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2 years ago

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What is the exact value of BC?A. 3.16B. 5\|2C. 7.07D. 25

1 answer:

Natalija [7]2 years ago

3 0

Answer:

$C. \: \: 7.07$

Step-by-step explanation:

Coordinates of B are

$(5,5)$

Coordinates of C are

$(4, - 2)$

Distance between two points

$\sqrt{({x_2 - x _1 {)}^{2} + (y_2 - y_1 {)}^{2} }}$

Distance of BC

$\sqrt{(4 - 5) {}^{2} + ( - 2 - 5 {)}^{2} }$

$\sqrt{ { (- 1}^{2}) + ({ - 7}^{2}) }$

$\sqrt{1 +49 }$

$\sqrt{50}$

$7.07$

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A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 34.5 ft3. what dimensions

____ [38]

Answer:

$l \approx 3.3\,ft$ , $x = 3.2\,ft$

Step-by-step explanation:

The equations of volume and surface area are presented below:

$34.5 = l^{2}\cdot x$

$A_{s} = 2\cdot l^{2} + 4\cdot l \cdot x$

The length of the tank is:

$x = \frac{34.5}{l^{2}}$

The expression fo the surface area is therefore simplified into an univariable form:

$A_{s} = 2\cdot l^{2} + 4\cdot \left(\frac{34.5}{l} \right)$

$A_{s} = 2\cdot l^{2} + \frac{138}{l}$

The first and second derivatives of the expression are, respectively:

$A_{s}' = 4\cdot l -\frac{138}{l^{2}}$

$A_{s}'' = 4 +\frac{276}{l^{3}}$

The first derivative is equalized to zero and length of the square side is now found:

$4\cdot l -\frac{138}{l^{2}} = 0$

$4\cdot l^{3}-138 = 0$

$l^{3} = \frac{138}{4}$

$l = \sqrt[3]{\frac{138}{4} }$

$l \approx 3.3\,ft$

Now, the second derivative offers a criteria to determine if solution leads to an absolute minimum:

$A_{s}'' = 4 + \frac{276}{(3.3\,ft)^{3}}$

$A_{s}'' = 11.7$ (Absolute minimum)

The depth of the tank is:

$x = \frac{34.5\,ft^{3}}{(3.3\,ft)^{2}}$

$x = 3.2\,ft$

6 0

3 years ago

Help math<br>look at pic

Sloan [31]

Answer: $\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Step-by-step explanation:

<u>Given the system of equation</u>

$1)~y=-(x+2)^2+1$

$2)~y=2x+5$

<u>Expand the parenthesis of the 1) equation</u>

$y=-(x+2)^2+1$

$y=-(x^2+4x+4)+1$

$y=-x^2-4x-4+1$

$y=-x^2-4x-3$

<u>Current System</u>

$1)~y=-x^2-4x-3$

$2)~y=2x+5$

<u>Substitute the y value of the 1) equation with the 2) equation</u>

$2x+5=-x^2-4x-3$

<u>Add ( x² + 4x + 3) on both sides</u>

$2x+5+(x^2+4x+3)=-x^2-4x-3+(x^2+4x+3)$

$2x+5+x^2+4x+3=0$

<u>Combine like terms</u>

$x^2+2x+4x+5+3=0$

$x^2+6x+8=0$

<u>Factorize the quadratic equation</u>

$(x+4)(x+2)=0$

$x=-4~\text{or}~x=-2$

<u>Substitute the x values into one of the equations to find the y value</u>

$y=2x+5$

$y=2(-4)+5=-8+5=-3$

$y=2(-2)+5=-4+5=1$

<u>Therefore, the two solutions are:</u>

$\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

2 years ago

Who has a constant rate of pay

Setler79 [48]

Answer:

Jane has a constant rate of pay because her earnings go up by 12 every unit of time.

7 0

3 years ago

Please help quickly I don’t understand

bekas [8.4K]

Answer:

15y^5

Step-by-step explanation:

Formula for the area of a rectangle is length times width.

so in this case, it would be 15y^5!! Trust me I just did this!

5 0

3 years ago

Read 2 more answers

-3/5x - 7/20x + 1/4x= -56

romanna [79]

Answer:

x = 80

Step-by-step explanation:

Combine − 3/5x and 7/20x to get -19/20x.

Then combine -19/20x and 1/4x and you get -7/10x.

Then you multiply both sides by -10/7 which is the reciprocal of -7/10.

Make -56(-10) one fraction.

Multiply -56 and -10 and you get 560.

Then divide 560 by 7 to get 80.

8 0

3 years ago

Read 2 more answers