In a rhombus, the sides are 14 inches long. two intersecting sides form a 60 degree angle. what are the exact lengths of the two diagonals

Answers

Answer 1

Answer: Long Diagonal AD = Square Root (2•Side² + 2•Side² • cos(A) )
Long Diagonal AD = Square Root (2*14^2 + 2*14^2 * cos(60) )
Long Diagonal AD = Square Root ( 392 + 392*.5)
Long Diagonal AD = Square Root (392 + 196)
Long Diagonal AD = Square Root (588)
Long Diagonal AD = 24.248711306

Short Diagonal BC = Square Root (2•Side² - 2•Side² • cos(A) )
Short Diagonal AD = Square Root ( 392 - 392*.5)
Short Diagonal AD = Square Root ( 392 - 196)
Short Diagonal AD = Square Root (196)
Short Diagonal AD = 14

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Find the volume of a rectangular prism if the length is 3x2, the width is 2x, and the height is x2 + 3x + 5. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
5x^5 + 18x^4 + 30x^3
5x^6 + 18x^4 + 30x^3
6x^5 + 18x^4 + 30x^3
6x^6 + 18x^4 + 30x^3

Answers

You are given the length of arectangular prism of 3x^2, width of 2x and height of x^2 + 3x +5. You arerequired to find the volume of a rectangular prism. Using the equation V = l xw x h, we multiply the three dimensions.

V = l x w x h
V = (3x^2)(2x)( x^2 + 3x +5)
V = 2x (3x^4 + 9x^3 + 15x^2)
V = 6x^5 + 18x^4 + 30x^3
The volume of the rectangularprism is 6x^5 + 18x^4 + 30x^3.

A cosmetics company that makes small cylindrical bars of soap wraps the bars in plastic prior to shipping. Find the surface area of a bar of soap if the diameter is 5cm and the height is 2cm.

Answers

we would have two circles of 5cm diameter each, and a rectangle of the length pi*diameter and 2cm, so lets add them:
total = 2circles + rectangle
total = 2(2*pi*(5/2)^2) + pi*diameter*heigth
= 4*pi*(2.5)^2 + pi*5*2
= 109.9
that is the surface area of a bar soap 109.9 cm^2

The formula you use is pi x radius ^ 2 + pi x radius x l ( l stands for lateral height)
pi x 2.5^2 + pi x 2.5(2)
3.14 x 6.25 + 3.14 x 5
19.6 + 15.7
= 35.3 cm^2

I just need it simplified, thank you!
4>-x/4

Answers

Answer:

x>-16

Step-by-step explanation:

First

4> -x/4

switchsides

-x/4<4

then multipy both sides by 4

4(-x/4)<4*4

then multipy bothsides by -1 and reverse the inequality

(-x)(-1)> 16(-1)

How do you simplify this

Answers

You ALWAYS remove parentheses first.

That gives you [ 1/4 a⁴ b⁻² ] in the denominator, and then
you can start dividing the numerator and denominator by
their common factors ("canceling").

I think the answer to that might be 1/2 or .5ab^3 because I multiplied the bottom part -2*-2 which is 4ab^4 then the top part is 2ab -3+2= 2ab^-1 then divide 2/4 and subtract -1-4 so it's = 1/2 or .5ab^3

Dosha is creating a new dessert that has two layers shaped like cones. The inner cone is frozen ice cream and has a diameter of 12 cm and a height of 6 cm. The outer layer is a thin wafer shell, like an upside-down ice cream cone, with a height of 15 cm and the same diameter as the inner layer. Dosha will inject a cream filling into the space.What is the volume of the cream filling?
Use 3.14 to approximate pi and express your final answer in hundredths.

cm3

nvm.. it was 339.12 !

Answers

Given:
Inner cone: diameter = 12 cm ; height = 6 cm
Outer layer: diameter = 12 cm ; height = 15 cm

Volume of a cone = π r² h/3

Inner cone: V = 3.14 * (6cm)² * 6cm/3 = 3.14 * 36cm² * 2cm = 226.08 cm³
Outer layer: V = 3.14 * (6cm)² * 15cm/3 = 3.14 * 36cm² * 5cm = 565.20 cm³

Volume of Outer layer : 565.20 cm³
less: Volume of inner layer: 226.08 cm³
Volume of cream filling: 339.12 cm³

a Potter uses three fifths of a pound of clay to make a bowl how many bowls could the potter make from 10 pounds of clay

Answers

3/5 - 1 bowl
10 - x bowls

x=10/(3/5)=10*(5/3)=50/3= 16 2/3

He can make 16 bowls.

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The difference of a number and 4/ 3 is 11/3. what is the number

A fishery is an area with the specific purpose of controlling fish populationsfor commercial or recreational fishing. Population dynamics describe how afish population changs over time. The population is changed by birth, death,and migration of fish. While the supply of fish (population growth) can bemodeled with a linear equation, so can the demand of fish (the amount caught).In one commercial venture, fishermen recorded their daily catch in an oceanfishery. Using their data, the demand model for the total number y of fish caughtfor x days is y = 349x + 50. What is the meaning of the slope?

Simplity. (2+7) / (7/2 x 2)