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2 years ago

Find the distance between (3,7) and (6,5)

Mathematics

1 answer:

zubka84 [21]2 years ago

8 0

Answer:

square root of five but if it needs to be simplified then 2.24 (rounded)

Step-by-step

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

2 years ago

Help ASAP please

Agata [3.3K]

Answer:

55,000

Step-by-step explanation:

I already explained it on another problem but I'll show the equation again.

0.74x = 40,700

x = 55,000

7 0

3 years ago

Which visualization tool is more helpful for detecting outliers in data? Select one: a. scatter plot b. histogram c. Boxplot

Tpy6a [65]

Answer:

(A) Scatterplot

Step-by-step explanation:

The most helpful visualization to spot outliers would be a scatterplot.

When collecting data on a scatterplot, you can see how the results are similar and which areas have the most answers and such.

There can be multiply outliers on a scatterplot, and they stand out because while most answers will be clumped together, the outliers will not.

7 0

3 years ago

11x + x helppp plzzz

Juliette [100K]

This answers would be 12x

4 0

2 years ago

Use the net as an aid to compute the surface area of the triangular prism. A) 112 m2 B) 136 m2 C) 160 m2 D) 184 m2

Aloiza [94]

Answer:

136 m2 Option c

Step-by-step explanation:

136 m2

1 base = 6 × 7 = 42

2 sides = 2(7 × 5) = 70

2 triangles = 2(6 × 4

) = 24

SA = 42 + 70 + 24 = 136 m2

7 0

2 years ago

Read 2 more answers