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Shalnov [3]
2 years ago
10

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h = -16t² +90t gives

the height h of the ball after t seconds.
a Explain what the a, b, &c mean in this problem.
b. How many seconds will it take for the ball to reach the ground?​
Mathematics
1 answer:
Tanya [424]2 years ago
5 0

Answer:

See below

Step-by-step explanation:

a = -16    =   - 1/2 a    where a is acceleration of gravity (32 ft/s^2)

b = 90    = initial velocity     90 ft/s

c = 0      = initial height = 0 ft ( kicked from off of the ground )

Height = 0   when the ball hit the ground

             0 = -16t^2 + 90t

               0 = -t ( 16t-90)       t = 0     or  90/16 =<u> 5.63 seconds </u>

<u />

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At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as
MAXImum [283]

<u>Answer-</u>

At x= \frac{1}{2304e^4-16e^2} the curve has maximum curvature.

<u>Solution-</u>

The formula for curvature =

K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}

Here,

y=4e^{x}

Then,

{y}' = 4e^{x} \ and \ {y}''=4e^{x}

Putting the values,

K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

 {k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}

Now, equating this to 0

(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0

\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})

\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})

\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}

\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}

\Rightarrow 2304e^{2x}-16e^{2x}-1=0

Solving this eq,

we get x= \frac{1}{2304e^4-16e^2}

∴ At  x= \frac{1}{2304e^4-16e^2} the curvature is maximum.




6 0
3 years ago
Joel has d dimes and q quarters with a total value of $25.50. Which equation represents the total amount in dollars in terms of
ElenaW [278]

Answer:

10d + 25q = $25.50

Hope this helps

4 0
3 years ago
20. Solve 3(5x − 4) &lt; 15x.<br> All Real Numbers<br> x&gt;-4 <br>x&lt;4<br>no solution ​
Natasha2012 [34]

Answer:

No solution

Step-by-step explanation:

3(5x - 4) < 15x \\ 15x - 12 < 15x \\ 15x - 15x < 12 \\ 0 < 12

8 0
2 years ago
Abbey Co. sold merchandise to Gomez Co. on account, $29,300, terms 2/15, net 30. The cost of the goods sold is $20,510. Abbey Co
yawa3891 [41]

Answer:

The amount of gross profit earned by Abbey Co. on the above transactions is $7,554.00

Step-by-step explanation:

What is the gross profit of Abbey Co?

Note that after sales of goods of $29,300 whose cost is $20,510 to Gomez Co, Gomez returned goods whose selling price is $2,500 and cost originally $1,800 to Abbey Co.

The implication of such goods returned is that $2,500 would be deducted from selling price and $1,800 would be deducted from cost of goods sold.

selling price=$29,300-$2,500

selling price=$26,800.00

cost of goods sold=$20,510-$1,800

cost of goods sold=$18,710.00

Note again that Gomez paid the invoice within the discount period, which means that net sales is the selling price of $26,800.00  minus 2% discount(2/15 means a discount of 2% is available if credit sales is settled in cash within the first 15 days of making sales0

net sales=$26,800.00*(1-2%)

net sales=$26,264.00

The gross profit is net sales minus the cost of goods sold

gross profit= $26,264.00-$18,710.00

gross profit=$7,554.00

Below is the link to a similar question which gives further guidance

brainly.com/question/14680275

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6 0
2 years ago
Can you figure this out for me ? I’m having issues .
Verdich [7]

Answer:

71

you just had to add them

Step-by-step explanation:

7 0
3 years ago
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