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2 years ago

Find two numbers that multiply to make the 1st number and add to make the 2nd number. Multiply -42; Add 1 _, and _

Mathematics

1 answer:

dedylja [7]2 years ago

5 0

Answer:

-6 and 7

Step-by-step explanation:

It is useful to look at the factor pairs of -42.

-42 = -1(42) = -2(21) = -3(14) = -6(7)

Sums of these factor pairs are 41, 19, 11, 1.

You want the last pair of factors: -6 and 7.

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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

Triangle STU is located at S (2, 1), T (2, 3), and U (0, −1). The triangle is then transformed using the rule (x−4, y+3) to form

sp2606 [1]

Triangle STU is located at : S(2,1) , T(2,3) and U(0,-1)

transformation rule : (x - 4, y + 3)

so S' is : (2 - 4 , 1 + 3) = (-2,4) <==
and T' is : (2 - 4, 3 + 3) = (-2,6) <==
and U' is : (0 - 4, -1 + 3) = (-4,2) <==

4 0

3 years ago

Read 2 more answers

The number of miles driven varies directly with the number of gallons of gas used. If 8 gallons of gas are used to drive 204 mil

Alik [6]

Answer:

3672

Step-by-step explanation:

If 8 gallons of gas were used to drive 204 miles multiply 18x204=3,672 miles

8 0

2 years ago

Graph the equation below by plotting the y-intercept and a second point on the line. (Zoom in if blurry)

pishuonlain [190]

Answer:

The coordinates I chose are (0,-4) and (-2,0)

Step-by-step explanation:

7 0

3 years ago

The midpoint of UV is M(8,1). One endpoint is U(10,2). Find the coordinates of the other

nadya68 [22]

(10 + a / 2, 2 + b / 2) = (8, 1)

10 + a / 2 = 8
10 + a = 16
a = 6

2 + b / 2 = 1
2 + b = 2
b = 0

so V(6, 0)

8 0

2 years ago

Find two numbers that multiply to make the 1st number and add to make the 2nd number. Multiply -42; Add 1 _____, and _____

Find two numbers that multiply to make the 1st number and add to make the 2nd number. Multiply -42; Add 1 _, and _