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3 years ago

A parachutist descends 52 feet in 4 seconds. Express the rate of the parachutists change in height as a unit rate.

Mathematics

1 answer:

rosijanka [135]3 years ago

5 0

Answer:

the answer is 13 per one sec

Step-by-step explanation:

4 times 13 is 52 so every one sec its 13

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What is the slope of this line? A: - 1/3 B: - 2/3 C: 2/3 D: 1/3

bezimeni [28]

Answer:

The answer is C. 2/3

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

0.5a − 0.3 = 5 (solve for a)

Alla [95]

0.5a - 0.3 = 5

Add 0.3 to both sides:

0.5a = 5.3

Divide both sides by 0.5:

a = 10.6

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3 years ago

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Using the binomial theorem , obtain the expansion of :

andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1 6 15 20 15 6 1

Decreasing powers of 1 from $1^{6}$ to $1^{0}$

Increasing powers of 3x from $(3x)^{0}$ to $(3x)^{6}$

$1+3x)^{6}$

= 1. $1^{6}$ $(3x)^{0}$ + 6. $1^{5}$ $(3x)^{1}$ + 15. $1^{4}$ $(3x)^{2}$ + 20. $1^{3}$ $(3x)^{3}$ + 15.1² $(3x)^{4}$ + 6. $1^{1}$ $(3x)^{5}$ + 1. $1^{0}$ $(3x)^{6}$

= 1 + 18x + 135x² + 540x³ + 1215 $x^{4}$ + 1458 $x^{5}$ + 729 $x^{6}$

--------------------------------------------------------------------------------------

$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

----------------------------------------------------------------------------------

Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

----------------------------------------------------

(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

= 1 + 10x + 40x² + 80x³ + 80 $x^{4}$ + 32 $x^{5}$

8 0

3 years ago

Theorem: A line parallel to one side of a triangle divides the other two proportionately.

Kisachek [45]

Answer:

Segment BF = 16

Step-by-step explanation:

The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately

The given theorem is the Triangle Proportionality Theorem

According to the theorem, given that segment DE is parallel to segment BC, we have;

$\dfrac{AD}{BD} = \dfrac{AE}{EC}$

Therefore;

$BD = \dfrac{AD}{\left(\dfrac{AE}{EC} \right) } = AD \times \dfrac{EC}{AE}$

Which gives;

$BD = 6 \times \dfrac{18}{12}= 9$

Similarly, given that EF is parallel to AB, we get;

$\dfrac{AE}{EC} = \dfrac{BF}{FC}$

Therefore;

$BF = FC \times \dfrac{AE}{EC}$

Which gives;

$BF = 24 \times \dfrac{12}{18} = 16$

Therefore, the statement that can be proved using the given theorem is segment BF = 16.

8 0

3 years ago

A 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 5 fee

Tanzania [10]

The answer is 12 because (a^2 + b^2 = c^2)

5^2 + b^2 = 13^2
25 + b^2 = 169

169- 25 = 144
$\sqrt{144}$ Sqaure root of 144 is 12 so If we plug that in..
25 + 144 = 169
5^2 + 12^2 =13^2
This all checks out
~Hope This helps

8 0

2 years ago