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2 years ago

For the given true statements, what can you conclude using the Law of Syllogism?

Mathematics

1 answer:

musickatia [10]2 years ago

5 0

Answer: If a quadrilateral is a square, then it is a rectangle. (choice D.)

Step-by-step explanation:

The Law of Syllogism states that if the following two statements are true: If p , then q . If q , then r . Then we can derive a third true statement: If p , then r .

We can apply this rule in the conditional statements:

If a quadrilateral is a square, (p) then it has four right angles. (q)

If a quadrilateral has four right angles, (q) then it is a rectangle. (r)

Therefore:

If a quadrilateral is a square, (p) then it is a rectangle. (r)

I hope this helps!

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6,500 acres of a 41,000 acre forest burned in a fire. what percentage of forest was damaged?

Tems11 [23]

Answer:

15.85%

Step-by-step explanation:

Given:

Acres damaged (burned) = 6,500 acres

Acres in total forest = 41,000 acres

Hence the amount of damaged forest as a fraction of the total forest,

= $\frac{6500}{41000}$ = $\frac{13}{82}$

expressed as percentage = $\frac{13}{82}$ x 100% = 15.85%

8 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a

8090 [49]

Answer:

C. 14 metres cubed

Step-by-step explanation:

The volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius, while the volume of a cylinder is denoted by: $V=\pi r^2h$ , where r is the radius and h is the height.

Here, we know that the sphere and cylinder have the same radius and height. However, the "height" of the sphere is technically just the diameter, which is twice the radius. So, h = 2r. We know the volume of the cylinder is 21, so:

$V=\pi r^2h=\pi r^2*2r=2\pi r^3$

$21=2\pi r^3$

πr³ = 21/2 = 10.5

Now plug this into the volume of a sphere formula:

$V=\frac{4}{3} \pi r^3$

$V=\frac{4}{3} *10.5=14$

The answer is C, 14 metres cubed.

5 0

3 years ago

Read 2 more answers

Please help and tell me how you got your answer

svlad2 [7]

It’s 6x6=36, because if 4 over 2 was 4 twice then 6 over 2 is 6 twice.

3 0

3 years ago

Read 2 more answers

If x^2y-3x=y^3-3, then at the point (-1,2), (dy/dx)?

zavuch27 [327]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2866883

_______________

 dy
Find —— for an implicit function:
 dx

x²y – 3x = y³ – 3

First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:

$\mathsf{\dfrac{d}{dx}(x^2 y-3x)=\dfrac{d}{dx}(y^3-3)}\\\\\\
\mathsf{\dfrac{d}{dx}(x^2 y)-3\,\dfrac{d}{dx}(x)=\dfrac{d}{dx}(y^3)-\dfrac{d}{dx}(3)}$

Applying the product rule for the first term at the left-hand side:

$\mathsf{\left[\dfrac{d}{dx}(x^2)\cdot y+x^2\cdot \dfrac{d}{dx}(y)\right]-3\cdot 1=3y^2\cdot \dfrac{dy}{dx}-0}\\\\\\
\mathsf{\left[2x\cdot y+x^2\cdot \dfrac{dy}{dx}\right]-3=3y^2\cdot \dfrac{dy}{dx}}$

 dy
Now, isolate —— in the equation above:
 dx

$\mathsf{2xy+x^2\cdot \dfrac{dy}{dx}-3=3y^2\cdot \dfrac{dy}{dx}}\\\\\\
\mathsf{2xy+x^2\cdot \dfrac{dy}{dx}-3-3y^2\cdot \dfrac{dy}{dx}=0}\\\\\\
\mathsf{x^2\cdot \dfrac{dy}{dx}-3y^2\cdot \dfrac{dy}{dx}=-\,2xy+3}\\\\\\
\mathsf{(x^2-3y^2)\cdot \dfrac{dy}{dx}=-\,2xy+3}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{-\,2xy+3}{x^2-3y^2}\qquad\quad for~~x^2-3y^2\ne 0}$

Compute the derivative value at the point (– 1, 2):

x = – 1 and y = 2

$\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{-\,2\cdot (-1)\cdot 2+3}{(-1)^2-3\cdot 2^2}}\\\\\\
\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{4+3}{1-12}}\\\\\\
\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{7}{-11}}\\\\\\\\ \therefore~~\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=-\,\dfrac{7}{11}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: implicit function derivative implicit differentiation chain product rule differential integral calculus

6 0

3 years ago

The product of twice a number and six is the same as the difference of eleven times the number and 6/5 . Find the number

Rom4ik [11]

Answer:

-6/5

Step-by-step explanation:

solution;

let,the number be x,

product of twice of x and six = the difference

difference of eleven times x and 6/5

or, (2x×6)=(11×x)-(6/5)

or, 12x = 11x - 6/5

or, 12x - 11x = -6/5

therefore,x =-6/5

Therefore, the number required is (-6/5) whose product of twice a number and six is the same as the difference of eleven times the number and 6/5 .

3 0

3 years ago