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4 years ago

13.

Mathematics

2 answers:

RUDIKE [14]4 years ago

8 0

Answer: $2,596 cm^2$

Step-by-step explanation:

Given dimensions of rectangular prism :

length: 8 cm

width: 13 cm

height: 10.5 cm

If all the dimensions of the prism are doubled, then the new dimensions will be:

length: 16 cm

width: 26 cm

height: 21 cm

The surface area of rectangular prism is given by :-

$S.A.=2(lw+wh+hl)\\\\\Rightarrow\ S.A.=2(16*26+26*21+21*16)\\\\\Rightarrow\ S.A.=2,596 cm^2$

Hence, its new surface area $2,596 cm^2$

svetlana [45]4 years ago

7 0

The answer is 2,596 so it would be C

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Antonio earns $6 an hour helping his grandmother. Write and solve an equation to find out how many hours she needs to work to ea

Ilia_Sergeevich [38]

48/6 = 8 (just divide)
ANSWER: $8

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3 years ago

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Step-by-step explanation:

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3 years ago

Consider points A(1, 6) and B(8, 8). Find point C on the x-axis so AC +BC is a minimum.

Kay [80]

Answer:

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

Step-by-step explanation:

The given coordinates of the points A and B are A(1, 6) and B(8, 8)

The location of the point C = The x-axis

Therefore;

The coordinates of the point C = (x, 0)

The length of the segment AC = √((1 - x)² + (6 - 0)²) = √((1 - x)² + 6²)

The length of the segment BC = √((8 - x)² + (8 - 0)²) = √((8 - x)² + 8²)

At minimum distance of AC + BC, we have;

d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = (1 - x) × 2 × (0.5 - 1)× (√((1 - x)² + 6²)^(0.5 - 1) + (8 - x) × 2 × (0.5 - 1)× √((8 - x)² + 8²)^(0.5 - 1)

∴ d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = -(1 - x)/√((1 - x)² + 6²) - (8 - x)/√((8 - x)² + 8²)

-(1 - x)/√((1 - x)² + 6²) = (8 - x)/√((8 - x)² + 8²)

(8 - x)·√((1 - x)² + 6²) = -(1 - x)·√((8 - x)² + 8²)

Squaring both sides gives;

(8 - x)²·((1 - x)² + 6²) = (1 - x)²·((8 - x)² + 8²)

Expanding, using an online tool, we get;

x⁴ - 18·x³ + 133·x² -720·x + 2368 = x⁴ - 18·x³ + 161·x² - 272·x + 128

Which gives;

(161 - 133)·x² - (272 - 720)·x + 128 - 2368 = 28·x² + 448·x - 2240 = 0

Dividing by 28 gives;

x² + 16·x - 80 = 0

(x + 20)·(x - 4) = 0

Therefore, x = -20 or x = 4

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

4 0

3 years ago

Is the z score corresponding to a number or score below the mean always negative?

rusak2 [61]

Answer:

Yes

Step-by-step explanation:

The z-score corresponding to a number or score can be calculated using:

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Where x stands for the individual scores, and

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Since

$x \: \: < \: \mu$

for all numbers or scores below the mean, the difference will always be negative these values below the mean.

This will always result in a negative z-score for all numbers below the mean.

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4 years ago