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2 years ago

Find the exact volume of the cylinder.

Mathematics

2 answers:

Vesna [10]2 years ago

6 0

Answer:

It's D, hope this helps.

Step-by-step explanation:

netineya [11]2 years ago

4 0

Step-by-step explanation:

The volume of a cylinder can be found with the equation

So, plug in the values. The diameter of the circle is 10m, which means that the radius is 5m. The height of the cylinder is 13m.

V = π (5)^2 (13)

Answer:

D. 325π m^3

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Solve the following logarithmic equations.<br> log[(x^2 + 2x − 3)^4] = 0

saw5 [17]

Answer:

The solutions are x = 1.24 and x = -3.24

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log[(x² + 2x -3)⁴] = 0

Apply the logarithm property: log(xᵃ) = a log(x)

4 log[(x² + 2x -3)⁴] = 0

Divide by 4 both sides

log(x² + 2x -3) = 0

if log(x² + 2x -3) = 0, then x² + 2x -3 = 1 because only log 1 = 0

x² + 2x -3 = 1

Subtract 1 at both sides of the equation

x² + 2x -4 = 0

Using the quadratic formula let´s solve this quadratic equation:

a = 1

b = 2

c = -4

x = [-b± √(b² - 4ac)]/2a

x = [-2 + √(4 - 4(-4)·1)]/2 = 1.24

and

x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24

The solutions are x = 1.24 and x = -3.24

Have a nice day!

4 0

3 years ago

Ryan works at at the donut shop where he makes $10.25 per hour . He also works part time at the school bookstore where he makes

SCORPION-xisa [38]

Answer:

6 hours

Step-by-step explanation:

Let

x----> the number of hours worked at the donut shop

y----> the number of hours worked at the school bookstore

we know that

x+y=20

x=20-y -----> equation A

10.25x+8.75y=196 -----> equation B

Substitute equation A in equation B and solve for y

10.25(20-y)+8.75y=196

205-10.25y+8.75y=196

10.25y-8.75y=205-196

1.5y=9

y=6 hours at the school bookstore

7 0

3 years ago

Which function is the inverse of f(x) = 2x+37

WINSTONCH [101]

Answer:

$f^{-1} (x)=\frac{x-3}{2}$

Step-by-step explanation:

y = f(x)

y = 2x+3

You need to switch the places of x and y, into this:

x = 2y + 3

Then solve for y:

2y = x-3

$y=\frac{x-3}{2}$

$f^{-1} (x)=\frac{x-3}{2}$

3 0

3 years ago

Help find the missing lengths round to nearest tenth

Mama L [17]

Answer:

Step-by-step explanation:

Theta is 21 degrees

x is the adjacent side
8 is the opposite side
y is the hypothenuse

SOH - CAH - TOA

Since the opposite side is given and we need to find the length of the adjacent side, we can use tangent to solve for x.

$tan 21=\frac{opposite}{adjacent} \\tan 21 =\frac{8}{x} \\0.384 =\frac{8}{x} \\0.384x =8 \\x=\frac{8}{0.384} \\x=20.84$

Since the opposite side is given and we need to find the length of the hypotenuse, we can use sine to solve for y.

$sin 21=\frac{opposite}{hypotenuse} \\sin21 =\frac{8}{y} \\0.358 =\frac{8}{y} \\0.358y=8 \\y=\frac{8}{0.358} \\y=22.32$

6 0

2 years ago

According to the article "Fatigue Testing of Condoms" (Polymer Testing, 2009: 567–571), "tests currently used for condoms are su

daser333 [38]

Answer:

99% Confidence interval: (1196,1973)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 20

Mean, μ = 1584

Standard Deviation, σ = 607

99% Confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.01} = \pm 2.86$

$1584 \pm 2.86(\dfrac{607}{\sqrt{20}} )\\\\ = 1584 \pm 388.18\\ = (1195.82 ,1972.18)\\ \approx (1196,1973)$

Thus, there is a 99% chance that it will break in approximately 1196 to 1972

6 0

2 years ago