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3 years ago

triangle abc is a right triangle. If AC = 4 and BC = 10, find AB. Leave your answer in simplest radical form.

Mathematics

1 answer:

kolbaska11 [484]3 years ago

3 0

The answer is 2 radical 21

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Express the measurement 4.29478416 kg with 8, 6, 4, and 2 significant figures

ira [324]

Significant figures refers to digits within a number which must be included in other depict correct quantity of the figure.

4.29478416 = 4.2947842 ( 8 significant figures)
4.29478416 = 4.29478 (6 significant figures)
4.29478416 = 4.295 ( 4 significant figures)
4.29478416 = 4.3 (2 significant figures)

To round a number to a certain number of significant figures,

Only leading 0 which comes before the decimal Point are regarded as insignificant.
Once the number of significant figures have been identified, the next number after this is either rounded up to 1 and added to the last value(if number is ≥5) or rounded to 0 (if number is less than 5)

Learn. More : brainly.com/question/13386983?referrer=searchResults

3 0

2 years ago

An animals heart beats 80 beats per minute how many minutes does it take to beat a million times?

Klio2033 [76]

The key calculation in this problem is figuring out <em>how many times 80 goes into 1,000,000</em>. I'll build up in steps here.

80 x 5 = 400. This gives us a building block on our way to 1,000,000. From here, we can go further and say that 400 x 5 = 2,000; that 2,000 x 5 = 10,000; and finally that 10,000 x 100 = 1,000,000. Altogether, starting from 80, that's

80 x 5 x 5 x 5 x 100 = 80 x 25 x 500 = <em>80 x 12,500</em>

So, since 80 goes into one million 12,500 times, it takes 12,500 minutes for the animal's heart to beat that 1,000,000 times.

4 0

2 years ago

Is this a complementary ,linear pair,vertical or adjacent?

Simora [160]

Step-by-step explanation:

Adjacent angles.

......

3 0

2 years ago

Read 2 more answers

A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru

Viktor [21]

Answer:

1) $S = 2\cdot w\cdot l - 8\cdot x^{2}$ , 2) The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$ , 3) $S = 176\,in^{2}$ , 4) $x \approx 4.528\,in$ , 5) $S = 164.830\,in^{2}$

Step-by-step explanation:

1) The function of the box is:

$S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)$

$S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w$

$S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x$

$S = 2\cdot w\cdot l - 8\cdot x^{2}$

2) The maximum cutout is:

$2\cdot w \cdot l - 8\cdot x^{2} = 0$

$w\cdot l - 4\cdot x^{2} = 0$

$4\cdot x^{2} = w\cdot l$

$x = \frac{\sqrt{w\cdot l}}{2}$

The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$

3) The surface area when a 1'' x 1'' square is cut out is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}$

$S = 176\,in^{2}$

4) The size is found by solving the following second-order polynomial:

$20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}$

$20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}$

$8\cdot x^{2} - 164\,in^{2} = 0$

$x \approx 4.528\,in$

5) The equation of the box volume is:

$V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x$

$V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x$

$V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}$

$V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}$

$V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}$

The first derivative of the function is:

$V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}$

The critical points are determined by equalizing the derivative to zero:

$12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0$

$x_{1} \approx 4.952\,in$

$x_{2}\approx 1.548\,in$

The second derivative is found afterwards:

$V'' = 24\cdot x - 78\,in$

After evaluating each critical point, it follows that $x_{1}$ is an absolute minimum and $x_{2}$ is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

$x \approx 1.548\,in$

The surface area of the box is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}$

$S = 164.830\,in^{2}$

4 0

2 years ago

What is the elimination of 20x+5y=120 and 10x+7.5=80

Grace [21]

20x+5y=120
10x+7.5y=80 multiply this one by 2
___________

20x+5y=120
20x+15y=160 subtract

___________

-10y=-40 divide both sides by -10
____________

y=4

20x+5(4)=120 plug 4 in for y in the first equation
20x+20=120 multiply
20x=100 subtract
x=5 divide to find x

5 0

3 years ago