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Ghella [55]
2 years ago
11

P varies inversely with x. If P = 14 when x= 16, find the value of P when x = 21.

Mathematics
1 answer:
Oliga [24]2 years ago
7 0

Answer:

Option C. 32/3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form p*x=k or p=k/x

we know that

For p=14, x=16

Find the value of k

k=p*x

substitute the values

k=(14)*(16)=224

so

The equation is equal to

p=\frac{224}{x}

Find the value of p when x=21

substitute the value of x in the equation

p=\frac{224}{21}    

simplify

Divide by 7 both numerator and denominator

p=\frac{32}{3}    

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is the formula which gives us the total number of ways of forming groups of r objects out of n objects.


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<span>Thus, there are C(6, 3) many ways of forming different triples out of 6.</span>


C(6, 3)= \frac{6!}{3!(6-3)!}=\frac{6!}{3!3!}=\frac{6\cdot5\cdot4\cdot3!}{3!3!}=\frac{6\cdot5\cdot4}{3!}=\frac{6\cdot5\cdot4}{3\cdot2\cdot1}=5\cdot4=20


Answer: A.20

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2 years ago
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Your current test average in Science is an 81. You’ve taken 5 tests. You only have one test remaining (there is not extra credit
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What exactly are you asking?
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Two parabolas have the same focus, namely the point $(3,-28).$ Their directrices are the $x$-axis and the $y$-axis, respectively
jeyben [28]

Answer:

the slope of the common cord is: -1

Step-by-step explanation:

Given the focus (a,b) = (3,-28)

  • for a parabola with directrix at x-axis the equation will be

\left(x-a\right)^{2}+\left(y-b\right)^{2}=y^{2}

\left(x-a\right)^{2}+\left(y-b\right)^{2}-y^{2}=0

  • for a parabola with directrix at y-axis the equation will be

\left(x-a\right)^{2}+\left(y-b\right)^{2}=x^{2}

\left(x-a\right)^{2}+\left(y-b\right)^{2}-x^{2}=0

The common chord is the line between two points where the two parabolas intersect. For intersection, we can equate the two parabolas!

In other words, at the point of intersection of these two parabolas the values of the two parabolas will be the same.

\left(x-a\right)^{2}+\left(y-b\right)^{2}-y^{2}=\left(x-a\right)^{2}+\left(y-b\right)^{2}-x^{2}

\left(x-3\right)^{2}+\left(y+28\right)^{2}-y^{2}=\left(x-3\right)^{2}+\left(y+28\right)^{2}-x^{2}

we can now simplify the equation. (we can see that (x-3) and (y+28) both cancel out by -(x-3) and -(y+28))

-y^{2}=-x^{2}

y=\sqrt{x^{2}}

y=\pm x

this the equation of the common cord. but we need to select whether its

y=+ x or y=-x.

This can be found by realizing that the focus lies on the 4th quadrant of the xy-plane! And the equation y=-x also generates a line that exists in the 2nd and 4th quadrant.

Hence the slope of the common cord is the slope of the line y=-x

that is : -1

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2 years ago
Maxine bought items costing $5.25, $18.99, $2.99, and $17.50. She used a coupon worth $5.50. If Maxine had $60.00 before she wen
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The answer is 20.77. You add 5.25+18.99+2.99+17.50=44.73. Then subtract 44.73 - 5.50 = 39.23. And then 60 - 39.23 = 20.77.
8 0
2 years ago
From a height of 50 meters above sea level on a cliff, two ships are sighted due west. The angles of depression are 61° and 28°.
Olenka [21]

Answer:

The ships are 66 meters apart.

Step-by-step explanation:

For the sake of convenience, let us label ships A and B

As shown in the figure, the distances to the ships from right triangles.

The distance to the ship A is d_1 and it is given by

tan (61^o)= \dfrac{50}{d_1}

d_1=\dfrac{50}{tan (61^o)}

\boxed{d_1= 27.71m}

And the distance to the ship B is d_2 and is given by

tan (28^o)= \dfrac{50}{d_2}

d_2=\dfrac{50}{tan (28^o)}

\boxed{ d_2=94.04m}

Therefore, the distance d between the ships A and B is

d= d_2-d_1=94.04-27.7\\\\\boxed{d=66m}

In other words, the ships are 66 meters apart.

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