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1 year ago

20.

Mathematics

1 answer:

DiKsa [7]1 year ago

7 0

Answer:

49x-21y-6

Step-by-step explanation:

7(7x) 7(-3y) -6

49x-21y-6=0

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When a number x is multiplied by 4, the result is 2/5. What is t he value of x

PIT_PIT [208]

The equation:

$x\cdot4=\dfrac{2}{5}\ \ \ \ |\text{divide both sides by 4}\\\\x=\dfrac{2}{5}:4\\\\x=\dfrac{2}{5}\cdot\dfrac{1}{4}\\\\x=\dfrac{1}{5}\cdot\dfrac{1}{2}\\\\\boxed{x=\dfrac{1}{10}}$

5 0

2 years ago

Two cards are drawn in succession and without replacement from a standard deck of 52 cards. Find the probability that the second

Svetllana [295]

Answer:

The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497

Step-by-step explanation:

Total number of face cards = 12

Total cards = 52

Probability of getting face card on first draw= $\frac{12}{52}$

Remaining no. of face cards = 11

Remaining number of total cards = 51

Probability of getting face card on second draw= $\frac{11}{51}$

The probability that the second card is a face card if it’s known that the first card was a face card = $\frac{12}{52} \times \frac{11}{51}= \frac{12}{52} \times \frac{11}{51}=0.0497$

Hence The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497

4 0

2 years ago

If y is directly proportional to x and y = -15 when x=3 find the value of y when x is 20?

leonid [27]

Answer: y = 2

Explanation:

When x = 3, y = -15

And x and y are directly proportional.

thus x + k ==> y + k

when x = 3 + 17 ==> y = -15 + 17

=> x = 20 ==> y = 2

5 0

2 years ago

find the coordinates of the point P on the parabola y=1-x^2 with domain 0≤x≤1 that minimize the area of the triangle enclosed by

coldgirl [10]

Let point P be with coordinates $(x_0,y_0).$ Find the equation of the tangent line.

1. If $y=1-x^2,$ then $y'=-2x.$

2. The equation of the tangent line at point P is

$y-y_0=-2x_0(x-x_0).$

Find x-intercept and y-intercept of this line:

when x=0, then $y=y_0+2x_0^2;$
when y=0, then $x=\dfrac{y_0}{2x_0}+x_0=\dfrac{y_0+2x_0^2}{2x_0}.$

The area of the triangle enclosed by the tangent line at P, the x-axis, and y-axis is

$A=\dfrac{1}{2}\cdot (2x_0^2+y_0)\cdot \left(\dfrac{y_0+2x_0^2}{2x_0}\right)=\dfrac{(y_0+2x_0^2)^2}{4x_0}.$

Since point P is on the parabola, then $y_0=1-x_0^2$ and

$A=\dfrac{(1-x_0^2+2x_0^2)^2}{4x_0}=\dfrac{(1+x_0^2)^2}{4x_0}.$

Find the derivative A':

$A'=\dfrac{2(1+x_0^2)\cdot 2x_0\cdot 4x_0-4(1+x_0^2)^2}{16x_0^2}=\dfrac{12x_0^4+8x_0^2-4}{16x_0^2}.$

Equate this derivative to 0, then

$12x_0^4+8x_0^2-4=0,\\ \\3x_0^4+2x_0^2-1=0,\\ \\D=2^2-4\cdot 3\cdot (-1)=16,\ \sqrt{D}=4,\\ \\x_0^2_{1,2}=\dfrac{-2\pm4}{6}=-1,\dfrac{1}{3},\\ \\x_0^2=\dfrac{1}{3}\Rightarrow x_0_{1,2}=\pm\dfrac{1}{\sqrt{3}}.$