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3 years ago

9

A recipe for punch requires 20 grams of drink mix for 5 liters of water how many grams of drink mix are needed per liter of wate

r

1 answer:

tester [92]3 years ago

3 0

20/5
4 grams per liter of water

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A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

3 years ago

Dwayne's garden is triangle-shaped with two equal sides and a third side that is 4 ft more than the length of an equal side. The

poizon [28]

D because its a triangle so it would be 3x but then you have to add the 4 for the longer side.

8 0

3 years ago

Un vehiculo parte del reposo con una velocidad constante de 2 m/seg 2 y se mueve durante 5 segundos, su desplazamiento durante e

Andreas93 [3]

Answer:

The BLM presents awards to companies that minimize negative effects on the environment while mining natural resources. One such award is called the Hardrock Mineral Environmental Award. The BLM awards it to the mining company that has best fulfilled federal, state, or local requirements with little help from government agencies.

How does giving this award help the BLM more effectively manage land resources?

It prevents the companies from mining land resources such as gold and coal.

It informs companies about which minerals can be mined and which cannot be mined.

It encourages companies to follow rules set by government agencies.

It educates the companies about ways hard rock mining can destroy land resources.

7 0

3 years ago

Can someone help me plzzzzzz

Alex

Big rectangle
3x-4 (2x+2) = 6x^2-8x+6x-8
=6x^2-2x-8 = 3x^2-x-4

Small rectangle
(X-3) (x-6) = x^2-3x-6x+18
=x^2-9x+18

Big-small= 2x^2+8x-22 is the area of the shaded region

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3 years ago

7. What is the cardinality of each of the following sets?

zysi [14]

Answer:

The cardinality of set (a) is 0,

the cardinality of set (b) is 1

and

the cardinality of set (c) is 3.

Step-by-step explanation: We are given to find the cardinality of each of the following sets :

(a) { }.

(b) { { } }.

(c) {a, {a}, {a, {a}} }.

We know that

CARDINALITY of a set is the number of elements present in the set.

(a) The given set is A = { }.

The set A is an empty set, so it does not contain any element. Hence, the cardinality of the set A is 0.

(b) The given set is B = { { } }.

The set is B is singleton set, contains only one element (that is empty set). So, the cardinality of the set B is 1.

(c) The given set is C = {a, {a}, {a, {a}} }.

The set C has three elements, a, the set {a} and the set {a, {a}}. So, the the cardinality of set C is 3.

Thus,

the cardinality of set (a) is 0,

the cardinality of set (b) is 1

and

the cardinality of set (c) is 3.

8 0

3 years ago