Evaluate 6 C 3 . 18 20 60 120

Bryn invested $2700 into an account that grows at a 4% annual interest rate. If she made no additional deposits of withdrawals o

dsp73

Answer: are their any options or?

3 0

3 years ago

PLEASE HELP.

krek1111 [17]

Answer:

Part a) The radii are segments AC and AD and the tangents are the segments CE and DE

Part b) $DE=4\sqrt{10}\ cm$

Step-by-step explanation:

Part a)

we know that

A radius is a line from any point on the circumference to the center of the circle

A tangent to a circle is a straight line which touches the circle at only one point. The tangent to a circle is perpendicular to the radius at the point of tangency.

In this problem

The radii are the segments AC and AD

The tangents are the segments CE and DE

Part b)

we know that

radius AC is perpendicular to the tangent CE

radius AD is perpendicular to the tangent DE

CE=DE

Triangle ACE is congruent with triangle ADE

Applying the Pythagoras Theorem

$AE^{2}=AC^{2}+CE^{2}$

substitute the values and solve for CE

$14^{2}=6^{2}+CE^{2}$

$CE^{2}=14^{2}-6^{2}$

$CE^{2}=160$

$CE=\sqrt{160}\ cm$

$CE=4\sqrt{10}\ cm$

remember that

CE=DE

so

$DE=4\sqrt{10}\ cm$

7 0

3 years ago

Which statements about the cylinder are true? Select two

Rus_ich [418]

Answer:

The radius of the cylinder is (1/2)x units

The area of the cylinder’s base is (1/4)πx2 square units

The height of the cylinder is 4x units

Step-by-step explanation:

The complete question is

A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is (1/2)x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder’s base is (1/4)πx2 square units.

(4) The area of the cylinder’s base is (1/2)πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units

we know that

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=\frac{x}{2}\ units$ ----> the radius is half the diameter

$V=\pi x^{3}\ units^3$

substitute the given values in the formula of volume

$\pi x^3=\pi (\frac{x}{2})^{2}h$

solve for h

simplify

$x=(\frac{1}{4})h$

$h=4x\ units$

Verify each statement

(1) The radius of the cylinder is (1/2)x units

The statement is true

see the explanation

(2) The radius of the cylinder is 2x units.

The statement is false

Because, the radius of the cylinder is x/2 units

(3) The area of the cylinder’s base is (1/4)πx2 square units

The statement is true

Because, the area of the cylinder's base is equal to

$A=\pi r^{2}$

$r=\frac{x}{2}\ units$

substitute

$A=\pi (\frac{x}{2})^{2}$

$A=\frac{\pi x^2}{4}\ units^2$

(4) The area of the cylinder’s base is (1/2)πx2 square units.

The statement is false

Because, the area of the cylinder's base is equal to

$A=\frac{\pi x^2}{4}\ units^2$

see the part (3)

(5) The height of the cylinder is 2x units.

The statement is false

Because, the height of the cylinder is 4x units (see the explanation)

(6) The height of the cylinder is 4x units

The statement is true

see the explanation

7 0

3 years ago

What is 5 2/5 multiplied by 2 as a mixed number or fraction

erica [24]

Answer:

54/5

Step-by-step explanation:

So 5 2/5 is 27/5 . So 54/5

5 0

3 years ago

The two dot plots below compare the forearm lengths of two groups of schoolchildren:

Oliga [24]

B.

as a, none is longer than 11 inches
b, 2 are longer than 11 inches
c, 3 have 9 inches (which is the shortest)
s, one has 9 inches

7 0

3 years ago

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