this function by derivatives, we have;

dA/dy = (y/8) - (√3)/18)(23 - y)

d²A/dy² = ⅛ + (√3)/18)

So, d²A/dy² > 0

Now,let's find the maximum or minimum of the function.

So, we equate dA/dy to zero.

Thus;

(y/8) - (√3)/18)(23 - y) = 0

y/8 = (√3)/18)(23 - y)

(y/8) + (√3)/18)y = 23((√3)/18)

Multiply through by 8 to give;

y + 0.0962y = 2.2132

1.0962y = 2.2132

y = 2.2132/1.0962

y = 2.019 m

2.019 will be a minimum because d²A/dy² > 0

The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.

Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.

6 0

3 years ago

john found a pair of jeans that cost $55.00. If he had a 10%-off coupon, how much would the jeans cost?

mash [69]

THE ANSWER IS 49.50

Because if you divide 55 and 10 it gives you 5.5. So with that answer you just subtract to the price of the jeans giving you 49.50

6 0

3 years ago

Read 2 more answers

How do you find the percent of increase from 12 to 18?

olga nikolaevna [1]

Let's get the data out of the problem:

Nv = 18

Ov = 12

Now, we can apply in this equation that relates the new and the old values:

i = Nv / Ov

i = 18 / 12

i = 1.5

Now, we just consider what has passed from 1, and this is 0.5, converting to percentage it is:

p = 0.5 . 100

p = 50%

The increase was 50%.

Hope it helps.

4 0

2 years ago

Use the operation signs +,-, x, and ⌯ once each in the expression below to make the number sentence true. Why does your answer m

Zepler [3.9K]

Answer:

$6 * (3 - 1) + 5 \div 1 = 17$

Step-by-step explanation:

Given

$6\ [\ ]\ (\ 3\ [\ ]\ 1\ )\ [\ ]\ 5\ [\ ]\ 1\ =\ 17$

Required

Fill in the box with +,-, x, and ⌯ (once each)

This question is solved using trial by error approach.

After some tests, the solution that matches the equation is:

$6 * (3 - 1) + 5 \div 1 = 17$

6 0

2 years ago