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4 years ago

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D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2

and less than 9} Which of the following is an element of D ∩ (E ∩ F)?

1 answer:

ser-zykov [4K]4 years ago

4 0

<span>E = {x|x is a perfect square between 1 and 9} = {1,4
</span><span>F = {x|x is an even number greater than or equal to 2 and less than 9}
</span><span>D = {x|x is a whole number}
</span>
answer
D ∩ (E ∩ F) = 4

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3. In the fig. AD = DC and AB = BC. Prove that ΔADB = ΔCDB<br>

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Answer:

The two column proof is presented as follows;

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Step-by-step explanation:

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3 years ago

Adrian jogs 3/4 mile each morning how many days will take to jog 3 miles

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Given Information
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Adrian can run 3/4 mile in 1 morning.

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3 years ago

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.

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Answer:

$\displaystyle 1)48.2 \: \: \text{sec}$

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Step-by-step explanation:

<h3>Question-1:</h3>

so when <u>flash down</u><u> </u>occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

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$\displaystyle - 4.9 {t}^{2} + 229t + 346 = 0$

to solve the equation can consider the quadratic formula given by

$\displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a}$

so let our a,b and c be -4.9,229 and 346 Thus substitute:

$\rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

remove parentheses:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

simplify square:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)}$

simplify multiplication:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8}$

simplify Substraction:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8}$

by simplifying we acquire:

$\displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5$

since time can't be negative

$\displaystyle t = 48.2$

hence,

at <u>4</u><u>8</u><u>.</u><u>2</u><u> </u>seconds splashdown occurs

<h3>Question-2:</h3>

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

$\displaystyle x _{ \text{max}} = \frac{ - b}{2a}$

let a and b be -4.9 and 229 respectively thus substitute:

$\displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)}$

simplify which yields:

$\displaystyle t _{ \text{max}} = 23.4$

now plug in the maximum t to the function:

$\rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346$

simplify:

$\rm \displaystyle h(23.4) = 3021.6$

hence,

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