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EastWind [94]
2 years ago
10

10 < 3 (r-3) + 1 Round Decimals to the nearest hundredth place

Mathematics
1 answer:
hjlf2 years ago
7 0

Answer:

r>6

Step-by-step explanation:

10<3r+3 x -3+1

Solve by distributing:

10<3r-9+1

Simplify the arithmetic:

10<3r-8

Simplify the arithmetic:

3r-8>10

Add  8 to both sides:

3r-8+8>10+8

Simplify the arithmetic:

3r>10+8

Simplify the arithmetic:

3r>18

Divide both sides by 3:

3r/3 > 18/3

Simplify the fraction:

r>18/3

Find the greatest common factor of the numerator and denominator:

r> 6x3/1x3

Factor out and cancel the greatest common factor:

r>6

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Find the volume of the solid under the plane 5x + 9y − z = 0 and above the region bounded by y = x and y = x4.
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<span>For the plane, we have z = 5x + 9y

For the region, we first find its boundary curves' points of intersection.
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Since x > x^4 for y in [0, 1],

The volume of the solid equals

\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx  \\  \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx  \\  \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\  \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0

=\frac{19}{6} - \frac{5}{6} - \frac{1}{2} =\bold{ \frac{11}{6} \ cubic \ units}</span>
8 0
3 years ago
What is  5.63×10−6in decimal form?a. 0.00000563 b. 0.000000563 c.5,630,000d. 56,300,000
Lelu [443]

5.63 \times  {10}^{ - 6}

To convert into decimal, move the decimal to the left by 6 positions.

It will be 0.00000563

Answer is A.
3 0
3 years ago
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