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otez555 [7]
3 years ago
10

a tram moved upward 27 meters in 3 seconds at a constant rate. what was the change in the tram's elevation each second?

Mathematics
1 answer:
Vesnalui [34]3 years ago
5 0
I believe the answer is 9
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Joe makes belts. He has 9 buckles. He uses 12 rivets on each of 4 belts and 15 rivets on each of 2 belts. He has 22 rivets left
Lerok [7]

Answers:

1. There are rivets on the belts.

2. Extra information given in the problem:

a. He has 9 buckles.

b. He has 22 rivets left over.


Solution:

1. Total rivets on the belts=(12 rivets/belt)(4 belts)+(15 rivets/belt)(2 belts)

Total rivets on the belts=48 rivets+30 rivets

Total rivets on the belts=78 rivets


2. The extra information given in the problem is the information that we didn't use to solve it. In this case:

a. He has 9 buckles.

b. He has 22 rivets left over.

4 0
3 years ago
The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π
Gennadij [26K]
(a)

\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta

or, via symmetry

\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta

____________

(b)

By the chain rule:

\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}

For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that

x = (3 + 2\cos\theta) \cos \theta \\ &#10;y = (3 + 2\cos\theta) \sin \theta

Differentiating with respect to theta

\begin{aligned}&#10;\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\&#10;&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\&#10;\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}&#10;&= 2/3&#10;\end{aligned}

2/3 is the slope

____________

(c)

"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time

</span><span />\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}
5 0
3 years ago
Solve the inequality.
Flauer [41]
-2p<span><20-4
-2p</span><span><16
thus,
p</span><span>>-8</span>
6 0
3 years ago
Anyone want to ta lk plz dont report or delete
givi [52]

Answer:

hey hru

Step-by-step explanation:

and id.k the answer to the second question

4 0
2 years ago
Read 2 more answers
An object was launched off the top of a building. The function f(x)=-16x^2+16x+672 represents the height of the object above the
Katarina [22]

Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

4 0
2 years ago
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