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Tju [1.3M]
3 years ago
11

Question: A man standing in a field in New Hampshire sees Cannon Mountain in front of him. He knows that the height of Cannon Mo

untain is 4080 feet high and that he is 3 miles from the base. If he is looking at the top of the mountain through binoculars, what is his angle of elevation (in degrees) to the top?
Mathematics
1 answer:
KIM [24]3 years ago
4 0
First step is to convert the miles to feet
1 mile = 5280 feet

3 miles x 5280 feet = 15,840 feet.
 now both the height and distance is in feet
 
the angle of elevation is found by calculating the arctan of the height/ distance

arctan(4080 / 15840) = 14.44 degrees

round the answer if needed.

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Mulch to cover a rectangle garden cost $48. Mulch is needed to cover a larger,similar garden. the ratio of dimensions 2:3. how m
Annette [7]
It would cost $72 dollars to cover the larger garden
7 0
4 years ago
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 5 mm. What is
alexgriva [62]
<h2>Answer:</h2>

<em>Rounded to the nearest hundredth the volume of the composite figure is:</em>

<em>1308 33 cubic millimeters</em>

<h2>Explanation:</h2>

Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:

V_{c}=\pi r^2 h \\ \\ r:radius \\ \\ h:height

While the volume of half a sphere is:

V_{hs}=\frac{2}{3}\pi r^3

Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:

V_{s}=\frac{4}{3}\pi r^3

Then, the composite figure is:

V=\pi r^2 h +\frac{4}{3}\pi r^3 \\ \\ V=\pi r^2(h+\frac{4}{3}r)

The radius of the cylinder is the same of the radius of each half sphere. So:

r=5mm \\ \\ h=10mm \\ \\ \\ V=(3.14) (5)^2((10)+\frac{4}{3}(5)) \\ \\ V=25(3.14)(10+\frac{20}{3}) \\ \\ \boxed{V\approx 1308.33mm^3}

7 0
3 years ago
Expand and simplify <img src="https://tex.z-dn.net/?f=%20%283x-2%29%5E%7B2%7D%20" id="TexFormula1" title=" (3x-2)^{2} " alt=" (3
Rus_ich [418]
You can just 1) multiply the binomial by itself, or you can use 2) the square of a binomial pattern. I'll show it to you both ways.

1) Multiply the binomial by itself.

(3x - 2)^2 = (3x - 2)(3x - 2) =

Multiply every term of the first binomial by every term of the second binomial, then collect like terms. (This is often called using FOIL.)

= 9x^2 - 6x - 6x + 4

= 9x^2 - 12x + 4

2) Use the square of a binomial pattern

The square of a binomial is

(a - b)^2 = a^2 - 2ab - b^2

a^2 is the square of the first term.
b^2 is the square of the second term.
-2ab is the product of the two terms and 2.

You have

(3x - 2)^2,
where the first term is 3x, and the second term is -2

square the first term: 9x^2
square the last term: 4
the product of the terms and 2 is: -12x

Put it all together, and you get

9x^2 - 12x + 4

just like we got above with the other method.
7 0
3 years ago
What value has a z-score of -0.67, if the mean is 18 and the standard deviation is 1.68?
uranmaximum [27]
The data point is 1.6 standard deviations above the mean.
Step-by-step explanation:
Z-score
It is the number of standard deviations from the mean that a data point is. It's a measure of how many standard deviations below or above the population mean a raw score is.
A Z-score is also known as a standard score and it can be placed on a normal distribution curve.
As in this case the Z-score is +1.6, so it means the data point is 1.6 standard deviations above the mean. Hope this helps I am kinda knew to this so I hope I helped you
7 0
3 years ago
(20 points) Can someone explain to me how to multiply polynomials? Practice question: (y - 3) (y - 4)
kramer

Answer:

y² -7y+12

Step-by-step explanation:

first, you have to multiply each character on the first parenthesis to the second one, one by one. just like the picture attached.

then, combine all of the same variable. like the 2 variable that has y.

6 0
3 years ago
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