A man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 20ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight.

Answers

Answer 1

Answer: Now note that tan(y) = x=20,
so that sec^2y *dy/dt=1/20 dx/dt
At the instant describedin the problem,
x = 15 and the hypotenuse of the above triangle
thus has length25,
so we compute:(25/20)^2 dy/dt=1/20*4 ==>dy/dt=1/2*400/625

=16/125 rad/sec

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if a worker is paid $8.16 per hour and works 8.5 hours in one week how much is she or he paid for that week

Answers

8.16x8.5 = 69.36 what I did to find 69.36 was multiplied 8.16x8 then 8.16x .5 and then added the 2 answers together

-37= n/23
what is n?

Answers

-37 = n
23

to solve for n, undo what is happening to the n. if the n is being divided by 23 to get -37, then multiply both sides by 23 to figure out what n is.

-37 * 23 = n * 23
23

-851 = n

the 23 is crowding the n by division
so to undo that we multiply both sides by 23
to get n alone

n = -37 * 23 = - 851

so n = - 851

Algebraically solve the system of equations shown below. Note that you can use either factoring or the quadratic formula to find the X – coordinates, but the quadratic formula is probably easier.

Answers

$6x^2+19x-15=-12x+15\n6x^2+31x-30=0\n6x^2+36x-5x-30=0\n6x(x+6)-5(x+6)=0\n(6x-5)(x+6)=0\nx=(5)/(6) \vee x=-6\n\ny=-12\cdot(5)/(6) +15\vee y=-12\cdot(-6)+15\ny=-10 +15\vee y=72+15\ny=5 \vee y=87\n\nx=(5)/(6) \wedge y=5\nx=-6 \wedge y=87$

$y=6x^2+19x-15 \ny=-12x+15 \n \n6x^2+19x-15=-12x+15 \n6x^2+19x+12x-15-15=0 \n6x^2+31x-30=0 \n \n a=6 \n b=31 \n c=-30 \n \n x=(-b \pm √(b^2-4ac))/(2a)=(-31 \pm √(31^2-4 \cdot 6 \cdot (-30)))/(2 \cdot 6)=(-31 \pm √(1681))/(12)=(-31 \pm 41)/(12) \n x=(-31 -41)/(12) \ \hbox{or} \ x=(-31+41)/(12) \nx=-6 \ \hbox{or} \ x=(5)/(6)$

$y=-12 \cdot (-6)+15 \ \hbox{or} \ y=-12 \cdot (5)/(6)+15 \ny=87 \ \hbox{or} \ y=5 \n \n \hbox{the answer:} \n \boxed{x=-6, \ y=87} \ \hbox{or} \ \boxed{x=(5)/(6), \ y=5}$

35 =-4w+7(w+8)
I need help please I keep trying but im getting the wrong answer

Answers

I think this is it
I hope this is right lol

Answer:

-7

Step-by-step explanation:

35=-4 w +7w+56

35-56=3w

-21/3=w

w=-7

Luis walked 2 3/4 miles in 2 hours. How many miles did he walk in one hour?

Answers

The number of miles walked by Louis in 1 hour is given by the equation

A = 11/8 miles = 1 3/8 miles

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of miles walked by Louis in 1 hour be A

Now , the equation will be

The number of miles walked by Louis in 2 hours = 2 3/4 miles

The number of miles walked by Louis in 2 hours = 11/4 miles

Now ,

The number of miles walked by Louis in 1 hour A = ( 1/2 ) x number of miles walked by Louis in 2 hours

Substituting the values in the equation , we get

The number of miles walked by Louis in 1 hour A = ( 1/2 ) x 11/4 )

On simplifying the equation , we get

The number of miles walked by Louis in 1 hour A = 11/8 miles

Therefore , the value of A is 1 3/8 miles

Hence , the number of miles is 11/8 = 1 3/8 miles

To learn more about equations click :

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Answer:

1 3/8

Step-by-step explanation: divide by 2 (11/16) then add them together to see if you get 2 3/4

A manufacturer produces soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 14% of the cans are defective. What is the probability that the two selected cans are defective if the quality control worker selects the two cans from a batch of 50 cans?P(Both defective) = 7/50
P(Both defective) = 49/2500
P(Both defective) = 3/175
P(Both defective) = 7/25

Answers

Probability of being defective is 14% = 14/100 = 7/50

P(Both defective) = 7/50 * 7/50 = 49/2500

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