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makkiz [27]
3 years ago
12

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate

pH of a solution whose hydrogen ion concentration is 2*10^-9
A. 1.0
B. 2.9
C. 8.7
D. 9.3
Mathematics
2 answers:
wariber [46]3 years ago
6 0

Answer:

ANSWWER IS C.8.7

Step-by-step explanation:

I JUST TOOK THE TEST

Korolek [52]3 years ago
5 0
PH = -log[H+]
= -log(2*10^-9)
= -(log(2) +log(10^-9))
= -(0.3 -9)
= 8.7

The appropriate choice is
  C. 8.7
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Solve following equation<br> 3+x+1 =2
Rufina [12.5K]

Answer:

x = -2

Step-by-step explanation:

4 + x = 2

-4 -4

x = -2

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4 years ago
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The circle Ci, intersects the y-axis at two points, one of which is (0.4).
Anuta_ua [19.1K]

Answer:

Part 1) r=5 units (see the explanation)

Part 2) (x-4)^2+(y-7)^2=25

Part 3) The center of the circle is (-3,4) and the radius is 4 units

Part 4) see the explanation

Step-by-step explanation:

Part 1)

step 1

Find the center of circle C_1

we know that

The distance between the center and point (0,4) is equal to the radius

The distance between the center and point (4,2) is equal to the radius

Let

(x,y) ----> the coordinates of center of the circle

Remember that

The tangent y=2 (horizontal line) to the circle is perpendicular to the radius of the circle at point (4,2)

That means ----> The segment perpendicular to the tangent is a vertical line x=4

so

The x-coordinate of the center is x=4

The coordinates of center are (4,y)

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Remember

The distance between the center (4,y) and point (0,4) is equal to the radius

The distance between the center (4,y) and point (4,2) is equal to the radius

so

substitute

\sqrt{(y-4)^{2}+(4-0)^{2}}=\sqrt{(4-4)^{2}+(y-2)^{2}}

\sqrt{(y-4)^{2}+16}=\sqrt{(0)^{2}+(y-2)^{2}}

squared both sides

(y-4)^{2}+16=(y-2)^{2}

solve for y

y^2-8y+16+16=y^2-4y+4

y^2-8y+32=y^2-4y+4\\8y-4y=32-4\\4y=28\\y=7

The coordinates of the center are (4,7)

step 2

Find the radius of circle C_1

r=\sqrt{(y-4)^{2}+(4-0)^{2}}

substitute the value of y

r=\sqrt{(7-4)^{2}+(4-0)^{2}}

r=\sqrt{(3)^{2}+(4)^{2}}

r=\sqrt{25}

r=5\ units

Part 2)

Find the equation of the circle C, in standard form.

we know that

The equation of a circle in standard form is

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center

r is the radius

substitute the given values

(x-4)^2+(y-7)^2=5^2

(x-4)^2+(y-7)^2=25

Part 3) Another circle C2 has equation x² + y2 + 6x – 8y +9=0

Find the centre and radius of C2

we have

x^2+y^2+6x-8y+9=0

Convert to standard form

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center

r is the radius

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x^2+6x)+(y^2-8y)=-9

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

(x^2+6x+9)+(y^2-8y+16)=-9+9+16

(x^2+6x+9)+(y^2-8y+16)=16

Rewrite as perfect squares

(x+3)^2+(y-4)^2=16

(x+3)^2+(y-4)^2=4^2

therefore

The center of the circle is (-3,4) and the radius is 4 units

Part 4) Show that the circle C2 is a tangent to the x-axis

we know that

If the x-axis is tangent to the circle, then the equation of the tangent is y=0

so

The radius of the circle must be perpendicular to the tangent

That means ----> The segment perpendicular to the tangent is a vertical line The equation of the vertical line is equal to the x-coordinate of the center

so

x=-3

The circle C_2, intersects the x-axis at point (-3,0)

<em>Verify</em>

The distance between the center (-3,4) and point (-3,0) must be equal to the radius

Calculate the radius

r=\sqrt{(0-4)^{2}+(-3+3)^{2}}

r=\sqrt{16}

r=4\ units ----> is correct

therefore

The circle C_2 is tangent to the x-axis

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Answer:

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Step-by-step explanation:

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Find the value of the expression below. Express your answer in scientific notation.
nirvana33 [79]

The value of the expression is 8.8 \times 10^{-2}.

Solution:

Given expression:

$\frac{\left(4.8 \times 10^{8}\right)}{\left(1.2 \times 10^{4}\right)} \times\left(2.2 \times 10^{-6}\right)

<u>To find the value of the given expression:</u>

Using exponent rule: a^m\times a^n=a^{m+n}

$\Rightarrow\frac{\left(4.8 \times 10^{8-6}\right)}{\left(1.2 \times 10^{4}\right)} \times\left(2.2 \right)

$\Rightarrow\frac{\left(4.8 \times 10^{2}\right)}{\left(1.2 \times 10^{4}\right)} \times\left(2.2 \right)

Using exponent rule: \frac{a^m}{a^n} =a^{m-n}

$\Rightarrow\frac{\left(4.8 \times 10^{2-4}\right)}{1.2} \times 2.2

$\Rightarrow\frac{\left(4.8 \times 10^{-2}\right)}{1.2} \times 2.2

Since \frac{4.8}{1.2}=4

$\Rightarrow(4 \times 10^{-2})\times 2.2

$\Rightarrow 8.8 \times 10^{-2}

Hence the value of the expression is 8.8 \times 10^{-2}.

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3 years ago
Sam is selling homemade cookies to raise money for charity. Each cookie sells for $.50. Sam spent $90 on baking supplies and eac
Hunter-Best [27]

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Answer:

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Step-by-step explanation:

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Sam needs to sell 360 cookies before he can start making a profit.

_____

If you like, you can find Sam's break-even point by equating revenue and cost. The is the number of cookies Sam must sell for a profit of 0, that is, for non-negative profit.

  P = R - C

  0 = R - C

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You may notice this is similar to our description above.

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3 years ago
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