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AleksandrR [38]
3 years ago
13

Complete the following statements.

Mathematics
1 answer:
masha68 [24]3 years ago
8 0
  • A conjunction is true only if both statements are true.

The conjunction is the AND logical operator, and the result of A AND B is true only when both A and B are true. For example, "We are on planet earth, and elephants fly" is false, even if the first part is actually true.

  • A disjunction is true if at least one statement is true

In fact, the disjunction is the OR operator, and this time one true statement is sufficient to make the whole expression true: "You are reading this answer on brainly or I am 4 meters tall" is true, although I'm not 4 meters tall.

  • For a conditional statement, a true hypothesis cannot imply a false conclusion

In fact, the latin expression "ex falso sequitur quodlibet" translates as "you can deduce whatever you want from a false premise". Using formulas, this means that the implication A \implies B is always true, no matter the truth value of B. So, both these implications

1+2 = 4 \implies \pi = 8

1+2 = 4 \implies 10-3=7

are true.

Conversely, if the hypothesis is true, then the implication is true only if the conclusion is true as well: if we change the previous example to

1+2 = 3 \implies \pi = 8

1+2 = 3 \implies 10-3=7

Only the second implication will hold.

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The market price of a house is directly proportional to the total area of the house in square feet. If the price of a 1,500 squa
IrinaK [193]

Answer:

The price of a 2,000 square foot home is \$400,000

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

Let

x -----> the total area of the house in square feet

y -----> the price of the house

we have

The point (1,500,300,000)

Find the constant of proportionality k

k=y/x

substitute

k=300,000/1,500=200

The direct equation is equal to

y=200x

so

For x=2,000\ ft^{2}

Find the value of y

substitute the value of x in the equation

y=200(2,000)

y=\$400,000

5 0
3 years ago
What is the slope of the line that passes through the points (1, 1) and (4, 4)?
gizmo_the_mogwai [7]

Answer:

The answer is 1

Step-by-step explanation:

Formula for finding the slope: \frac{y2-y1}{x2-x1}

Take y2 and y1 from (4,<u>4</u>) (1,<u>1</u>)

Take x2 and x1 from (<u>4</u>,4) (<u>1</u>,1)

\frac{y2-y1}{x2-x1}  = \frac{4-1}{4-1} = \frac{3}{3} = 1

This is how the answer is 1

Hope it helps :)

8 0
1 year ago
Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
irga5000 [103]

Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

Also, the conditions are

y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50

and

y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

8 0
3 years ago
Read 2 more answers
Using an ideal machine a worker exerts an effort force of 8.00 N to life a 2.95 kg weight a distance of 6:00 am over what distan
cestrela7 [59]

Answer:

29.5 ×6= 8×d

d = 29.5×6/8 = 22.12 m

3 0
3 years ago
cruising works three and a half hours every day and earns $12 per hour she works 5 days a week how much does Kevin earn in 4 wee
IRISSAK [1]
Kevin makes $840 in 4 weeks.

how much he makes per day $42
(3.5* 12= 42)

How much he makes per week
(42*5=210)
8 0
3 years ago
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