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2 years ago

10

What is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree, and enter the

number only.

1 answer:

svlad2 [7]2 years ago

8 0

Answer: 13°

Explanation: x = tan^-1 ( 9/40) ≈ 13°

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The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/m

Mnenie [13.5K]

Answer:

The base is reducing at a rate of 3.4cm per min.

Step-by-step explanation:

Let The Height of the Triangle, h

Area of the triangle = A

Area of a Triangle, $A= \frac{1}{2}bh$

When $A=190 cm^2, h=10cm$

$190= \frac{1}{2}*b*10\\b=38cm$

$\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}+ \frac{1}{2}b\frac{dh}{dt}\\\frac{dh}{dt}=1 cm/min, \frac{dA}{dt}=2cm^2/min,$

$2=\frac{1}{2}*10*\frac{db}{dt}+ \frac{1}{2}*38*1\\2=5\frac{db}{dt}+19\\2-19=5\frac{db}{dt}\\-17=5\frac{db}{dt}\\\frac{db}{dt}=-\frac{17}{5} =-3.4 cm/min$

The base is reducing at a rate of 3.4cm per min.

8 0

3 years ago

The number of pizzas ordered on friday evenings between 5:30 and 6:30 at a pizza delivery location for the last 10 weeks is show

Ainat [17]

For a smoothing constant of 0.2

Time period – 1 2 3 4 5 6 7 8 9 10

Actual value – 46 55 39 42 63 54 55 61 52

Forecast – 58 55.6 55.48 52.18 50.15 52.72 52.97 53.38 54.90

Forecast error - -12 -.6 -16.48 – 10.12 12.85 1.28 2.03 7.62 -2.9
The mean square error is 84.12

The mean forecast for period 11 is 54.38
For a smoothing constant of 0.8

Time period – 1 2 3 4 5 6 7 8 9 10

Actual value – 46 55 39 42 63 54 55 61 52

Forecast – 58 48.40 53.68 41.94 41.99 58.80 54.96 54.99 59.80

Forecast error - -12 6.60 -14.68 0.06 21.01 -4.80 0.04 6.01 -7.80The mean square error is 107.17

The mean forecast for period 11 is 53.56

Based on the MSE, smoothing constant of .2 offers a better model since the mean forecast is much better compared to the 53.56 of the smoothing constant of 0.8.

7 0

3 years ago

The surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²? What is the scale factor of the smaller

max2010maxim [7]

Answer:

scale factor of the smaller prism to the larger prism is B. 21/23

Step-by-step explanation:

Given

surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²?

scale factor is ratio of sides of two similar objects

thus scale factor for given prism will be = side of smaller prism / side of larger prism

in general rule

If shape of solid has scale factor of k

scale factor of area = k²

scale factor of volume = k³

_____________________________

Given in the problem area of two prism is given

we know area = side^2

scale factor of area = k²

k^2 = area of smaller prism / area of larger prism

$k^2 = 882 / 1058 = 441/529\\k = \sqrt{ 441/529} \\k = 21/23$

Thus, correct option is B 21/23.

7 0

3 years ago

Hastings Diner reported losses of $475 each day for three days. What wa the loss for the three days?

Evgen [1.6K]

Answer:

-1425

Step-by-step explanation:

Day 1 - 475

Day 2 -475

Day 3 - 475

-475+ -475 + -475 = -1425

7 0

2 years ago

Alicia and 3 of her friends entered a robotics competition. The rules

natima [27]

Answer:

A. x/4 = 12

Step-by-step explanation:

Alicia and 3 of her friends are 4 people in total. To find what they spent, you do 4 • 12 = x, which is the same as x/4 = 12

4 0

3 years ago