From the graph shown, what is an approximate solution of the system of equations?

Solution :

From the triangle,

[tex]$x^2 = s^2 + 90^2$[/tex]

[tex]$x = \sqrt{s^2 + 90^2}$[/tex]

Now differentiating w.r.t "t", we get

[tex]$\frac{dx}{dt}=\frac{d}{dt}\left(s^2 +90^2 \right)^{1/2}$[/tex]

    [tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{\frac{1}{2}-1} \cdot 2s \cdot \frac{ds}{dt}$[/tex]     [chain rule]

    [tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{-\frac{1}{2}} \cdot 2s \cdot \frac{ds}{dt}$[/tex]

    [tex]$=\frac{s}{\left(s^2 + 90^2\right)^{\frac{1}{2}}} . \frac{ds}{dt}$[/tex]  

But given that [tex]$\frac{ds}{dt}$[/tex] = 100 ft/s

When all the ball crosses the third base, this means that s = 90. So substituting the value of s and [tex]$\frac{ds}{dt}$[/tex]  in [tex]$\frac{dx}{dt}$[/tex] , we get

[tex]$\frac{dx}{dt} = \frac{90}{\left(90^2 +90^2\right)^{1/2}} \times 100$[/tex]

[tex]$\frac{dx}{dt} = \frac{90}{\sqrt{8100+8100}} \times 100$[/tex]

[tex]$\frac{dx}{dt} = 50\sqrt2$[/tex]

    = 70.710 ft/s    

Answer:

39.5 [tex]ft^{2}[/tex]

Step-by-step explanation:

We need to take this shape by shape

Top triangle

a = b*h/2

a = 3*2/2

a = 6/2

a = 3

__________________________________________________________

Bottom triangle:

a = b*h/2

a = 3*3/2

a = 9/2

a = 4.5

__________________________________________________________

Rectangle:

a = b*h

a = 8*4

a = 32

__________________________________________________________

Now add them all up

3 + 4.5 + 32 = 39.5

The area of the shape is 39.5 [tex]ft^{2}[/tex]

Hope this helped!

Answer:

(5, 1) is the answer.

Step-by-step explanation:

This is because the point (5, 1) is NOT in the shaded area of the inequality. All the other points are either in the shaded area of the inequality, or on the line of the inequality equation.

Hope this helps!! :)

#teamtrees #WAP (Water And Plant)

Answer:

(5,1)

Step-by-step explanation:

Answer:

Rock costs $3.20 per pound.

Step-by-step explanation:

Because sand costs three times as much as rocks per pound, you can determine the cost of rocks per pound by dividing the cost of sand per pound by three:

[tex]\frac{9.60}{3}[/tex] [tex]= 3.20[/tex]

Answer:

B and C are correct Hope this helps <3

Step-by-step explanation:

Answer:

B and C?

Step-by-step explanation:

Im a little unsure about C but im about99% sure that is correct

Answer: G

7/9 yd= 28 in

2.5ft = 30 in

2 2/3 ft= 32 in

33in = 33in

I hope this helps:

CCCCCC"CCCCCCCCCCC"CCCCCCCCCCCCCCCCCCCCC

Answer:

24)

[tex] \frac{4}{5} [/tex]

[tex]25) - \frac{4}{5} [/tex]

[tex]14)1[/tex]

15)19

16)5

17)3

18)5√5

19)8n²√2

Answer:

a.5/2

b.5/3

because dave eat 2 of the pizza pices from 5 pices

and sue eats 3 of the pizza pices of 5

Answer:

Noah types faster because he can type more words per minute.

Step-by-step explanation:

For Andre you would divide 208 words by 4 minutes getting 52 words per minute. Then, for Noah divide 342 words by 6 minutes getting 57 words per minute.

Answer:

49 square feet

Step-by-step explanation:

Area of square

[tex] = {7}^{2} \\ \\ = 49 \: {ft}^{2} \\ [/tex]

Answer:

-29.988 or if you round up -30

Step-by-step explanation:

1) Convert fractions to decimals  

    3.6 x (-8.33) = -29.988

Answer:

I think its this but not sure

Answer:

x ≥ $750

Step-by-step explanation:

Answer:

b.430

Step-by-step explanation:

Answer:

286.

Step-by-step explanation:

9.85^3 /3.875 + 6.3^2

= 10^3/ 4 + 6^2

= 1000/4 + 36

=250 + 36

=286.

Answer:

b=9

(assuming you meant -6x) x = -2

h = -4

a = 6

Step-by-step explanation:

Answer:

which team has the taller player (picture involve

B the skyview ravens

Answer:

the davis tigers has taller player

because their player is 0.625 inches taller more than the Skyview Ravens player

Answer:

2610/10730

2610/10730 = 0.24324324

0.24324324 X 100 = 24.324324

24%

Answer:

1. 1.925 Liters

2.  0.075 Liters  less than the 2 Liter of special drink

Step-by-step explanation:

Step 1

Quantity of lemon juice = 0.375 Liters

Quantity of cranberry juice = 0.35 liters

Quantityof water = 1.2liters

Total Quantity of  Special drink = 0.375 L+ 0.35L + 1.2 L= 1.925 Liters

Step 2

But since she wanted to make 2 Liters of the special drink she will have

2 Lter - 1.925L= 0.075Liters  less than the initial 2 Liter of special drink planned.

Answer:

a. 1.925 litres

b. 0.075 litres less

Step-by-step explanation:

a. How much of the special drink can she make?

To find out the quantity of juice produced, add the component juice quantities and the water:

= 0.375 + 0.35 + 1.2

= 1.925 litres

b. How much more or less than 2 litres will she have?

= 2 - 1.925

= 0.075 litres less

Answer:

His percent markup is 150%

Step-by-step explanation:

Answer:

She baked 90 cookies.

Step-by-step explanation:

From the information given you know that 36 cookies represent 40% of the cookies that were baked. With this information, you can use a rule of three to find the total mount of cookies that she baked:

36 cookies →  40%

        x         ← 100%

x=(36*100)/40=90

According to this, the answer is that she baked 90 cookies.

Answer:

Its 50/50 with T or B I say the answer is B

Step-by-step explanation:

Answer:

2a+7b-5

Step-by-step explanation:

7b + 7 + 5b – 5b + 2a – 12

2a+7b+5b-5b+7-12

2a+7b-5

Answer:

Step-by-step explanation:

Initial value of house:

Yearly increase rate of value:

Time

Since the increase is concerning the current price it would be exponential growth.

The function would be:

For t= 13 we get:

Profit made would be:

Correct option is D.

Answer:

Cost of Tammy's house =$184000

Rate of interest = 3.5% per annum

After 13years price will be

[tex]P(t) = 184000 {(1 + \frac{3.5}{100}) }^{t} \\ P(t) = 184000 {(1 + 0.035)}^{t} \\ P(13) = 18400 {(1.035)}^{13} \\ P(13) =\$ 287768[/tex]

Total profit= $(287767-184000)= $103768

Answer:

The first one

Step-by-step explanation:

Answer:

Try 2.75 it should work

Step-by-step explanation:

prove me wrong