Convert 7.23 to a fraction

Three forces act on a hook. Determine the magnitude of the resultant of the force.

Novay_Z [31]

Use Hooke's law... (just kidding)

Break down each force vector into horizontal and vertical components.

$\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y$

$\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y$

$\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y$

The resultant force is the sum of these vectors,

$\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y$

and has magnitude

$|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N$

The closest answer is D.

5 0

2 years ago

Find radius of a hemisphere given volume of 144 cm³

marysya [2.9K]

Answer:

The radius is 4.097396898

Step-by-step explanation:

A hemisphere is 1/2 of a sphere so the volume is 1/2 of the volume

V = 1/2 ( 4/3 pi r^3)

= 2/3 pi r^3

144 = 2/3 pi r^3

Multiply each side by 3/2

3/2 *144 = 3/2 * 2/3 pi r^3

216 = pi r^3

Divide each side by pi

216/ pi = pi r^3/pi

68.78980892 = r^3

Take the cube root of each side

(68.78980892 )^1/3= (r^3)^1/3

4.097396898 = r

The radius is 4.097396898

8 0

3 years ago

WORTH 50 points pls answer.<br> The two polygons are similar. Find the values of x and y

Digiron [165]

Answer:

y = 120

x = 10.6

Step-by-step explanation:

Given polygons are parallelograms.

In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.

Since two parallelograms are similar:

60 + y = 180 subtract 60 from both sides

y = 120

To find the value of x:

side lengths are proportional because these are similar polygons

$\frac{x+4}{22} = \frac{12}{18}$ cross multiply fractions

18x + 72 = 264 subtract 72 from both sides

18x = 192 divide both sides by 18

x = 10.6 approximately

6 0

1 year ago

0= -115<br> sin=<br> cos =<br> tan

Alina [70]

Answer:

Step-by-step explanation:

Tito wants to buy some peanut butter to donate as much as possible.

There some brands are given with their price.

we will calculate the price of per ounce peanut butter of each brand.

A. Nutty : 12 ounces for $2.19

cost per ounce =

= $0.1825 ≈ $0.18 per ounce

B. Grandma's : 18 ounces for $2.79

cost per ounce =

= $0.155 ≈ $0.16 per ounce

C. Bee's : 0.28 ounces for $4.69

cost per ounce =

= $16.75 per ounce

D. Save-A-Lot : 40 ounces for $6.60

cost per ounce =

= $0.165 ≈ $0.17 per ounce

The lowest price is $0.16 per ounce. So he should buy Grandma's peanut butter.

8 0

2 years ago

Are these two lines perpendicular?

lys-0071 [83]

Answer:

Step-by-step explanation:

This is the image of the graph you determine if that's perpendicular.

Perpendicular definition - In elementary geometry, the property of being perpendicular is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle.

6 0

2 years ago