Using properties of logarithms:
log(m+n) = log(m.n)
log(m-n) = log (m/n)
we get,
log(32x16/64)
On simplifying:
log(8)
and 8= 2^3
therefore,
log(2^3)
again using another property for exponents in logarithms we get:
3 log 2 <---- Answer
<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)
0 = ln (x - 4)
1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)
1 = ln (x - 4)
e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
*************************************************************************
transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>
Answer:
part a: 52%
part b: 0.4
part c: 0.24
Step-by-step explanation:
For part one, you find the frequency of the number of people that are less that 20. You add the number of tics in each bar and you divide by the total.
so for part a it is (7+6+9+4)/ (7+6+9+4+4+12+8)
for part b you add up the values that are greater than 25(less than 35)
(12+8)/total
part c you find the number of people between 25 and 30
that's 12
over total
12/total
Answer:
8,000
Step-by-step explanation:
after 35 years 1000
after 70 2000
after 105 4000
qfter 140 8000
i might be wrong but hope this helped there is probs a faster way to do this tho.
Answer:
(i) The name of the part of the circle, OQ is a radius
(ii) The radius of the sector QOR is 21 cm
Step-by-step explanation:
The given figure is a sector of the circle O
∵ Any sector of a circle formed from 2 radii and an arc
∴ OQ is a radius
(i) The name of the part of the circle, OQ is a radius
The rule of the length of an arc of a circle is L = × 2 π r, where
- α is the angle of the sector
- r is the radius of the circle
∵ The length of the arc QR is 22 cm
∴ L = 22
∵ The measure of the angle of the arc is 60°
∴ α = 60°
∵ π =
→ Substitute them in the rule above
∵ 22 = × 2 × × r
∴ 22 = r
→ Divide both sides by
∴ 21 = r
(ii) The radius of the sector QOR is 21 cm