Answers
ratio of short leg: long leg :hypo = a: a√3: 2a
So if hypo = 52 cm then short leg = 52/2 = 26 cm
The other right triangle on the left is 45 45 90 because it has 2 equal sides
ratio of leg: leg :hypo = a: a: a√2
the leg = 26 cm
so hypo x = 26√2
Answer
26√2 cm
[tex]\huge \boxed{\sf 26\sqrt{2}\ cm } \\\\\\\sf Using\ trigonometric\ functions \\\\\displaystyle cos \theta = \frac{adj}{hyp} \\\\cos(60)=\frac{adj}{52} \\\\adj=cos(60) \times 52=26 \\\\Using\ the\ Pythagorean\ theorem \\\\x=\sqrt{26^2+26^2} =26\sqrt{2}[/tex]
Related Questions
David, Egil and Frances share money in the ratio 2:7:9. David gets £25. Work out how much Egil and Frances get.
Please help. Needed for tomorrow.
Answers
Egil:
(ratio of Egil to David)×(Amount David gets)
7/2×25
=£87.5
Frances:
(ratio of Frances to David)×(Amount David gets)
9/2×25
=£112.5
A briefcase lock has 3 roating cylinders, each containing 10 digits. How many numerical codes are possible?
Answers
10*10*10=1000
There would be 1000 possible numerical codes
I hope this helps.. sorry if it’s confusing or anything
Step-by-step explanation:
If the numbers can be repeated, we have such numeric codes:
10 · 10 · 10 = 1,000
If the numbers can not be repeated, then we have such numeric codes:
10 · 9 · 8 = 720
On a coordinate plane, a shape is plotted with vertices of (3, 1), (0, 4), (3, 7), and (6, 4). what is the area of the shape if each grid unit equals one centimeter?
Answers
A (3, 1)
B (0, 4)
C(3, 7)
D (6, 4)
step 1
find the distance AB
d=√[(y2-y1)²+(x2-x1)²]------> dAB=√[(4-1)²+(0-3)²]-----> dAB=√18 cm
step 2
find the distance CD
d=√[(y2-y1)²+(x2-x1)²]------> dCD=√[(4-7)²+(6-3)²]-----> dCD=√18 cm
step 3
find the distance AD
d=√[(y2-y1)²+(x2-x1)²]------> dAD=√[(4-1)²+(6-3)²]-----> dAD=√18 cm
step 4
find the distance BC
d=√[(y2-y1)²+(x2-x1)²]------> dBC=√[(7-4)²+(3-0)²]-----> dBC=√18 cm
step 5
find slope AB and CD
m=(y2-y1)/(x2-x1)
mAB=-1
mCD=-1
AB and CD are parallel and AB=CD
step 6
find slope AD and BC
m=(y2-y1)/(x2-x1)
mAD=1
mBC=1
AD and BC are parallel and AD=BC
and
AB and AD are perpendicular
BC and CD are perpendicular
therefore
the shape is a square wit length side √18 cm
area of a square=b²
b is the length side of a square
area of a square=(√18)²------> 18 cm²
the answer is
18 cm²
see the attached figure
What is the volume of a pyramid with slant height 17 feet and square base with edges of 16 feet?
Answers
[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ ------\\ B=\stackrel{16\times 16}{256}\\ h=15 \end{cases}\implies V=\cfrac{1}{3}(256)(15)\implies V=1280[/tex]
The volume of the pyramid is 1280 cubic feet.
To find the volume of a pyramid, we can use the formula:
Volume = (1/3) * Base Area * Height
Given that the pyramid has a square base with edges of 16 feet, the base area (A) is calculated as:
[tex]Base Area (A) = side^2\\A = 16^2 = 256 square feet[/tex]
The height of the pyramid can be found using the Pythagorean theorem. The height, slant height, and half the length of a side form a right triangle. The half length of a side is 16/2 = 8 feet. The slant height is 17 feet. So, using the Pythagorean theorem:
[tex]Height^2 + (Half side length)^2 = Slant height^2\\Height^2 + 8^2 = 17^2\\Height^2 + 64 = 289\\Height^2 = 289 - 64\\Height^2 = 225\\Height = \sqrt{225}\\Height = 15 feet\\[/tex]
Now that we have the base area (A = 256 square feet) and the height (h = 15 feet), we can find the volume:
Volume = (1/3) * 256 * 15
Volume = (1/3) * 3840
Volume = 1280 cubic feet
Therefore, the volume of the pyramid is 1280 cubic feet.
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Find the difference sqrt 20- sqrt 80
Answers
in the case of sqrt(20), that boils down to 4*5, so sqrt(20)=sqrt(4)*sqrt(5), or 2sqrt(5).
sqrt(80) = sqrt(16)*sqrt(5) = 4sqrt(5).
Final answer: subtract 4 sqrt(5) from 2 sqrt(5). Can you do this?
Final answer:
The difference between sqrt(20) and sqrt(80) is -2sqrt(5).
Explanation:
To find the difference sqrt(20) - sqrt(80), we can simplify each square root by factoring out perfect squares.
The number 20 can be factored into 4×5, and 80 can be factored into 16×5. Since 4 and 16 are perfect squares, they can be taken out of the square root as 2 and 4, respectively.
Therefore, the expressions simplify to:
sqrt(20) = sqrt(4×5) = sqrt(4) × sqrt(5) = 2sqrt(5)
sqrt(80) = sqrt(16×5) = sqrt(16) × sqrt(5) = 4sqrt(5)
Now we can find the difference:
2sqrt(5) - 4sqrt(5) = -2sqrt(5)
So the difference between sqrt(20) and sqrt(80) is -2sqrt(5).
A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°.What is the volume of the pyramid?2.4 cm33.6 cm34.8 cm37.2 cm3
Answers
Answer:4.8cm^3
Step-by-step explanation:I got it right on edge.
On average, Carson spends $2 of his $20 monthly allowance on library fines. What percent of his allowance is spent on library fines?
Answers
2 x 5 = 10
10/100 = .1
he spends 10%
PLZZZZZZ HELPPPP MEEEE!!!!!!!!
Determine the number of real solutions for each system of equations.
Answers
System A. Since the graph of the equations intercepts two times, we can conclude that the system has 2 real solutions.
System B. Since the graph of the equation don't intercept, we can conclude that the system has 0 real solutions.
System C. Since the graph of the equations intercepts two times, we can conclude that the system has 2 real solutions.
Answer:
First box is 2, second box is 0, and the third box is 1.
Step-by-step explanation:
HELP PLS!! FIND THE AREA!!!
Answers
notice the blue triangle has a base of 3 and a height of 2,
the green triangle has a base of 6 and a height of 1,
the yellow triangle has a base of 2 and a height of 6,
and the rectangle is a 7x6 rectangle.
we can simply get the area of each and sum them up, that's the area of the figure.
[tex]\bf \stackrel{\textit{blue triangle}}{\frac{1}{2}(3)(2)}~~~~+~~~~\stackrel{\textit{green triangle}}{\frac{1}{2}(6)(1)}~~~~+~~~~\stackrel{\textit{yellow triangle}}{\frac{1}{2}(2)(6)}~~~~+~~~~\stackrel{\textit{rectangle}}{7\cdot 6}[/tex]
In a 3-4-5 right triangle which expression would provide the measure of the smallest acute angle
Answers
[tex]sin\:\theta =\frac{3}{5}\:or\:\theta =sin^{-1}\left(\frac{3}{5}\right)[/tex]
[tex]cos\:\theta =\frac{4}{5}\:or\:\theta =cos^{-1}\left(\frac{4}{5}\right)[/tex]
[tex]tan\:\theta =\frac{3}{4}\:or\:\theta =tan^{-1}\left(\frac{3}{4}\right)[/tex]
These three expressions are the possible measure of the smallest acute angle.
For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced
Answers
In mathematics, a conic section is
a curve obtained as the intersection of the surface of
a cone with a plane. The four types of conic section are
the hyperbola, the parabola, the circumference and the ellipse.
For the problem we have this parametric
equation:
(1) [tex]\left\{{{x=acost}\atop{y=bsint}}\right[/tex]
From geometry, we know that we can express a
circumference in terms of parameters like this:
(2) [tex]\left \{ {{x=rcost} \atop {y=rsint}}\right[/tex]
being r the radius of the circumference.
On the other hands, we know that a ellipse can
be expressed in terms of parameters like this:
(3) [tex]\left \{ {{x=acost} \atop {y=bsint}}\right[/tex]
Therefore, we will have three answers that are
the cases for the values a and b, namely.
Case 1:
Circumference
To the case of a circumference, the more simple
ordinary equation is given by:
(4) [tex]x^{2} + y^{2} = r^{2}[/tex]
Substituting (1) into (4):
[tex]a^{2}cos^{2}t+b^{2}cos^{2}t=r^{2}[/tex]
But because of the equation (2), necessarily:
[tex]a = b = r[/tex]
Case 2: Ellipse
(focal axis matches the x-axis)
In this case, the simple ordinary equation is
given by:
(5) [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]
being a and b semi-major axis and semi-minor
axis respectively.
Given that a an b are variables of the
parametrization, and a and b are variables of the ellipse as well, to avoid
confusion we will modify the equation (5) like this:
(6) [tex]\frac{x^{2}}{a'^{2}}+\frac{y^{2}}{b'^{2}}=1[/tex]
So, substituting (2) into (6):
[tex]\frac{a^{2}cos^{2}t}{a'^{2}}+\frac{b^{2}cos^{2}t}{b'^{2}}=1[/tex]
Necessarily:
[tex]a=a'[/tex] and [tex]b=b'[/tex]
and given that the focal axis matches the
x-axis, then:
[tex]a>b[/tex]
Case 3: Ellipse
(focal axis matches the y-axis)
In this case, applying the same previous
reasoning, the simple ordinary equation is given by:
(7) [tex]\frac{x^{2} }{b'^{2}}+\frac{y^{2}}{a'^{2}}=1[/tex]
being a' and b' semi-major axis and semi-minor
axis respectively.
So, substituting (2) into (7):
[tex]\frac{a^{2}cos^{2}t}{b'^{2}}+\frac{b^{2}cos^{2}t}{a'^{2}}=1[/tex]
Necessarily:
[tex]a = b'[/tex] and [tex]b = a'[/tex]
and given that the focal axis matches the y-axis, then:
[tex]a<b[/tex]
Finally, the conclusions are:
1. If [tex]a = b[/tex] then a circumference will be traced. (See Figure 1)
2. If [tex]a>b[/tex] then a ellipse will be traced with focal axis matching the x-axis. (See Figure 2)
3. If [tex]a<b[/tex] then a ellipse will be traced with focal axis matching the y-axis. (See Figure 3)
How the values of a and b determine which conic section will be traced was discussed thoroughly.
What is a conic section?A conic section is a curve obtained as the intersection of the surface of a cone with a plane.
The given parametric equations are:
[tex]x=acos t[/tex]
[tex]\frac{x}{a} =cost[/tex]....(1)
[tex]y=bsint[/tex]
[tex]\frac{y}{b} =sint[/tex]....(2)
Adding the squares of (1) and (2)
[tex](\frac{x}{a} )^2+(\frac{y}{b} )^2=cos^{2} t + sin^{2} t[/tex]
We know [tex]cos^{2} t + sin^{2} t=1[/tex]
So, [tex]\frac{x^{2} }{a^{2} } +\frac{y^2}{b^2} =1[/tex]........(3)
If [tex]a=b[/tex], (3) will be reduced into:
[tex]x^{2} +y^{2} =a^{2}[/tex] representing a circle.
If [tex]a > b[/tex], (3) will represent an ellipse with the length of the major axis > length of the minor axis.
if [tex]a < b,[/tex] (3) will represent an ellipse with the length of the major axis < length of the minor axis.
Thus, How the values of a and b determine which conic section will be traced was discussed thoroughly.
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how many terms are in the arithmetic sequence shown below?
15, 7, -1, -9...,-225
Answers
Final answer:
To determine the number of terms in the given arithmetic sequence, we calculate the common difference and apply the formula for the nth term. With a common difference of -8 and an nth term of -225, we find that there are 31 terms in the sequence.
Explanation:
To find out how many terms are in the arithmetic sequence 15, 7, -1, -9,..., -225, we need to determine the common difference and use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
In this sequence, the common difference d is 7 - 15 = -8. Now we use the formula with an = -225, a1 = 15, and d = -8 to find n.
Plugging these values into the formula, we get:
-225 = 15 + (n - 1)(-8)
-225 = 15 - 8n + 8
-225 = 23 - 8n
-248 = -8n
n = 31
Therefore, there are 31 terms in the arithmetic sequence.
Find the surface area 4cm 5cm 6cm 13cm
Answers
A cube has a side length of 120 cm, what is its volume in cubic meters? (100 cm = 1 m)
Answers
a=120 cm and a=1.2m
V=120^3=1,728,000 cm^3
V=1,728 m^3
The value of volume of cube is,
⇒ V = 1.728 meter³
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
A cube has a side length of 120 cm.
Since, We know that;
1 m = 100 cm
Hence,
120 cm = 120 / 100 m
= 1.2 m
So, Volume of cube is,
⇒ V = side³
⇒ V = 1.2³
⇒ V = 1.728 meter³
Thus, volume of cube is,
⇒ V = 1.728 meter³
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If you buy a computer directly from the manufacturer for $ 2,469 and agree to repay it in 48 equal installments at 2.1 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
Answers
Final answer:
The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.
Explanation:
To calculate the monthly payments, you can use the formula for the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^-n)
Where:
P is the monthly paymentr is the monthly interest ratePV is the present value or the loan amountn is the total number of paymentsUsing the given values, we can calculate:
P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)
P ≈ $61.02
Therefore, the monthly payments would be approximately $61.02.
To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:
Total Interest = (P * n) - PV
Total Interest ≈ ($61.02 * 48) - $2469
Total Interest ≈ $1704.96 - $2469
Total Interest ≈ -$764.04
Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.
the height h of the equilateral triangle below is given by y= 5 cot theta where theta = 30 degrees
A) 2.9
B)4.3
C)7.1
D)8.7
Answers
1. We can substitute theta by 30° and evaluate our expression using a calculator:
[tex]y=5cot( \alpha )[/tex]
[tex]y=5cot(30)[/tex]
[tex]y=8.7[/tex]
2. We can use the unitary circle and the fact that [tex]cot \alpha = \frac{cos( \alpha }{sin( \alpha )} [/tex], so we can rewrite our expression as follows:
[tex]y=5cot( \alpha )[/tex]
[tex]y=5 \frac{cos( \alpha )}{sin( \alpha )} [/tex]
[tex]y= \frac{cos(30)}{sin(30)} [/tex]
From our unitary circle we can check that [tex]cos(30)= \frac{ \sqrt{3} }{2} [/tex] and [tex]sin(30)= \frac{1}{2} [/tex].
Lets replace those values in our expression and simplify:
[tex]y= \frac{ 5(\frac{ \sqrt{3} }{2})}{ \frac{1}{2} }[/tex]
[tex]y=5 \sqrt{3} [/tex]
[tex]y=8.7[/tex]
Either way we can conclude that the correct answer is: D)8.7
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+23x-15=0
Answers
the answer to this is going to be
hope it helped
if u need more help plz let me know
thanks have a good day boi
see u
if u need more help plz let me know
thanks
-im out
x ^ 3-9x ^ 2 + 23x-15 = 0
Rewriting we have:
(x-5) * (x-3) * (x-1) = 0
Therefore, the solutions are given by:
Solution 1:
x-5 = 0
x = 5
Solution 2:
x-3 = 0
x = 3
Solution 3:
x-1 = 0
x = 1
Answer:
x = 5
x = 3
x = 1
T (2,10) is the midpoint of CD. The coordinates of D are (2,13). What are the coordinates of C?
A. (2, 16)
B. (2, 20)
C. (2, 11.5)
D. (2, 7)
Answers
Simplify the rational expression. state any excluded values. 4x - 4/ x - 1
Answers
[tex] \frac{4x-4}{x-1} [/tex]
So, we will call this expression as:
[tex] f(x) = \frac{4x-4}{x-1} [/tex]
We can write this equation like this:
[tex]f(x) = \frac{4(x-1)}{(x-1)} [/tex]
So, if we simplify it, this can be written like this:
f(x) = 4 but given that the denominator can't be zero, then:
[tex] x-1 \neq 0 [/tex] ∴ [tex]x \neq 1[/tex]
Therefore:
f(x) = 4 if and only if [tex]x \neq 1[/tex]
Answer:
1 and 4 i believe
Step-by-step explanation:
A number is chosen at random from 1 to 10. find the probabilty of not selecting a multiple of 3
Answers
So the probability is 7/10 = .7 = 70%
You hold $25 in a savings account and you deposit an equal amount into your account each week after 5 weeks the account holds $170 write an equation that represents the amount y in dollars of money in the account after x weeks
Answers
25+5w=170
5w=145
w=29
You deposit $29 each week, so after x weeks:
25+29x=y
The diagram below shows triangle MNR with ray NM.
-
What is the measure of MRN?
Answers
Answer:
The answer is 18
Step-by-step explanation:
Subtract 115 from 180
Add 65 and 97
Subtract 162 from 180
The measure of ∠MRN is 18°
What is sum of angles of a triangle?The sum of angles of a triangle equals the straight angle which is 180°.
According to ques
∠RNM= 97°
∠RMA = 115°
∠RMA +∠RMN = 180° ( sum of angles on straight line )
115° + ∠RMN = 180°
∠RMN = 180° - 115°
∠RMN = 65°
∠RMN + ∠MRN + ∠RNM = 180° ( Sum of angles of triangle )
65° + ∠MRN + 97° = 180°
162° + ∠MRN = 180°
∠MRN = 180° - 162°
∠MRN = 18°
Hence , measure of ∠MRN is 180°
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What is 3X times 1/6X
Answers
[tex] \frac{3x}{1} * \frac{1}{6x} = \frac{3x}{6x} [/tex]
The x's cancel out, since they're both on the numerator and denominator, so you'll be left with this fraction:
[tex] \frac{3}{6} [/tex]
The fraction can be further simplified by dividing both the numerator and denominator by 3:
[tex]\frac{3}{6} \div \frac{3}{3} = \frac{1}{2}[/tex]
The answer is 1/2.
multiply 1/3 and 6
Is my work correct?
Given: ABCD is an inscribed polygon.
Prove: ∠A and ∠C are supplementary angles.
Answers
Solution:
Given: A B CD is an inscribed polygon.
To Prove: ∠A and ∠C are supplementary angles.
Proof: Join AC and B D.
Angle in the same segment of a circle are equal.
∠ACB=∠ADB→→AB is a segment.
Also, ∠A B D=∠A CD→→AD is a Segment.
In Δ ABD
∠A+∠ABD+∠ADB=180°→→Angle sum property of triangle.
∠A+∠A CD+ ∠ACB=180°
∠A+∠C=180°
Hence proved, that is, ∠A and ∠C are supplementary angles.
The method Adopted by you
∠1=2 ∠A----(1)
and, ∠2=2 ∠C-------(2)
The theorem which has been used to prove 1 and 2, Angle subtended by an arc at the center is twice the angle subtended by it any point on the circle.→(Inscribed angle theorem)
Also, angle in a complete circle measures 360°.→→Chord arc theorem
∠1+∠2=360°→→Addition Property of Equality
2∠A+2∠C=360°→→[Using 1 and 2, Called Substitution Property]
Dividing both sides by 2→→Division Property of Equality
2∠A+2∠C=360°→→[Using 1 and 2]
∠A+∠C=180°
→→Correct work.
A two-column proof to prove that angles A and C are supplementary angles should be completed as follows;
Statement Reason______________
ABCD is an inscribed polygon Given
mBCD = 2(m∠A) Inscribed Angle Theorem
mDAB = 2(m∠C) Inscribed Angle Theorem
mBCD + mDAB = 360° The sum of arcs that make a circle is 360°
2(m∠A) + 2(m∠C) = 360° Substitution Property
m∠A + m∠C = 180° Division Property of Equality
∠A and∠C are supplementary angles Defintion of supplementary angles.
In Mathematics and Euclidean Geometry, the inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle or the inscribed angle of a circle is equal to half of the central angle of a circle.
Generally speaking, a supplementary angle refers to two angles or arc whose sum is equal to 180 degrees.
Based on the defintion of supplementary angles, we can logically deduce that angle A and angle C are supplementary angles.
Answer ASAP for five stars and brainliest!
1. The half-life of a radioactive kind of antimony is 60 days. How much will be left after 240 days, if you start with 960 grams of it?
2. The half-life of a radioactive kind of tellurium is 70 minutes. How much will be left after 280 minutes, if you start with 480 grams of it?
3. A town's population is currently 10,000. If the population doubles every 38 years, what will the population be 76 years from now?
Answers
Given that the half-life of a radioactive kind of antimony is 60 days. The amount of substance left of a radioactive substance with a half life of [tex]t_{ \frac{1}{2} }[/tex] after time t, is given by:
[tex]N(t)=N_0\left( \frac{1}{2} \right)^{ \frac{t}{t_{ \frac{1}{2} }} }[/tex]
where: [tex]N_0[/tex] is the original amount of the substance.
Thus, in 240 days, the amount that will be left of the antimony given that the original amount of the antimony is 960 grams is given by:
[tex]N(t)=960\left( \frac{1}{2} \right)^{ \frac{240}{60} } \\ \\ =960\left( \frac{1}{2} \right)^4=960\left( \frac{1}{16} \right) \\ \\ =60\ grams[/tex]
Part 2:
Given that the half-life of a radioactive kind of tellurium is 70 minutes. The amount of substance left of a radioactive substance with a half life of [tex]t_{ \frac{1}{2} }[/tex] after time t, is given by:
[tex]N(t)=N_0\left( \frac{1}{2} \right)^{ \frac{t}{t_{ \frac{1}{2} }} }[/tex]
where: [tex]N_0[/tex] is the original amount of the substance.
Thus, in 280 minutes, the amount that will be left of the tellurium given that the original amount of the antimony is 480 grams is given by:
[tex]N(t)=480\left( \frac{1}{2} \right)^{ \frac{280}{70} } \\ \\ =480\left( \frac{1}{2} \right)^4=480\left( \frac{1}{16} \right) \\ \\ =30\ grams[/tex]
Part 3:
Given that a town's population is currently 10,000. If the population of the town doubles every 38 years, than in 76 years from now, the population of the town must have doubled twice, thus in 76 years from now, the population of the town is given by:
[tex]10000(2)^2=10,000(4)=40,000[/tex]
Let f(x)=-4x+7 and g(x)=10x-6. Find f(g(x))
Answers
The base edge of the regular triangular pyramid is b=10 cm and altitude of the base hb ≈ 8.66 cm. The slant height of the pyramid is k=8 cm. Find:
Lateral area and Surface area of the pyramid
Answers
Answer:
Step-by-step explanation:
It is given that the base edge of the regular triangular pyramid is b=10 cm and altitude of the base h =8.66 cm. The slant height of the pyramid is k=8 cm.
Now, the lateral surface area of the pyramid is given as:
[tex]LSA={\frac{3}{2}}(b)(k)[/tex]
Substituting the given values, we have
[tex]LSA=\frac{3}{2}(10)(8)[/tex]
[tex]LSA=120cm^2[/tex]
Thus, the Lateral surface area of the pyramid is [tex]120cm^2[/tex].
Now, the surface area is given as:
[tex]SA=\frac{1}{2}bh+LSA[/tex]
[tex]SA=\frac{1}{2}bh+120[/tex]
[tex]SA=\frac{1}{2}(10)(8.66)+120[/tex]
[tex]SA=43.3+120[/tex]
[tex]SA=163.3cm^2[/tex]
Thus, the surface area of the pyramid will be [tex]163.3cm^2[/tex].
The Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
What is a pyramid?A polyhedron that has a polygonal base and triangles for sides, is a pyramid.
The lateral area of the pyramid is equal to the area of its three triangular lateral faces is;
[tex]\rm Lateral \ Area=3 \times \dfrac{1}{2}\times b \times k\\\\ Lateral \ Area=3 \times \dfrac{1}{2}\times 10 \times 8\\\\ Lateral \ Area=120[/tex]
The surface area of the pyramid is;
[tex]\rm Surface \ area=\dfrac{1}{2}bh + Lateral \ area\\\\Surface \ area=\dfrac{1}{2}\times 10 \times 8.66 +120\\\\Surface \ area=43.3+120\\\\Surface \ area=163.3 \ cm^3[/tex]
Hence, the Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
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Geometry Problem (PIC)
Answers
[tex]\Delta ADC\ and\ \Delta CDB\ are\ similar\ therefore\\\\\dfrac{y}{4}=\dfrac{9}{y}\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot9\\\\y^2=36\to y=\sqrt{36}\to y=6[/tex]
In football, a field goal is worth 3 points, and the extra point after a touchdown is worth 1 point. During the 2006 season, John Kasay, of the Carolina Panthers scored a total of 100 points for his team by making a total of 52 field goals and extra points combined. How many 3 point field goals did he make?
Answers
You can get this by setting up the system of equations:
x + y = 52 (total number of kicks)
3x + y = 100 (points)
Jack runs 3 miles in 27 minutes. at this constant rate how long will it take him to run 10 miles answer
Answers
[tex] \frac{3 miles}{27 min} = \frac{10 miles}{x min} [/tex]
Now we cross-multiply
3x = 27(10)
3x = 270
x = 90
It will take Jack 90 minutes to run 10 miles.
Apologies for the delayed answer. I'm surprised no one saw this before.