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solmaris [256]
2 years ago
15

A ladder 10 ft long rests against a vertical wall. Let theta be the angle between the top of the ladder and the wall and let be

the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta=pi/3?
Mathematics
1 answer:
IgorC [24]2 years ago
4 0

Answer:

5 ft/s

Step-by-step explanation:

Let L be the length of the ladder. The relation between the angle and distance X is:

X = L * sin θ      the change of X will be:

dX/dt = L * cos θ    If we evaluate the expression when θ = π/3, we get the change of X:

dX/dt = 10 * cos(π/3)

dX/dt = 5 ft/s

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An arithmetic series has seven terms. the first term is 5 and the last term is 53. find the sum of the series!
Kisachek [45]
The easiest way is to use (& to memorize) the sum formula for a AP:


Sum = 1st term added to the last term & multiplied by half the number of terms
S = (a+l)n/2

S = (5 + 53)(7/2) = 203 
5 0
3 years ago
Kenji is traveling in Europe and renting a car. He is used to thinking of gasoline amounts in gallons, but in Europe it is sold
finlep [7]
10.3 gallons

Good luck!!!!!
7 0
3 years ago
What’s the area? Please help
Nana76 [90]

Answer:

24.5

Step-by-step explanation:

3 0
3 years ago
The number of customers in a grocery store is modeled by the function y -X? + 10x + 50, where y is
vova2212 [387]

Using the vertex of the quadratic function, it is found that:

a) The maximum number of customers in the store is at 12 P.M.

b) 75 customers are in the store at this time.

The number of customers in x hours after 7 AM is given by:

y = -x^2 + 10x + 50

Which is a quadratic equation with coefficients a = -1, b = 10, c = 50

Item a:

The maximum value, considering that a < 0, happens at:

x_v = -\frac{b}{2a}

Hence:

x_v = -\frac{10}{2(-1)} = 5

5 hours after 7 A.M, hence, the maximum number of customers in the store is at 12 P.M.

Item b:

The value is y(5), hence:

y(5) = -(5)^2 + 10(5) + 50 = 75

75 customers are in the store at this time.

A similar problem is given at brainly.com/question/24713268

7 0
2 years ago
Help pls!! this is a presentation I’m doing in class and I NEED this completed rn, ASAP!!! . What I need is just the answers for
nataly862011 [7]

15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.

16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.

17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.

18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.

19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.

20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.

Hope this helps! :)

5 0
2 years ago
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