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son4ous [18]
3 years ago
11

The numbers 2/1/3,h,k,7/7/8 firm a geometric progression. find the value of h and of k

Mathematics
1 answer:
taurus [48]3 years ago
8 0

\text{We have }\ 2\dfrac{1}{3},\ h,\ k,\ 7\dfrac{7}{8}.\\\\\text{Convert the mixed numbers to the improper fractions}\\\\2\dfrac{1}{3}=\dfrac{2\cdot3+1}{3}=\dfrac{7}{3}\\\\7\dfrac{7}{8}=\dfrac{7\cdot8+7}{8}=\dfrac{63}{8}\\\\\text{If}\ a_1,\ a_2,\ a_3,\ a_4\ \text{is a geometric seqence, then:}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=r\\\\a_2=a_1r\\\\\text{and}\ \dfrac{a_4}{a_1}=r^3\\\\\text{Substitute:}

r^3=\dfrac{\frac{63}{8}}{\frac{7}{3}}\\\\r^3=\dfrac{63}{8}\cdot\dfrac{3}{7}\\\\r^3=\dfrac{9\cdot3}{8\cdot1}\\\\r^3=\dfrac{27}{8}\to r=\sqrt[3]{\dfrac{27}{8}}\\\\r=\dfrac{3}{2}\\\\h=2\dfrac{1}{3}\cdot\dfrac{3}{2}=\dfrac{7}{3}\cdot\dfrac{3}{2}=\dfrac{7}{2}\\\\k=\dfrac{7}{2}\cdot\dfrac{3}{2}=\dfrac{21}{4}\\\\Answer:\ \boxed{h=\dfrac{7}{2}=3\dfrac{1}{2}\ and\ k=\dfrac{21}{4}=5\dfrac{1}{4}}

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netineya [11]

Answer:

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Step-by-step explanation:

Y=e×6x×(6x+1) × 5

y'= d/dx (e×6x ×(6x+1)×5)

y'=d/dx(30ex ×(6x+1))

y'=d/dx(180ex^2 + 30ex)

y'=d/dx(180ex^2) + d/dx (30ex)

Calculate the derivative

y'=180e×2x +30e

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6 0
3 years ago
Given f(x)=3^(x-2) and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur
klio [65]

Answer with Step-by-step explanation:

We are given that

f(x)=3^{x-2}

g(x)=f(3x)+4

We have to write the rule for function g and describe the transformation between f and g.

Compress the function by scale factor 3 and the translation rule is given by

(x,y)\rightarrow (3x,y)

Then, we get h(x)=f(3x)=3^{3x-2}

Now, shift the y coordinate 4 units above the origin.

Then, the translation rule is given by

(x,y)\rightarrow (x,y+4)

Then , we get

g(x)=3^{3x-2}+4

3 0
3 years ago
Find the net change in the value of the function between the given inputs. h(t) = t2 + 2; from −5 to 8
pashok25 [27]

Answer:

39

Step-by-step explanation:

Given the function :

h(t) = t² + 2

From t = 5 to t = 8

when, t = 5

h(5) = 5² + 2

h(5) = 25 + 2

h(t) at t = 5 ; equals 27

when, t = 8

h(5) = 8² + 2

h(5) = 64 + 2

h(t) at t = 8 ; equals 66

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Which one of the following solids can produce this two-dimensional shape when sliced vertically?
Oksana_A [137]

Answer:

option 2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
1/2y+2/5=4 2/5 how do I solve this matter
Inessa [10]

Answer:

y =8

Step-by-step explanation:

1/2y+2/5=4 2/5

Subtract 2/5 from each side

1/2y+2/5-2/5=4 2/5-2/5

1/2 y = 4

Multiply each side by 2

1/2y *2 = 4*2

y = 8

3 0
3 years ago
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