All categories

3 years ago

55 POINTS AVAILABLE!!

Mathematics

2 answers:

Kobotan [32]3 years ago

5 0

the height can be given as

AB = a sin theta

here a = 4 and theta is 60 so

AB = 4 sin 60 = 4 × √3/2 = 2√3

so area of a parallelogram is

= base × height

= 7 × 2√3 = 14√3

Len [333]3 years ago

3 0

Answer:

Your answer is 7 × 2√3 = 14√3

Step-by-step explanation:

You might be interested in

A 250-gal tank is initially filled with brine (salt-water mixture) containing 100 lb of salt. Brine containing 3 lb of salt per

gulaghasi [49]

Answer:

x(t) = 581.66 lb

Step-by-step explanation:

From the given information:

Consider the salt quantity in the tank at time t be x(t) lb.

∴ the rate of change of salt content in the tank is $\dfrac{dx}{dt}= Rate \ of \ \ inflow - rate \ of \ \ outflow$

where:

the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons

=21 lb/s

rate of outflow = salt conc. in the tank × flow rate

= x/250 × 9

= 9x/250 lb/s

∴

$\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}$

$\dfrac{dx}{dt} + \dfrac{9x}{250}= 21$

This is a 1st order linear differentiation,

The integrating factor if $e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}$

∴

$e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C$

$e^{^{ \dfrac{9t }{250}}} \ \ x(t) = 21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C$

$x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}$ at t = (0) and x(0) = 100 lb

Hence;

$100 = \dfrac{1750}{3}+C$

$C = \dfrac{1750}{3} -100$

$C = - \dfrac{1450}{3}$

∴ $x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}$

after time t = 1 minute i.e 60 s

$x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}$

$x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}$

x(t) = 581.66 lb

5 0

3 years ago

Moe puts $1500 in a bank certificate that pays an annual rate of 4.5% compounded annually. No withdrawals or deposits are made.

SpyIntel [72]

Answer:

FV= $2,041.29

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $1,500

Number of periods (n)= 7 years

Interest rate (i)= 4.5% = 0.045

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

FV= 1,500*(1.045^7)

FV= $2,041.29

6 0

3 years ago

Find the volume of a half sphere with a radius of 10

Ugo [173]

The volume of a sphere is calculated like so:
v = 4*pi*r^3/3
so half sphere will have half that volume:
v = (4*pi*r^3/3)(1/2)
v = 4*pi*r^3/6
plug in the data:
v = 4*pi*(10)^3/6
v = 2094.4
that is the volume of the half sphere

7 0

3 years ago

Find the height of a cylinder with radius 13 and surface area 1470.3.

g100num [7]

First you need the formula for SA of a cylinder: SA = 2(πr^2) + 2πr*h
(area of the top and bottom circles plus the side)
Then plug your values into the equation and rearrange to make h the subject:
1470.3 = 2π13^2 + 2π*13*h
26πh = 1470.3 - 338π
h = (1470.3 - 338π)/26π
=5.00042...
so h is approximately 5 units :)

8 0

3 years ago

Read 2 more answers

Which algebraic expression represents the phrase below? five times the sum of a number and eleven, divided by three times the su

anyanavicka [17]

The overall algebraic expression will be: $\frac{5(x+11)}{3(x+8)}$

Definition of algebraic expression -

An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

Five times the sum of a number and eleven, divided by three times the sum of the number and eight.

Let the number be x.

Five times the sum of a number and eleven means 5 multiplied to the sum of x and 11. In expression this will be written as:

5(x + 11)

Three times the sum of the number and eight means 3 multiplied to the sum of x and 8. In expression this will be written as:

3(x + 8)

So, the overall algebraic expression will be: $\frac{5(x+11)}{3(x+8)}$

Learn more about algebraic expression

brainly.com/question/953809

#SPJ4

3 0

1 year ago