1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an apothem SM = √15 cm. Calculate the pyramid: 1) the base elevation AM; 2) the elevation SO; 3) the area of the base; 4) the area of the side surface; 5) the total surface area; 6) volume.
Answers
Given:
• AB = 6 cm
,• SM = √15 cm
Let's solve for the following:
• 1) the base elevation AM.
Given that we have a regular triangular pyramid, the length of the three bases are equal.
AB = BC = AC
BM = BC/2 = 6/2 = 3 cm
To solve for AM, which is the height of the base, apply Pythagorean Theorem:
[tex]\begin{gathered} AM=\sqrt{AB^2-BM^2} \\ \\ AM=\sqrt{6^2-3^2} \\ \\ AM=\sqrt{36-9} \\ \\ AM=\sqrt{27} \\ \\ AM=5.2\text{ cm} \end{gathered}[/tex]The base elevation of the pyramid is 5.2 cm.
• (2)., The elevation SO.
To find the elevation of the pyramid, apply Pythagorean Theorem:
[tex]SO=\sqrt{SM^2-MO^2}[/tex]Where:
SM = √15 cm
MO = AM/2 = 5.2/2 = 2.6 cm
Thus, we have:
[tex]\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\ \\ SO=\sqrt{15-6.76} \\ \\ SO=2.9\text{ cm} \end{gathered}[/tex]Length of SO = 2.9 cm
• (3). Area of the base:
To find the area of the triangular base, apply the formula:
[tex]A=\frac{1}{2}*BC*AM[/tex]Thus, we have:
[tex]\begin{gathered} A=\frac{1}{2}*6^*5.2 \\ \\ A=15.6\text{ cm}^2 \end{gathered}[/tex]The area of the base is 15.6 square cm.
• (4). Area of the side surface.
Apply the formula:
[tex]SA=\frac{1}{2}*p*h[/tex]Where:
p is the perimeter
h is the slant height, SM = √15 cm
Thus, we have:
[tex]\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\ \\ A=34.86\text{ cm}^2 \end{gathered}[/tex]• (5). Total surface area:
To find the total surface area, apply the formula:
[tex]TSA=base\text{ area + area of side surface}[/tex]Where:
Area of base = 15.6 cm²
Area of side surface = 34.86 cm²
TSA = 15.6 + 34.86 = 50.46 cm²
The total surface area is 50.46 cm²
• (6). Volume:
To find the volume, apply the formula:
[tex]V=\frac{1}{3}*area\text{ of base *height}[/tex]Where:
Area of base = 15.6 cm²
Height, SO = 2.9 cm
Thus, we have:
[tex]\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\ \\ V=15.08\text{ cm}^3 \end{gathered}[/tex]The volume is 15.08 cm³.
ANSWER:
• 1.) 5.2 cm
,• 2.) 2.9 cm
,• 3.) 15.6 cm²
,• 4.) 34.86 cm²
,• (5). 50.46 cm²
,• 6). 15.08 cm³.
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The answer is Option 2
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Suppose you have a piece of ribbon that is 6 feet long, and you cut off one piece that's 3 2/3
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inches of ribbon left
Answers
Answer:
65 1/2 inches of ribbon is left, my exact work is shown on a piece of paper below if you need it.
Step-by-step explanation:
1 foot = 12 inches
6 x 12 = 72 inches
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My explanation:
The rib ion originally started at 6 feet
You first cut 3 2/3 off, so your now left with 7/3 or 2 1/3 (simplified)
Now your left with 2 1/3.
Then you cut a second piece off, 2 5/6 inches….so 2 5/6 minus 2 1/3 = 1/2
So you should have about 1/2 of a ribbon left.
(I tried btw. I’m very sleepy rn.)
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Answers
Step 1
State the volume of a hemisphere.
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ANSWER:
2
STEP-BY-STEP EXPLANATION:
The average rate of change is given by the following formula:
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Michael studied the feather lengths of some adult fox sparrows.How long is the shortest feather in the data set?
Answers
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
Given,
The image is attached with this.
The length of fox sparrow feathers studied by Michael.
1 sparrow with 3/4 inches of feather4 sparrows with 2 inches of feather7 sparrows with 2 1/4 inches of feather5 sparrows with 2 1/2 inches of feather3 sparrows with 2 3/4 inches of feather.We have to find the shortest feather in the data set.
Here,
3/4 inches is the shortest feather and only 1 sparrow has the shortest feather.
2 3/4 inches is the longest feather and 3 sparrows have the longest feather.
That is,
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
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Sean, Kevin and Bill take classes at both JJC and CSU. Sean takes 8 credits at JJC and 4 credits at CSU; Kevin takes 10 credits at JJC and 6 at CSU: Bill takes 6 credits at JJC and 4 at CSU; the cost per credit at JJC is $103 and at CSU is $249. a) Write a matrix A that gives the credits each student is taking and B that gives the cost per credit at each school. b) Find the dimension of A and B. c) Find the product AB and the names of its rows and columns.
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ANSWER:
a)
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Dimension A = 3 x 2
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c)
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Kevin $2524
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Answers
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Answers
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To make an open box from a 175cm by 100cm piece of cardboard, equal-sized squares will be cut from each of the four corners and then the sides will be folded up. What is the approximate volume of the largest possible box that can be made?Group of answer choices:A) 324,146 cm^3B)162,073cm^3C) 251,707cm^3D)189,640cm^3
Answers
Given that dimensions of the piece of cardboard are:
[tex]\begin{gathered} l=175\text{ }cm \\ w=100\text{ }cm \end{gathered}[/tex]Where "l" is the length and "w" is the width, you can determine that it has the shape of a rectangle.
You know that equal-sized squares will be cut from each of the four corners and then the sides will be folded up. Then, you can make the following drawing:
By definition, the volume of a rectangle is:
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[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]Then:
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[tex]\begin{gathered} x_1\approx20.49 \\ x_2\approx71.18 \end{gathered}[/tex]Therefore, you can make the following Sign Chart:
Then, you can substitute these:
[tex]\begin{gathered} x=20 \\ x=50 \\ x=72 \end{gathered}[/tex]Into the factorize form of the derivated function:
[tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex][tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex]a point is chosen at random in the large square. find the probability that the point is in the smaller shaded square. each side of the large square: 16 cmeach side of the shaded square: 6 cm*round to the nearest hundredth
Answers
The Probability of the point being in the smaller shaded square is 0.79.
What is meant by probability?Probability equals possibility. It is a branch of mathematics concerned with the occurrence of a random event. The value ranges from 0 to 1. Probability has been introduced in mathematics to predict how likely events are to occur.Probability = the number of possible outcomes. the total number of possible outcomes For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and the total number of possible outcomes is two (a head or tail).The probability is a measure of the likelihood of an event occurring. It assesses the event's likelihood. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the probability formula.Therefore,
|Ω| = 6² = 36
< br / > |A| = 3.14.3² = 278.26
Then we get,
< br / > P |A| = 28.26/36 ≈ 0.79
∴ the probability that the point is in the smaller shaded square is 0.79
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Convert the polar equation r=3 to a Cartesian equation.x^2+y^2=√3x^2+y^2=3x^2+y^2=9
Answers
For the given equation:
[tex]\begin{gathered} \text{Polar form: } \\ r=3 \\ \\ \text{Cartesian form:} \\ x^2+y^2=3^2 \\ x^2+y^2=9 \end{gathered}[/tex]there are 5 adult cats, 6 middle aged cats, and ___ kittens, if there are 19 animals in total, how many kittens are there, solve for the blank.
Answers
ANSWER
There are 8 kittens
EXPLANATION
If the sum of the number of adult cats, middle aged cats and kittens is 19:
[tex]\begin{gathered} \text{adult}+\text{middle aged+kittens=19} \\ 5+6+\text{kittens}=19 \\ \text{kittens}=19-5-6 \\ \text{kittens}=8 \end{gathered}[/tex]Evaluate the expression [tex]9 + 7 - 3 \times 3 - 2[/tex]
Answers
The crew knows the amount of dirt the truck can hold each trip in cubic yards.
Answers
Given:
Measurements of hole are 48ft 39ft and and 9ft
Required:
Volume in cubic yd
total number of trip
total cost of trip
Explanation:
First we need to convert given measurements from ft to yd
[tex]\begin{gathered} 3ft=1yd \\ 48ft=16yd \\ 39ft=13yd \\ 9ft=3yd \end{gathered}[/tex]
A)
[tex]V=lhw=16*13*3=624yd^3[/tex]B)
11 cubic yd in 1 trip
then
624 cubic yd in x trip
[tex]x=\frac{624}{11}=56.7\approx57[/tex]C)
cost for 1 trip is $1175
then
cost for 57 trip is y
[tex]y=57*1175=66975[/tex]Final answer:
Volume in cubic yd is 624
total number of trips is 57
total cost of trip $66975
3(2x+4) - 2(4x-1)=20A. x=5B. x=-5C. x=3D. x=-3
Answers
we have the following:
[tex]3(2x+4)-2\left(4x-1\right)=20[/tex]solving for x:
[tex]\begin{gathered} 3(2x+4)-2\left(4x-1\right)=20 \\ 6x+12-8x+2=20 \\ -2x=20-12-2 \\ -2x=6 \\ x=\frac{6}{-2} \\ x=-3 \end{gathered}[/tex]The answer is x = -3
Convert decimal to 0.147 to fraction ( the last digit 7 repeating)
Answers
Answer:
133/900
Explanation:
To convert the decimal 0.147777 to a fraction, we first identify the decimal part, so we have 147 as a decimal part.
Then, we subtract 14 because that part is not repeating. So:
147 - 14 = 133
Now, we need to divide by 9 to get the repeating part, but the repeating part starts at the third decimal place, so we will divide by 900 instead of 9.
Therefore, 0.147777... as a decimal is:
[tex]0.14777\ldots=\frac{133}{900}[/tex]So, the answer is 133/900
graph the function y=sqrt(x+6)+2. which point lies on the graph
Answers
Explanation
We are given the following function:
[tex]y=\sqrt{x+6}+2[/tex]We are required to graph the function.
Using a graphing calculator, we have:
Hence, the answer is (-2, 4).
The last option is correct.
in slope intercept form what is the line perpendicular to y=2x -5 that passes through the (2, -5) point
Answers
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = -\frac{1}{2}x - 4[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
The given equation of line is y = 2x-5
Slope of this line = 2
Slope of the line perpendicular to this line = [tex]-\frac{1}{2}[/tex]
The line passes through (2 , -5)
Equation of the required line = [tex]y - (-5) = \frac{1}{2}(x - 2)[/tex]
[tex]y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4[/tex]
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The function table below is intended to represent the relationship y=-5x+1. However, one of the entries for y does not correctly fit the relationship with x.
Answers
Answer:
Step-by-step explanation:
none of the answers are correct
Kristy downloads two songs to her MP3 player. The songs are 3 1/10 minutes and 4 2/3 minutes long. About how many minutes of memory will these two songs use altogether?
Answers
We have:
Song 1 = 3 1/10 minutes
Song 2 = 4 2/3 minutes
Minutes of memory of two songs:
[tex]3\frac{1}{10}+4\frac{2}{3}=\frac{31}{10}+\frac{14}{3}=\frac{3\times31+10\times14}{30}=\frac{93+140}{30}=\frac{233}{30}=7\frac{23}{30}[/tex]Answer:
[tex]7\frac{23}{30}\text{ minutes}[/tex]Please help. I don't really understand monomials and negative exponets
Answers
The standard form of the monomial expression is -1x¹⁰
Monomial expression:
A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.
Given,
Here we have the expression
(-2x³)².(-1/4 x⁴)
Now, we have to convert the expression into standard form.
To convert the expression into standard monomial form,
First we have to expand the terms, then we get,
=> (-2²x⁶).(-1/4x⁴)
Then we have to divide the variables and constants separately.
=> (4 x -1/4).(x⁶⁺⁴)
=> -1 . x¹⁰
=> -1x¹⁰
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54 is 120 percent of what number ?
Answers
Answer:
120% of 54 =
120% × 54 =
120/100 × 54 =
(120 ÷ 100) × 54 =
120 × 54 ÷ 100 =
6,480 ÷ 100 =
64.8
Percentage of 120% of 54
120% of 54 = 64.8
and to prove that we got the right answer do what we did above in reverse below
64.8 ÷ 54 =
1.2 =
1.2 × 100/100 =
(1.2 × 100)/100 =
120/100 =
120%
Step-by-step explanation: