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2 years ago

7

Sam makes some read rolls. He gives 2/5 of the bread rolls to his neighbor and 4/9 of the remainder to his cousin. He has 15 bre

ad rolls left. How many bread rolls does Sam make?

1 answer:

blagie [28]2 years ago

4 0

2/5 + 4/9 +15 = 18+20+675/45 = 713/45 Answer: Sam made 713/45 or 15.84 bread rolls all in all.

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Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

$F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)$

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$

The magnitude force will be

$|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68$

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

$\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469$

The angle formed by F and y axis

$\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=$

The angle formed by F and z axis

$\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359$

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1 year ago

An angle t is drawn from the center of the unit circle. Find a formula in terms of t for the straight line distance d between th

Doss [256]

Answer:

$d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}$

Step-by-step explanation:

Let suppose that one of the radii meets the circle at the point (1,0). The straight line distance formula is:

$d = \sqrt{(\cos t - 1)^{2}+(\sin t - 1)^{2}}$

$d = \sqrt{(\cos^{2}t - 2\cdot \cos t + 1)+(\sin^{2}t - 2\cdot \sin t + 1)}$

$d = \sqrt{2-2\cdot (\cos t + \sin t )}$

$d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}$

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1 year ago

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble. The original statue in V

vagabundo [1.1K]

Answer:

0.08 cubic feet.

Step-by-step explanation:

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble.

The original statue in Vienna is 7 feet tall.

First we will convert this to inches as one relation is given in inches.

1 feet = 12 inches

7 feet = $12\times7=84$ inches

Let the amount of marble used for 84 inches statue be = x

We can relate both the conditions in the following way:

$\frac{10}{16} =\frac{84}{x}$

$10x=16\times84$

$10x=1344$

x = 134.40 cubic inches

Now, 1 cubic inch = $\frac{1}{1728}$ cubic foot

So, 134.40 cubic inches = $\frac{134.40}{1728}$ cubic foot

= 0.0777 cubic feet rounding to 0.08 cubic feet.

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2 years ago

What is the product? (-2x-9y^2)(-4x-3)

telo118 [61]

Answer:-8x^2-6x+36xy^2+27y^2

Step-by-step explanation:

using the FOIL method

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2 years ago

Read 2 more answers

D(-3+x)=kx+9 solve for x

Gnesinka [82]

d(-3 + x) = kx + 9

Distribute d inside the parentheses.

-3d + dx = kx + 9

Subtract kx from both sides.

-3d + dx - kx = 9

Add 3d to both sides.

dx - kx = 9 + 3d

Factor x out of dx - kx.

x(d - k) = 9 + 3d

Divide both sides by d - k.

x = $\frac{9+3d}{d-k}$

If you want to simplify this even more, factor 3 out of the numerator.

<h3>x = $\frac{3(d + 3)}{d-k}$ </h3>

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2 years ago