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RUDIKE [14]
3 years ago
5

Find the sum of the first 150 terms of the arithmetic series: 4, 5, 6, 7, 8, … 7,345 11,775 13,322 15,654

Mathematics
1 answer:
Tanya [424]3 years ago
7 0
4, 5, 6, 7, 8, . . .
a = 4, d = 5 - 4 = 1, n = 150
Sn = n/2[2a + (n - 1)d]
S(150) = 150/2[2(4) + (150 - 1)1] = 75[8 + 149] = 75(157) = 11,775
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Solve the following logarithmic equations.<br> ln(x^6) = 36
Hoochie [10]

Answer:

The solution is x = e⁶

Step-by-step explanation:

Hi there!

First, let´s write the equation

ln(x⁶) = 36

Apply logarithm property: ln(xᵃ) = a ln(x)

6 ln(x) = 36

Divide both sides of the equation by 6

ln(x) = 6

Apply e to both sides

e^(ln(x)) = e⁶

x = e⁶

The solution is x = e⁶

Let´s prove why e^(ln(x)) = x

Let´s consider this function:

y = e^(ln(x))

Apply ln to both sides of the equation

ln(y) = ln(e^(ln(x)))

Apply logarithm property: ln(xᵃ) = a ln(x)

ln(y) = ln(x) · ln(e)         (ln(e) = 1)

ln(y) = ln(x)

Apply logarithm equality rule: if ln(a) = ln(b) then, a = b

y = x

Since y = e^(ln(x)), then x =e^(ln(x))

Have a nice day!

8 0
3 years ago
The cost of one pound of bananas is greater than $0.41 and less than $0.50. Sarah pays $3.40 for x pounds of bananas. Which ineq
vredina [299]

Answer:

0.41<3.40/x<0.50

Step-by-step explanation:

Given that the cost of one pound of bananas is greater than $0.41 and less than $0.50. That is,

If the cost of one banana is P, then, the inequality will be

0.41 < P < 0.50

Sarah pays $3.40 for x pounds of bananas. The inequality that represents the range of possible pounds purchased will be achieved by below

3.40/0.41 = 8.29

3.40/0.50 = 6.8

Therefore, the inequality that represents the range of possible pounds purchased is

6 < x < 9 this is the same as 0.41<3.40/x<0.50

6 0
3 years ago
PLEASE ANSWER ASAP!!
Doss [256]

Answer:

It is 0.125

Step-by-step explanation:

5 0
3 years ago
PLEASE HURRY PLEASE PLEASE PLEASE
hram777 [196]

Answer:

b

Step-by-step explanation:

make a formula, its the easiest way to solve problems like these also its very efficent

3 0
3 years ago
When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?
amm1812

Answer:

(3x+4)(2x-5)

Step-by-step explanation:

Factor by grouping.

8 0
3 years ago
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