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3 years ago

Please help quickly !

Mathematics

1 answer:

Lyrx [107]3 years ago

3 0

Answer:

a,c

Step-by-step explanation:

if Jen covered m miles.

$m=\frac{1}{3}(45,000)\\and ~3~(m)=45,000\\$

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The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteri

Nady [450]

Do you notice anything strange about those points ?

(0, 1),
(1, 2),
(2, 4),
(3, 8).

The y-coordinate of each point is (2) raised to the power of the x-coordinate.

First point:   x=0, y=2⁰ = 1
Second point: x=1, y=2¹ = 2
Third point:    x=2, y=2² = 4
Fourth point: x=3, y=2³ = 8

The equation of the curve appears to be

   y = 2 ^ x .

So, after 10 hours, x=10, and y = 2¹⁰ = 1,024 .

3 0

3 years ago

Read 2 more answers

2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.

likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4 + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

$y = ^+_- \sqrt{-x^2+4x+4} -5$

Thus

$f(x) = \sqrt{-x^2+4x+4} - 5$

$g(x) = -\sqrt{-x^2+4x+4} - 5$

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

$\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0$

The quadratic has roots

$\frac{52 ^+_-\sqrt{1664}}{26}$

one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.

Also g(3.568) = - 7.354 and f(0.431) = -2.646

This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

5 0

3 years ago

What is the sum of each pair of hexadecimal integers?<br> a. 6b4 + 3fe<br> b. A49 + 6bd?

Korolek [52]

Answer:

a) AB2

b) 1106

Explanation:

Hex addition can be achieved through repeated subtraction of 16 from the decimal sum of same place values of hex numbers until the result is reached to one of the hex digits from 0 to F. The carry increases by 1 where each time the number 16 is subtracted from the hex numbers decimal sum. The below example lets you understand how to perform hex numbers addition

(a) 6B4 + 3FE

6 B 4

+ 3 F E

-------------------------------------------------

A B 2

(b) A 4 9

+ 6 B D

---------------------------

1 1 0 6

6 0

3 years ago

What type of number is <img src="https://tex.z-dn.net/?f=%5Csqrt%7B13%7D" id="TexFormula1" title="\sqrt{13}" alt="\sqrt{13}" ali

taurus [48]

The answer would be irrational since it can’t be written as fraction

8 0

3 years ago

Find the terms and the coefficients of the expression.

Sav [38]

The terms are -80, 4p, and -6z.
The coefficients are 4 and 6.

Terms are separated by the addition and subtraction sign.
Coefficients are the numbers that go in front of the variable.

3 0

3 years ago