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dangina [55]
4 years ago
9

Evaluate the following expression. Log8 64

Mathematics
1 answer:
viktelen [127]4 years ago
6 0

Answer:

2

Step-by-step explanation:

Using the rule of logarithms

• log_{b} x = n ⇔ x = b^{n}

let log_{8} 64 = n, then

64 = 8^{n}

note that 64 = 8², thus

8² = 8^{n} ⇒ n = 2

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A recursive rule for a geometric sequence is a1=4/9;an=3an−1. What is the explicit rule for this sequence?
Anettt [7]
<span>a1=4/9
r=an/a(nâ’1)=3
an=a1r^(nâ’1)=(4/9)*(3)^nâ’1</span>
4 0
3 years ago
Read 2 more answers
jose' is putting up wallpaper is $1.75 per square foot. one wall measures 10 by 9 feet. how much will wallpaper cost for this wa
Airida [17]
If you are finding the perimeter the answer would be:
$15.50
If you do 9*$1.75=$15.75
If you do 10*$1.75=17.50
When you find perimeter it’s length+length+ width+ width
This gives you $15.50
If you are finding the area the answer would be:
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4 0
4 years ago
Write the equation of a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2(sqrt5)
Xelga [282]

Answer:

\frac{x^2}{16}-\frac{b^2}{4}=1

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4

The foci c is at +/-2√5, using c² = a² + b²:

c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2

Substituting the value of a and b to get the equation of the hyperbola:

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1

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3 years ago
Li is making beaded necklaces.For each necklace, she uses 22 spaces, plus 5 beads per inch of necklace length. Write an equation
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X=22 spaces + 5 per inch
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If you vertically compress the absolute value parent function, f(x) =|x|, by a factor of 5, what is the equation of the new func
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Answer:

g(x) = 1/5 |x|

Step-by-step explanation:

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