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2 years ago

NEED HELP ASAP!!! Which of the following shows the prime factorization of 72 using exponential notation?

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

5 0

Answer:

D)2^3 x 3^2

Step-by-step explanation:

2 x 2 x 2 = 8

3 x 3 = 9

8 x 9 = 72

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Sergio ate 3.5 cookies. Each cookie contained 5.7 grams of sugar. How many grams of sugar did Sergio eat?

FrozenT [24]

I’ll get it correct here :)

He ate 19.95 grams of sugar.

3.5 x 5.7 = 19.95

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3 years ago

Please help me finish passing

Leto [7]

Answer:

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2 years ago

Find the volume of the wedge with vertices at points (0,0,0), (1,0,0), (0,1,0), (0,0,1) by integrating the area of cross-section

Angelina_Jolie [31]

Answer:

V = 1/6 cubic units

Step-by-step explanation:

Applying the concept of integrals for volume calculation:

$V = \int\limits^b_a {S(x)} \, dx$ (1)

V = volume of the solid bounded by x = a and x = b

S(x) = cross section area of the solid, perpendicular to the x axis

From the figure we have that S is the area of a triangle that has base Z and height Y

Area of the triangle = $S(x)=\frac{y(x)*z(x)}{2}$ (2)

Calculation of y(x) and z(x)

We apply the equation of the point-slope line (plane xy):

Slope = $m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$ (3)

Equation of the line = $y - y_{1} =m(x-x_{1} )$ (4)

Replacing the points (1,0) and (0,1) in (3):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (4):

$y-0=(-1)(x-1)$

y(x) = -x + 1 (Line A-B) (5)

We apply the equation of the point-slope line (plane xz):

Slope = $m = \frac{z_{2} - z_{1} }{x_{2} - x_{1}}$ (6)

Equation of the line = $z - z_{1} =m(x-x_{1} )$ (7)

Replacing the points (1,0) and (0,1) in (6):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (7):

$z-0=(-1)(x-1)$

z(x) = -x + 1 (Line A-C) (8)

Replacing (5) and (8) in (2)

$S(x) = \frac{(-x + 1) * (-x + 1)}{2} =\frac{(-x + 1)^{2} }{2}$ (9)

Replacing (9) in (1) and knowing that a = 0 and b = 1:

$V = \int\limits^1_0 {\frac{(-x + 1)^{2} }{2}} \, dx = \int\limits^1_0 {\frac{x^{2}-2x+1 }{2}} \, dx$

$V =\frac{1}{2} (\frac{x^{3} }{3} -2\frac{x^{2} }{2} +x)$ evaluated from x=0 to x=1

$V= \frac{1}{2} (\frac{1}{3} -1 +1) = \frac{1}{6}$

3 0

3 years ago

Evaluate the expression for a^2 + b ÷3 when a = 3 and b = 6

Flura [38]

Answer:

Step-by-step explanation:

3^2 + 6/3

9 + 2

8 0

3 years ago

What is the best estimate for the length of a baseball bat?

vredina [299]

Answer:

42 inches

By regulation it may be no more than 2.75 inches (7.0 cm) in diameter at the thickest part and no more than 42 inches (1.067 m) in length.

Step-by-step explanation:

baseball bat - is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher.

length- a measure of distance.

3 0

3 years ago