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3 years ago

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The length and width of a rectangle must have a sum of 80. Find the dimensions of the rectangle that will have the maximum area.

[Hint: Let x and 80−x be the length and width. The area can be described by the function f(x)=x(80−x).]

1 answer:

jok3333 [9.3K]3 years ago

6 0

I hope this helps you

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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.

Oliga [24]

Answer:

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

$\rm \displaystyle 2)3021.6 \: m$

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,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

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

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,

about <u>3</u><u>0</u><u>2</u><u>1</u><u>.</u><u>6</u><u> </u>meters high above sea-level the rocket gets at its peak?

5 0

2 years ago

Candace used 5/8 of her savings to buy a $531.25 laptop. How much did she have in savings before purchasing the laptop?

Serjik [45]

$x-savings\\\\\frac{5}{8}x=531,25\ \ \ \ |\cdot\frac{8}{5}\\x=850\\\\Candance\ had\ \$ 850\ savings.$

3 0

3 years ago

When adding fractions does the denominator stay the same?

hodyreva [135]

Answer: yes

Step-by-step explanation:

8 0

3 years ago

The larger of two numbers is 10 less than twice the smaller number. If the sum of the two

natka813 [3]

Answer:

Let the larger number = y and the smaller number = x.

The largest number is 10 less than twice the smaller number. Remember that less than means subtract the 10 from the other amount while twice means multiply by two. Therefore,

y = 2x - 10

The sum of the two numbers is 38. Remember sum means add the two numbers to get their result. Therefore,

x + y = 38

Since y = 2x - 10, we rewrite the lower equation as:

x + (2x - 10) = 38

Solving:

3x - 10 = 38

3x = 48

x = 16

The lesser number is 16 and the greater number is 2(16) - 10 or 22.

7 0

2 years ago

I need you guys to check if im correct! if not, show me step by step explanations

tamaranim1 [39]

● Answer:

b) 24 cm

● Step-by-step explanation:

l + 4 = 2w => l = 2w - 4

5w + 6 = P => 5w + 6 = 2w + 2l

5w + 6 = 2w + 2(2w - 4)

5w + 6 = 2w + 4w - 8

6 + 8 = 6w - 5w

w = 14

l = 2x14 - 4

l = 28 - 4

l = 24 cm

7 0

3 years ago

Read 2 more answers