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3 years ago

Solve for missing side lengths

Mathematics

1 answer:

Alinara [238K]3 years ago

4 0

Answer:

n = 6√2 and m = 12.

Step-by-step explanation:

This is a 45-45-90 right angled triangle. It is also isosceles because the 2 acute angles are equal,so n = 6√2.

Also by Pythagoras: m^2 = (6√2)^2 + (6√2)^2

m^2 = 72 + 72 = 144

m = 12.

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Tara wants to weigh her three stuffed animals. They will only fit on the scale two at a time. Together Addie and Missy weight 18

Pepsi [2]

Answer: Addie weighs 4 ounces

Missy weighs 14 ounces

Corky weighs 8 ounces

Step-by-step explanation:

Let a represent the weight of Addie.

Let m represent the weight of Missy.

Let c represent the weight of Corky.

Together Addie and Missy weigh 18 ounces. This means that

a + m = 18 - - - - - - - - - 1

Missy and Corky weigh 22 ounces. This means that

m + c = 22

m = 22 - c - - - - - - - - - - 2

Addie and Corky weigh 12 ounces. This means that

a + c = 12

a = 12 - c - - - - - - - - - - - 3

Substituting equation 2 and equation 3 into equation 1, it becomes

22 - c + 12 - c = 18

34 - 2c = 18

- 2c = 18 - 34 = - 16

c = - 16/ - 2 = 8

Substituting c = 8 into equation 2, it becomes

m = 22 - 8

m = 14

Substituting c = 8 into equation 3, it becomes

a = 12 - 8

a = 4

3 0

3 years ago

Can someone think of a poem which starts with "Today I feel ...." pls

GuDViN [60]

Yes, I shall give you an idea of how to start it. :)

Today I feel glad...
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Special and dear to my heart.

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3 years ago

Read 2 more answers

What are the terms in 4(2x + 3) ÷ 5y

puteri [66]

Answer:

downlaod photo math, take a pic of the question and boom. theres your answer

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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
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

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

2/3 is the slope

____________

(c)

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

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

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4 years ago

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atroni [7]

Answer:

Step-by-step explanation:

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