What is the slant height x of the square pyramid? Enter your answer in the box, express your answer in radical form.
Answers
hypotenuse of the triangle.
Angle between the base of the triangle and the hypotenuse.
We want to find the height of the triangle.
For this, we use the following trigonometric relationship:
[tex]sine (60) = x / 8 [/tex]
From here, we clear the value of x.
We have then:
[tex]x = 8 * sine (60) x = 6.93 m[/tex]
Answer:
The inclined height of the pyramid is given by:
x = 6.93 m
Related Questions
What are MODE,MEDIAN
EXPLAIN pls.
Answers
To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list.
To find the mode, identify which value in the data set occurs most often.
PART A: All but two of the pyramids built by the ancient Egyptians have faces inclined at 52 degree angles. Suppose an archaeologist discovers the ruins of a pyramid. Most of the pyramid has eroded, but the length of a side of the square base is 82 meters. How tall was the pyramid, assuming its faces were inclined at 52 degrees? Round your answer to the nearest meter.
25 m
32 m
52 m
105 m,
Answers
The height forms a right triangle with the slant height of the pyramid and half of the length of the square base. Half of the length of the square base would be 41m. The angle is 52°. The sides we have are the height, which is opposite the angle, and half of the base, which is adjacent to the angle. The ratio opposite/adjacent is used for the tangent. Our equation would be:
tan 52=h/41
We multiply both sides by 41:
41*tan 52 = (h/41)*41
41*tan 52 = h
Evaluating this we get 52m.
In the problem, we were asked to compute for the height of the pyramid. Given are the base of the pyramid which is 82 m and the angle of 52°.
If given an illustration, the height is opposite to the angle and the adjacent side is given by half the base.
Based on the mnemonics of trigonometry (SOH CAH TOA), the function to be used is tangent.
The computation is as follows:
Let h = height of pyramid (m)
tan52 = h/41
h = 41tan52
h ≈ 52.5 m
Hence, the height of the pyramid is approximately 52.5.
However, the closest answer based on the choices you provided is 52 m.
Write an exponential function that passes through the points (0, 3) and (-1, 6)
Answers
when x=0, y=3, 3=ab^0, so you can figure out that a=3
when x=-1, y=6, 6=3b^(-1), b^(-1)=2, b=1/2
so the equation is y=3(1/2)^x
after examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conclusion?
A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem
Answers
The Proportional Medians Theorem states:If two triangles are similar, then the ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
It is given the two triangles are similar.FG and TU are the medians of the triangle .
By Proportional Medians Theorem ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
So [tex] \frac{FG}{TU} =\frac{EF}{ST} [/tex]
Option D. Proportional Medians Theorem is the right answer.
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 190 grams of a radioactive isotope, how much will be left after 4 half-lives?
Answers
If arc SQ = 92° and arc QR = 86°, what is the measure percent of ∠RPS
Answers
Since it's a triangle the sum of all angles is 180. So 180-86-92=2
The answer is 45°. First combine arc SQ and QR: 178°. Then subtract that from the whole circle (360°) and that will give us 182°. Now subtract arc SQ from it and divide the difference (90°) by two.
The number of animals in a population is 775, and it increases by of 51% each year.
a. Model the situation with an exponential function.
b. Find how many animals there will be in 10 years.
c. How many years will it take for the population to become 1150.
Show all work!
Answers
Answer(a):
Exponential growth formula is given by
[tex]A=P(1+r)^t[/tex]
Where preset population = P= 775
Rate of increase = r = 51% = 0.51
t= number of years
A= Future value.
Plug these values into above formula:
[tex]A=775(1+0.51)^t[/tex]
[tex]A=775(1.51)^t[/tex]
Hence required exponential function is [tex]A=775(1.51)^t[/tex]
Answer(b):
plug t=10 years
[tex]A=775(1.51)^t=775(1.51)^{10}=775(61.6267795034)=47760.7541151[/tex]
which is approx 47761.
Answer(c):
Plug A=1150
[tex]1150=775(1.51)^t[/tex]
[tex]\frac{1150}{775}=(1.51)^t[/tex]
[tex]\ln(\frac{1150}{775})=t*\ln(1.51)[/tex]
[tex]0.394654192004=t*0.412109650827[/tex]
0.957643654334=t
Which is approx 1 year.
Factor completely. 12x^4+18x^3+45x^2
Answers
3x² ( 4x² + 6x + 15)
Answer: so is the answer 3^2 or the other?
Step-by-step explanation:
well anyway but what I know the answer should be the second thing because you want the numbers to be the LCM which for this it would be (4x^2 + 6x + 15) but not 100% bout this
Then, the dot ran from −34 to −66. What distance did it cover? If this run took the dot 5 minutes, what was its average speed?
Answers
Final answer:
The dot covered a distance of 32 units when it ran from -34 to -66. Assuming the distance is measured in meters, and the dot took 5 minutes (300 seconds) to cover this distance, the average speed would be 0.1067 m/s.
Explanation:
To determine the distance the dot covered when it ran from -34 to -66, we need to calculate the absolute value of the difference between the two points. The formula for distance in this case is |final position - initial position|, so the distance covered = |-66 - (-34)| = |-66 + 34| = | -32 | = 32 units.
Now, to determine the average speed of the dot, we divide the total distance traveled by the time it took to cover that distance. Given that it took the dot 5 minutes to cover the distance, we convert minutes to seconds because speed is typically measured in meters per second (m/s) in physics. There are 60 seconds in a minute, so 5 minutes is 300 seconds. Therefore, the average speed is distance/time = 32 units / 300 seconds.
The exact units of measurement for distance have not been specified in the question, but assuming the distance is in meters (m), the average speed would be calculated as 32 m / 300 s = 0.1067 m/s.
By what factor does the y-value change for y = 4x?
Answers
Simple answer: y increases by four every time x increases by one.
Answer:
the answer is 4
Step-by-step explanation:
Find the first four terms of the given sequence tn = (-1)n(n).
A.
-1, -2, -3, -4
B.
-1, 2, -3, 4
C.
1, ½, 2/3, ¾
D.
1, 2, 3, 4
Answers
tn = ((-1) ^ n) * (n)
We now look for each of the terms:
t1 = ((-1) ^ 1) * (1) = - 1
t2 = ((-1) ^ 2) * (2) = 2
t3 = ((-1) ^ 3) * (3) = - 3
t4 = ((-1) ^ 4) * (4) = 4
The first four terms of the sequence are then:
-1, 2, -3, 4
Answer:
B.
-1, 2, -3, 4
Type 3xxyyy using exponents.
Answers
The answer to your question is simple.
3xxyyy
Count how many xs there are. This is the exponent on the x.
3x²yyy
Count how many ys there are. This is the exponent on the y.
3x²y³
I really hope this helps!
Best wishes :)
Mrs. Gomez is sewing a dress for each of her four daughters. Each dress uses 2.25 yards of fabric, and the fabric costs $4.15 per yard. What will be the cost for fabric for all four dresses? Show your work, including labeling your answer with the appropriate units of measure.
Answers
Answer:
The cost for fabric for all four dresses is $37.35
Step-by-step explanation:
Each Dress requires fabric = 2.25 yards
Fabric required for 4 dresses = [tex]2.25 \times 4[/tex]
= [tex]9yards[/tex]
Cost of 1 yard fabric = $4.15
Cost of 9 yard fabric = [tex]4.15 \times 9[/tex]
= $37.35
Hence the cost for fabric for all four dresses is $37.35
SOMEONE HELP ME PLEASE MY LAST DAY TO TURN THIS IN!
Solving Systems of Equations by Elimination
1) 5x + 2y= 21
-x - y= -9
2) 3x + 2y= -13
3x+4y= 1
3) 7x + 3y= 22
4y= 20
4) -2x + y= 10
4x - y= -14
Answers
I'll solve the first two systems.
1)
[tex] \left \{ {{5x+2y=21} \atop {-x-y=-9}} \right. [/tex]
Multiply the second equation in the system by 2 to be able to cancel out y-terms:
[tex]-x-y=-9[/tex]
[tex]2(-x-y=-9)[/tex]
[tex]-2x-2y=-18[/tex]
Now, add the equations together:
[tex] \left \ {{5x+2y=21} \atop {-2x-2y=-18}} \right. [/tex]
_____________
[tex]3x-0=3[/tex]
[tex]3x=3[/tex]
[tex]x=1[/tex]
Plug 1 for x into one of the original equations to find y:
[tex]5x+2y=21[/tex]
[tex]5(1)+2y=21[/tex]
[tex]5+2y = 21[/tex]
[tex]2y=16[/tex]
[tex]y =8[/tex]
Check work by plugging your values for x and y back into both original equations:
[tex] \left \ {{5x+2y=21} \atop {-x-y=-9}} \right. [/tex]
[tex] \left \ {{5(1)+2(8)=21} \atop {-(1)-(8)=-9}} \right. [/tex]
[tex] \left \ {{5+16=21} \atop {-1-8=-9}} \right. [/tex]
Both are true; x = 1 and y = 8.
2)
[tex] \left \ {{3x+2y=13} \atop {3x+4y=1}} \right. [/tex]
For this system, to be able to cancel out x-terms, you can multiply either equation by -1; I'll use the bottom equation:
[tex]-1(3x+4y=1)[/tex]
[tex]-3x-4y=-1[/tex]
Now add the equations together:
[tex] \left \ {{3x+2y=-13} \atop {-3x-4y=-1}} \right. [/tex]
_____________
[tex]0-2y=-14[/tex]
[tex]-2y = -14[/tex]
[tex]y=7[/tex]
Plug 7 for y into either of the original equation to solve for x:
[tex]3x+2(7)=-13[/tex]
[tex]3x+14=-13[/tex]
[tex]3x = -27[/tex]
[tex]x=-9[/tex]
Plug -9 for x and 7 for y into each original equation to check work:
[tex] \left \ {{3(-9)+2(7)=-13} \atop {3(-9)+4(7)=1}} \right. [/tex]
[tex] \left \ {{-27+14=-13} \atop {-27+28=1}} \right. [/tex]
Both are correct; x = -9 and y = 7.
Apply these steps to the last two systems and you're good to go. (:
Write the equation of the circle with center (0, 0) and (5, 2) a point on the circle.
Answers
the equation of the circle with center (0, 0) is ---------> x²+y²=r²
Step 1
find the radius
the radius is simply the distance from the center to the point (5,2)
d=√[(5²+2²)]-------> d=√29
r=√29
the equation of the circle is
x²+y²=29
the answer is x²+y²=29
r²=(x-h)²+(y-k)²
2. The center of this circle is (0,0), then:
h=0
k=0
3. When you substitute the values of h and k into the equation, you have:
r²=(x-h)²+(y-k)²
r²=(x-0)²+(y-0)²
r²=x²+y²
3. Now, you must find the radius "r".
4. You know that the point is (5,2), so:
r²=x²+y²
5. Finally:
√29=x²+y²
find the difference 6x^2-14x+4/x(x-2) - 6x-1/x+1
Answers
Final answer:
To find the difference between two expressions in the given question, you need to simplify each expression first and then subtract them. The steps involve simplifying each expression separately and then performing the subtraction.
Explanation:
To find the difference 6x² - 14x + 4 / x(x - 2) - 6x - 1 / x + 1, you need to first simplify each expression and then subtract them from each other.
Step 1: Simplify each expression separately.
6x² - 14x + 4 / x(x - 2) = (3x - 2)(2x - 1) / x(x - 2) = 3(2x - 1) / x
- 6x - 1 / x + 1 = -6 - 1 / x + 1 = -7 / (x + 1)
Step 2: Subtract the two simplified expressions: 3(2x - 1) / x - 7 / (x + 1).
Parallelogram DEFG has been rotated. Which statements are correct? Check all that apply.
Answers
point F ⇒ point F'
Point D of the pre-image corresponds to pint D' of the image
Parallelogram DEFG maps to parallelogram D'E'F'G'
In geometry, rotation involves turning of an object about a center. The statements that are correct are:
point F [tex]\to[/tex] point F'point D of the preimage corresponds to point D' of the imageparallelogram DEFG maps to parallelogram D'E'F'GWhen rotation is applied to a shape, the orientation of the shape will change; however the corresponding points will be unchanged.
This means that:
DEFG will be mapped to D'E'F'GPoints D, E, F and G will correspond to points D', E', F' and G'.Hence, the true statements are: (a), (c) and (e)
Read more about rotation at:
https://brainly.com/question/1571997
Which expression can be used to find the value of X?
Answers
b / sin(B) = a / sin(A)
b / sin(32°) = 11 / sin(47°)
b = (sin(32°) x 11) / sin(47°) <---- You would use this, so rewritten
11(sin(32))/sin(47) would be the expression, or answer B.)
BTW b = 7.970
Hope this helps!
Which of the following forms of bonds has the least risk
Municipal bonds
Below investment grade bonds
Corporate bonds
Treasury bonds
Answers
Treasury Bonds is the correct answer.
Treasury Bonds has the least risk as these bonds are issued and backed by the United States federal government. They are credit-risk free as they have practically no default risk and thus the safest bonds to buy. These are issued by the government to finance its budget deficits.
Which rational number represents a decrease in water level from 8 feet to 6 feet?
Answers
Tell me if it is right or not
What is the value of b in the equation (yb) 4= 1/y24
Answers
Answer:
The value of b is [tex]\frac{1}{y^7}[/tex].
Step-by-step explanation:
Here the given expression is,
[tex](yb)^4=\frac{1}{y^{24}}[/tex]
[tex]y^4b^4=\frac{1}{y^{24}}[/tex] ( Using [tex](ab)^m=a^mb^m[/tex] on left side )
[tex]y^4b^4y^24 = 1[/tex] ( By cross multiplication )
[tex]y^{4+24}b^4=1[/tex] ( Using [tex]a^ma^n=a^{m+n}[/tex] on left side )
[tex]y^{28}b^4=1[/tex]
[tex]b^4=\frac{1}{y^{28}}[/tex]
[tex]b=(\frac{1}{y^{28}})^{\frac{1}{4}}[/tex] ( [tex]a^m=b^n\implies a=b^\frac{n}{m}[/tex] )
[tex]b=\frac{1^{\frac{1}{4}}}{(y^{28})^\frac{1}{4}}[/tex] ( [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex] )
[tex]b=\frac{1}{y^{28\times \frac{1}{4}}}[/tex] ( [tex](a^m)^n=a^{m\times n}[/tex] )
[tex]b=\frac{1}{y^7}[/tex]
Answer:
It is -6
Step-by-step explanation:
Find the volume of the sphere with a radius of 9. Express your answer in terms of π.
Answers
On this exercise is given the radius of the sphere and is asked to find its volume in terms of π. The first step would be substitute the values into the previous mention formula.
V=4/3πr^3
V=4/3π(9)^3
V=4/3π(729)
V=972π
The volume of the sphere in terms of pi is 972π.
two line segments ab and cd, have end points at A ( -5,11) , B( 3,5) , C (9,3) and D (2,10) which of the two lines segments is longer ?
Answers
segment AB is longer than segment CD
Line segment AB is longer than segment CD.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Two line segments AB and CD have endpoints at A (-5, 11), B(3, 5), C (9, 3) and D (2, 10).
To find the distance:
The distance of two points
= √ {(x₂-x₁)² + (y₂-y₁)²}
The distance of segment AB
= √ {(3+5)² + (5-11)²}
= √ {(8)² + (-7)²}
= √(64 + 49)
= √(64 + 49)
= √113
= 10.63 unit.
The distance of segment CD
= √ {(2-9)² + (10-3)²}
= √ {(-7)² + (7)²}
= √(49 + 49)
= √98
= 9.9 unit.
Clearly, distance of AB > distance of CD
Therefore, distance of AB > distance of CD.
To learn more about the distance between two points;
https://brainly.com/question/24485622
#SPJ2
The distance formula is d = rt. A trip of 92 miles traveled at 65 mph will take 1.35 hours.
A. True
B. False
Answers
65 * 1.35 = 87.75
87.75 does not equal 92
so this is False
Write the equation in slope-intercept form of the line that has a slope of -5 and a y-intercept of 2.
Answers
Slope intercept form is in the form y=mx+b
m is the slope, and that is given so we can plug that into the equation
y = -5x + b
We are also given the y-intercept (0,2) and we can plug that into the equation as well, to find b
2 = 5(0) + b
2 = b
So now that we know both m and b, plug only those two into the equation.
y = -5x + 2
That is your equation
Simplify using the distributive property.
8(y + 12)
8y + 12
20y
20 + y
8y + 96
Answers
= 8y + 96 (Answer D)
The expression 8(y + 12) simplifies to 8y + 96 using the distributive property, which involves multiplying 8 by both y and 12.
The question asks us to simplify the expression using the distributive property. The expression given is 8(y + 12). To simplify, we apply the distributive property by multiplying 8 with both y and 12.
So, we have:
8(y) + 8(12) = 8y + 96.
Therefore, the simplified form of the expression 8(y + 12) is 8y + 96.
What is the probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced?
twelve over fifty one
one over fifty two
one over fifty one
thirteen over fifty two,
Answers
Tough one!
For what values of a and b is the following equation true?
limx->0 ((sin2x)/x^3)+a+(b/x^2)) = 0
@Calculus1,
Answers
= > limx->0 (2a*sinx*cosx - (b /cosx)*sinx)/ 4x3 = 1/2 => limx->0 (a*sin2x - b*tanx)/ 4x3 = 1/2 [0/0 form],
applying L'Hospital rule again ,we get,
= > limx->0 (2a*cos2x - b*sec2x) / 12x2 = 1/2
For above limit to exist,Numerator must be zero so that we get [0/0 form] & we can further proceed.
Hence 2a - b =0 => 2a = b ------(A)
limx->0 (b*cos2x - b*sec2x) / 12x2 = 1/2 [0/0 form], applying L'Hospital rule again ,we get,
= > limx->0 b*(-2sin2x - 2secx*secx.tanx) / 24x = 1/2 => limx->0 2b*[-sin2x - (1+tan2x)tanx] / 24x = 1/2
[0/0 form], applying L'Hospital rule again ,we get,
limx->0 2b*[-2cos2x - (sec2x+3tan2x*sec2x)] / 24 = 1/2 = > 2b[-2 -1] / 24 = 1/2 => -6b/24 = 1/2 => b = -2
from (A), we have , 2a = b => 2a = -2 => a = -1
Hence a =-1 & b = -2
Express the fractions 3/4, 7/16, and 5/8with the LCD.
A. 24/32, 14/32, 24/32 B. 12/16, 7/16, 10/16 C. 9/16, 49/16, 36/16 D. 3/4, 2/4, 3/4
Answers
12/16
7/16
10/16
What does the 80 inches represent in an 80" TV
Answers
The 80 inches on an 80" TV refers to the diagonal measurement of the screen, which determines the size of the TV. This measurement is essential for potential buyers to know to match the TV to their space and optimal viewing distance. Other factors like screen resolution and whether to choose plasma or LCD also influence the viewing experience and cost.
When we refer to an 80" TV, the 80 inches represents the diagonal measurement of the screen. This measurement is taken from one corner to the opposite corner of the screen, not horizontally or vertically, which is the standard for sizing televisions and monitors. The importance of considering screen size arises from the need to match the viewer's space and viewing distance to optimize the viewing experience. With larger screens, such as an 80-inch TV, viewers can enjoy a more immersive viewing experience, especially when watching sports, movies, or DVDs. However, depending on the resolution, like 1080p for full HD or 768p for a lower resolution, the quality of the image may affect the perceived difference in quality, especially on smaller screens in which it might not be distinguishable to the nak.ed eye.