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4 years ago

Help and ill give extra (60 points)

Mathematics

1 answer:

murzikaleks [220]4 years ago

6 0

Answer:

1) substitution method

2) zero

Step-by-step explanation:

because it has no solution as the variables cancle out eachother.

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A ladder 16 feet long is leaning against the wall of a tall building. The base of the ladder is moving away from the wall at a r

svet-max [94.6K]

Answer:

a. 0.588

b. 0.0722

c. 4.576 sqft/sec

Step-by-step explanation:

Let b and h denote the base and height as indicated in the diagram. By pythagoras theorem, $h^2 + b^2 = 16^2 = 256 \dotsc\;(1)$ because it is a right angle triangle.

It is given that $\frac{db}{dt} = 1$

Now differentiate (1) with respect to t (time) :

$\displaystyle{2h\frac{dh}{dt} + 2b\frac{db}{dt} = 0 \implies \frac{dh}{dt} = -\frac{b}{h} \frac{db}{dt}}$

$\displaystyle{=-\frac{b}{\sqrt{256 - b^2}} \frac{db}{dt} = -\frac{8}{13.856} \times 1 = -0.588}$

The minus sign indicates that the value of h is actually decreasing. The required answer is 0.588.

b. From the diagram, infer that $16 \sin{\theta} = b$ . When b = 8, then $\theta = \arcsin{0.5} = \ang{30}$ .

Differentiate the above equation w.r.t t

$\displaystyle{16 \cos{\theta} \frac{d\theta}{dt} = \frac{db}{dt} \implies \frac{d\theta}{dt} = \frac{1}{16 \cos{\theta}} = \frac{1}{13.856} = \mathbf{0.0722}}$

c. The area of the triangle is given by $A = 0.5\times h \times b$ . Differentiating w.r.t t,

$\displatstyle{\frac{dA}{dt} = 0.5 b \frac{dh}{dt} + 0.5 h \frac{db}{dt}}$

Plugging in b = 8, h = 13.856, $\frac{dh}{dt} = -0.588$ ,

$\frac{dA}{dt} = -2.352 + 6.928 = \mathbf{4.576 ft^2/sec}$

8 0

4 years ago

A subway car travels at a rate of 32 meters per second. How far does it travel in 16 seconds? The subway travels _________. Plea

Tasya [4]

1.5 miles bc if you add them up and multiply you get 1.5 miles.

8 0

3 years ago

Read 2 more answers

What is the sales tax

hichkok12 [17]

Answer:

Before Tax Price: $110.00

Sale Tax: 6.10% or $6.71

After Tax Price: ($116.71)

Step-by-step explanation:

6 0

3 years ago

Find the equation of the line which passes through (-2,-2) and (2, -4).

Lana71 [14]

It should be B

Calculate the slopes using the change of y over the change in x

-2/2=-1

That’s the only option with a slope of -1

8 0

3 years ago

Read 2 more answers

Determine whether each of these sets is nite, countably in nite, or uncount- able. For those that are countably in nite, exhibit

ira [324]

Answer:

Integers that are divisible by 7 are countably infinite

The set are {7, 14, 21, 28, 35, 42, 49,......

Integers that are divisible by 10 are countably infinite

The set are {10, 20, 30, 40, 50, 60, 70,........

Also for the negative integers divisible by 7 or 10{.......,-49, -42, -35, -28, -21, -14, -7} or {........,-70, -60, -50, -40, -30, -20, -10} are countably infinite

Step-by-step explanation:

See the set of integers divisible by 7 or 10,

{7, 14, 21, 28, 35, 42, 49,........} Or

{10, 20, 30, 40, 50, 60, 70,.......}

Can be map one-to-one to {1,2,3,4,5,6,7,...... The set of natural numbers or positive Integers.

So also, it is applicable in negative integers divisible by 7 or 10.

Therefore, they are countably infinite

A set is uncountable if it contains so many elements that they cannot be put in one-to-one correspondence with the set of natural numbers(Positive Integers). In other words, there is no way that one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.

WHILE

A set is countable or countably finite if it contains so many elements that they CAN be put in one-to-one correspondence with the set of natural numbers(Positive Integers)

3 0

3 years ago