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shutvik [7]
3 years ago
7

Find the volume of the figure.

Mathematics
2 answers:
Yakvenalex [24]3 years ago
8 0

Answer:

233 in^3

Step-by-step explanation:

First we will find the volume of the square at the bottom

V = s^3  where s is the side length

V = 5^3

V = 125 in^3

Then we will find the volume of the rectangular prism at the top

V = l*w*h

V = 12*3*3

V =108 in^3

The total volume is the sum of the two volumes

V = 125+108

    = 233 in^3

Olegator [25]3 years ago
5 0

Answer:

233 in³

Step-by-step explanation:

Cube + cuboid

(5×5×5) + (3×3×12)

233 in³

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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
There were 6 friends who played a game of golf. Here were their scores. Player Score Sara -3 Steve 0 Kyle -2 Anna +3 Betsy +2 Mi
HACTEHA [7]

Answer: -4

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= -3 - 2 + 3 + 2 - 4

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6 0
3 years ago
Sofia invests her money in an account paying 7% interest compounded semiannually. What is the effective annual yield on this acc
vfiekz [6]

Answer:

7.12

Step-by-step explanation:

The formula for the effective annual yield is given as:

i = ( 1 + r/m)^m - 1

Where

i = Effective Annual yield

r = interest rate = 7% = 0.07

m= compounding frequency = semi annually = 2

i = ( 1 + 0.07/2)² - 1

i = (1 + 0.035)² - 1

= 1.035² - 1

= 1.071225 - 1

= 0.071225

Converting to percentage

0.071225 × 100

= 7.1225%

Approximately to 2 decimal places = 7.12

Therefore, the annual effective yield = 7.12

4 0
3 years ago
Find f(1/3) if f(n)=3n
tia_tia [17]
F(n)=3n
f(1/3)=3(1/3)
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Hope I didn't mess up for your sake
8 0
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