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Orlov [11]
3 years ago
7

Hi, the answer is K but can anyone show why

Mathematics
1 answer:
dlinn [17]3 years ago
3 0

Let's do 51 and 52.

51. The contrapositive has the same truth value as the original statement. That's opposed to the converse, which may or may not be true independent of the original statement.

The contrapositive of IF P THEN Q is IF not Q THEN not P.  They're equivalent.  Here that's If the cat is not female then it is not tricolor.

Answer: C

52.  

(x^3)^{(4-b^2)}=1

x^{3(4-b^2)} = 1

For the statement to be true, the exponent must be zero:

3(4-b^2) = 0

b^2 = 4

b = \pm 2

Both positive 2 and negative 2 have a square of 4.

Answer: K

By the way, usually we assume 0^0=1 so the restriction that x \ne 0 isn't really necessary.  Think of the definition of a polynomial or the binomial expansion:

\displaystyle f(x)=\sum_{k=0}^n a_k x^k

\displaystyle(x+y)^n=\sum_{k=0}^n {n \choose k} x^{k}y^{n-k}

For these common equalities to work when x=0 we need to define 0^0=1


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A well mixed tank with a capacity of 1500 gals originally contains 1000 gallons of freshwater. One pipe containing 1/2 lb of sal
Illusion [34]

Answer:

400 lb of salt

Step-by-step explanation:

Let us assume the water flows into the rank for x minutes.

There is an initial of 1000 gallons of water in the tank and water flows in through one pipe at 4 gal/min and through another pipe at 6 gal/min. In x minute, the amount of water in the tank = 1000 + 4x + 6x = 1000 + 10x

Water flows out at 5 gal/min, therefore in x minute the amount of water in the tank = 1000 + 10x - 5x = 1000 + 5x

The tank begins to overflow when it is full (has reached 1500 gallons). Therefore:

1500 = 1000 + 5x

5x = 1500 - 1000

5x = 500

x = 100 minutes.

1/2 lb salt per gallon flows into the tank at 4 gal/min and 1/3 lb of salt is flowing in at 6 gal/min, in 100 min the amount of salt that entered the tank = 4 gal/min × 100 min × 1/2 lb/gal + 6 gal/min × 100 min × 1/3 lb/gal= 400 lb

Therefore the amount of salt is in the tank when it is about to overflow = 400 lb of salt

7 0
3 years ago
Whaich calculation and answer show how to convert 3/12 to a decimal
Zolol [24]

Answer:

0.25

Step-by-step explanation:

3/12 = 1/4

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7 0
3 years ago
Trig proofs with Pythagorean Identities.
lorasvet [3.4K]

To prove:

$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1

Solution:

$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}

Multiply first term by \frac{1+cos x}{1+cos x} and second term by \frac{1-cos x}{1-cos x}.

        $= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}

Using the identity: (a-b)(a+b)=(a^2-b^2)

        $= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}

Denominators are same, you can subtract the fractions.

       $= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}

Using the identity: 1-\cos ^{2}(x)=\sin ^{2}(x)

       $= \frac{1+\cos^2 x}{\sin^2x}

Using the identity: 1=\cos ^{2}(x)+\sin ^{2}(x)

       $=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}

       $=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x} ------------ (1)

RHS=2 \cot ^{2} x+1

Using the identity: \cot (x)=\frac{\cos (x)}{\sin (x)}

        $=1+2\left(\frac{\cos x}{\sin x}\right)^{2}

       $=1+2\frac{\cos^{2} x}{\sin^{2} x}

       $=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x} ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1

Hence proved.

5 0
3 years ago
To find the number of centimeters in 10 inches, multiply the number of inches given (10) by _____.
Alenkinab [10]
We have that 1 in----- 2.54 cm
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x=10*2.54=25.4 cms

the answer is 2.54 cms
6 0
3 years ago
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F is located at the pole
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