Answers
Answer:
157.98 [tex]in^2[/tex]
Step-by-step explanation:
Given: volume of pyramid is equal to 100 cubic inches and height of the pyramid is 5 inches
To find: surface area of the pyramid
Solution:
Let h denotes the height of the pyramid and 'a' denotes side of the square base of the pyramid.
Volume of the pyramid = [tex]\frac{1}{3}a^2h[/tex]
Also,
Volume of the pyramid = 100 cubic inches
[tex]\frac{1}{3}a^2h=100\\\frac{1}{3}a^2(5)=100\\a^2=\frac{100\times 3}{5}=60\\a=\sqrt{60}[/tex]
Surface area of the pyramid [tex](S) =a\sqrt{4h^2+a^2}+a^2[/tex]
So,
[tex]S=\sqrt{60}\sqrt{100+60}+60\\=\sqrt{60}\sqrt{160}+60\\=\sqrt{9600}+60\\=97.9796+60\\=157.9796\\\approx 157.98[/tex]
Surface area = 157.98 [tex]in^2[/tex]
Answer:
Surface area of the pyramid = 157.99 in²
Step-by-step explanation:
Volume of a pyramid is given by the formula,
Volume = [tex]\frac{1}{3}(\text{Area of the base})\times \text{height}[/tex]
100 = [tex]\frac{1}{3}\text{(Side)}^{2} \times \text{height}[/tex]
300 = s² × 5
s² = 60
s = √60
s = 2√15 in ≈ 7.746 in
Now surface area of the pyramid = Area of base + 4×(Area of one lateral side)
Area of square base = (Side)² = 60 in
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
Since Lateral height = [tex]\sqrt{(h)^{2}+(\frac{S}{2})^{2}}[/tex] [By applying Pythagoras theorem in the given triangle]
= [tex]\sqrt{(5)^{2}+(3.873)^{2}}[/tex]
= [tex]\sqrt{25+15}[/tex]
= [tex]\sqrt{40}[/tex]
= 6.325 in.
Now area of lateral side = [tex]\frac{1}{2}(7.746)(6.325)[/tex]
= 24.497 in²
Surface area of the pyramid = 60 + (4×24.497)
= 60 + 97.987
= 157.987 in²
≈ 157.99 in²
Related Questions
(−5 + 3i) ⋅ (1 − 2i)
Answers
Answer:
[tex] - 1[/tex]
Step-by-step explanation:
[tex](-5 + 3i) \times (1 - 2i) \\ ( - 5 + 6) \times (1 - 2) \\ ( 1) \times ( - 1) \\ = - 1[/tex]
(-5+3i)(1-2i)
-5+10i+3i+6i^2
add like terms
-5+13i-6i^2
then put in order
-6i^2+13i-5
Which of the following are not polynomials?
Answers
Answer:
A B and D but don’t quote me on it
Step-by-step explanation:
what solution is 7x+7=6x+4+x+3
Answers
Answer:
infinite solutions (all real numbers)
Step-by-step explanation:
7x+7=6x+4+x+3
7x+7=7x+7
infinite solutions (all real numbers)
Answer:
Equation is alway true
All real numbers are solutions.
Step-by-step explanation:
Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 7*x+7-(6*x+4+x+3)=0 Step by step solution :
Step 1 : Equations which are always true : 1.1 Solve 0 = 0This equation is a tautology
Hope this helps.
How many litres of water (round to the nearest hundredth) can be poured into a tin can that has a diameter of 18 cm and a height of 0.3 m?
Answers
Answer:
Step-by-step explanation:
Diameter = 18cm
18 / 2 = Radius
Radius = 9cm
Formula: A=2πrh+2πr^2
2 x pi x 9 x 0.3 + 2 x pi x 9^2 = 525.90261
Nearest hundredth = 525.90
El impuesto general a las ventas ( IGV ) en el Perú es 18%.Este porcentaje incrementa el precio de cualquier artículo en venta . Si en una factura figura el precio de una cocina en 590 soles , ¿ Cual era el precio de la cocina antes de que fuera afectado por el IGV
Answers
Answer:
o preço da cozinha era 106,20 reais.
Step-by-step explanation:
porque 590-16% e iqual a 106,20 reais
foi o retirar o IGV
Lucy makes green paint by mixing yellow and blue paint in the ratio 5:2. Blue paint costs
£30 for 5 litres and yellow paint costs £28 for 7 litres.
Lucy sells her green paint for £4.50 per litre. Will she make a profit? Show your working
to justify your decision.
Answers
Answer:
No, she won’t make a profit
Step-by-step explanation:
Here, we are interested in determining if Lucy made a profit or a loss.
The cost of blue paint is 30 pounds for 5 liters. This means that a liter of blue paint is 30/5 = 6 pounds per liter
The cost of yellow paint is 28 pounds per 7 liters, the cost per liter is 28/7 = 4 pounds per liter
Now, in her mixing, she mixes 5 parts of yellow paint and 2 parts of blue paint.
This means that she mixed them the ratio as follows per liter;
For yellow, we have; 5/(5+2) = 5/7
For blue we have 2/(5+2) = 2/7
Now since a liter of yellow paint cost 4 pounds
5/7 of a liter will cost 5/7 * 4 = 20/7 pounds
For the blue paint, a liter cost 6 pounds, 2/7 of a liter will cost 2/7 * 6 = 12/7
The total cost in pounds in this;
20/7 + 12/7 = 32/7 = £4.57 pounds to 2 decimal place
Now she sells her green paint product at £4.5 per liter. Since this is less than the cost price of production which is £4.57, she is running at a loss
Use the diagram to find the value of x to the nearest tenth of a foot.
a. 74.6 ft.
b. 5.3 ft.
c. 15.5 ft.
d. 73.3 ft.
Answers
Answer:
a
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan15° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{20}{x}[/tex] ( multiply both sides by x )
x × tan15° = 20 ( divide both sides by tan15° )
x = [tex]\frac{20}{tan15}[/tex] ≈ 74.6 ft ( to the nearest tenth of a foot )
Pls help with this for brainliest answer
Answers
Answer:
the answer is 12pie
Step-by-step explanation:
6mm is radius
circumference is ×2
so its 12
Mr.Tola has a piece of wood that is 8 1/4 feet in length. He wants to cut it into pieces that are each 3/4 foot in length. How many 3/4 foot pieces of wood can Mr.Tola make?
Answers
Answer:
11
Step-by-step explanation:
1/4 is equal to 0.25. 3/4 is equal to 0.75.
8.25 divided by 0.75.
11
Solve the equation 2x-1=4x+5
Answers
Answer:
-3
Step-by-step explanation:
2x-1=4x+5
-1=2x+5
-6=2x
x=-3
Answer:
x = -3
Step-by-step explanation:
Solve for x:
2 x - 1 = 4 x + 5
Subtract 4 x from both sides:
(2 x - 4 x) - 1 = (4 x - 4 x) + 5
2 x - 4 x = -2 x:
-2 x - 1 = (4 x - 4 x) + 5
4 x - 4 x = 0:
-2 x - 1 = 5
Add 1 to both sides:
(1 - 1) - 2 x = 1 + 5
1 - 1 = 0:
-2 x = 5 + 1
5 + 1 = 6:
-2 x = 6
Divide both sides of -2 x = 6 by -2:
(-2 x)/(-2) = 6/(-2)
(-2)/(-2) = 1:
x = 6/(-2)
The gcd of 6 and -2 is 2, so 6/(-2) = (2×3)/(2 (-1)) = 2/2×3/(-1) = 3/(-1):
x = 3/(-1)
Multiply numerator and denominator of 3/(-1) by -1:
Answer: x = -3
The formula for the volume of a cone is V=1/3bh
Solve V=1/3bh
for b, the base of the cone.
Answers
Answer:
b = 3Vh
Step-by-step explanation:
When they ask to solve for b, you are essentially rearranging the equation so that b is alone on one side.
V = 1/3bh
(V)(3) = (1/3bh)(3)
3V = bh
(3V)/h = (bh)/h
3Vh = b
b = 3Vh
In RST, the measure of
Answers
Answer:
5.2 feet.
Step-by-step explanation:
The useful equation to use for this problem is sine. Given the angle of measure 64 degrees, we have O (opposite) and H (hypotenuse).
From SOH CAH TOA, we see that we have O and H, so thus we should use sine.
Sine of any angle= opposite/hypotenuse.
Sine of 64= x/5.8
Sine of 64 (times 5.8)=x
x= 5.2 feet.
Additionally, you could use a right triangle calculator to solve for side x.
Answer:
Step-by-step explanation:
sin 64=x/5.8
x=sin64* 5.8
x=0.92*5.8
x=5.3
pls hep for the brainliest
Answers
Answer:189.25 cm 189.3 cm if rounded to one decimal point
Step-by-step explanation:
You need to find the area of the rectangle, then the area of 1/2 the circle.
Rectangle Area =
L x w =
10 x 15 = 150cm
Circle Area =
A=πr^2 =
Diameter = 10, so radius = 5
π(5)^2 = 25π = (25)(3.14) = 78.5
Area of 1/2 Circle = 78.5/2 = 39.25
150 + 39.25 = 189.25 cm
The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth.
Answers
Question:
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)
B) The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth.
Answer:
A) 16.64 Feets
B) 7.65 feets
Step-by-step explanation:
Given the following :
The question above can be solved by applying Pythagoras rule :
A^2 = B^2 + C^2
PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
PR = 16.64feet
Now if PR is adjusted to 16 Feets, the New height of the scaffold will be:
QR² = PR² - PQ²
QR² = 16² - 14²
QR² = 256 - 196
QR² = 60
Take the Square root of both sides
QR = √60
QR = 7.7459666 Feets
Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for the correct calculation of velocity?
Answers
Answer:
Direction
Step-by-step explanation:
poop
somebody help me I’m struggling
Answers
Answer:
A. $ (5 + 2x), B. = $ 305
Step-by-step explanation:
x miles
A. cost for x miles = 5 + 2x ($)
B. cost for 150 miles = 5 + 2*150 =305 ($)
Answer:
A. let the mile driven = x
5 + 2x
B. × = 150 mile
taxi service = $5 + $2(150)
= $305
*in an equation u dont have to write the symbol . for example, $, ml, km, etc.
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!
Answers
Answer:
[tex](x-7)(x-7)[/tex]
Step-by-step explanation:
We begin with the given quadratic expression:
[tex]49-14x+x^2[/tex]
Just for my own ease, I will rewrite this in descending order of powers
[tex]x^2-14x+49[/tex]
In order to factor this expression, we need to look for two numbers that meet the following criteria.
When they are added together, you get [tex]-14[/tex]
When they are multiplied together, you get [tex]49[/tex]
A simple way to find our answer is to begin with the product of multiplication and list each of the numbers that can be multiplied together to get us our given result
To get 49, we could multiply
1 and 49
-1 and -49
7 and 7
-7 and -7
Now, we can just add both of these terms together to see while one gives us our desired result
[tex]1+49=50\\-1-49=-50\\7+7=14\\-7-7=-14[/tex]
As you can see, -7 and -7 were the two values that gave us -14.
This means that they are the terms within our factor.
Therefore, our factored form would be [tex](x-7)(x-7)[/tex]
Answer:
(7 - x) (7 - x)
Step-by-step explanation:
First, I'm multiplying 49 by the co-efficient of x(1) to get 49. Then I'm going to see what factors of 49 add up to -14. Those are -7 and -7.
Next, I'm going to rewrite this polynomial:
49 - 7x - 7x + x^2
Then, I group them into two groups:
49 - 7x
&
-7x + x^2
Then, I factor them out:
49 - 7x = 7 (7 - x)
-7x + x^2 = -x (7 - x)
After that, I take the outer coefficients and put them in parenthesis:
7 (7 - x)
&
-x (7 - x)
= (7 - x)
Finally, I put both of our grouped parenthesis together:
(7 - x) (7 - x)
which relation is a function ?
Answers
if a=(-1, -3) and b=(11, -8) what is the length of ab?
Answers
Answer: D. The length is 13 units.
Step-by-step explanation:
(-1, -3 ) Find the difference between the x values and y values.
(11, -8)
-3-(-8) = 5
-1-11 = -12 now find the absolute values.
The absolute value of 5 is 5 . The absolute value of -12 is 12.
Now use the Pythagorean Theorem formula a^2 + b^2 =c^2 where c square is the length between AB.
5^2 + 13^2 = C^2
25 + 144 = c^2
169=c^2
c= 13
Answer:
D. 13 Units
Step-by-step explanation:
I just took the test
What is the missing justification?
Answers
Answer:
The missing justification is the transitive property.
Step-by-step explanation:
The missing justification is the transitive property. The transitive property states that: If a = b and b = c, then a = c.
The transitive property of equality states that if A is equal to B, and B is equal to C. Then B is equal to C. The missing justification is the transitive property of equality.
What is the transitive property of equality?The transitive property of equality states that if A is equal to B, and B is equal to C. Then B is equal to C. For Example,
A = B and B = C, then,
A = C
Given ∠A≅∠B and ∠C≅∠B therefore, using the transitive property of equality we can write ∠A≅∠C.
Hence, the missing justification is the transitive property of equality.
Learn more about Transitive Property:
https://brainly.com/question/2437149
#SPJ2
A golfer hits a golf ball with a club. The mass of the ball is 0.05 kg.
The ball accelerates at 2,000 m/s2
What is the net force, to the nearest newton, that accelerates the
ball?
Answers
Answer:
100 N
Step-by-step explanation:
f= 0.05*2000=100 N
Answer:100
Step-by-step explanation:
What part of the circumstance is an arc whose measure is 30
Answers
Answer:
1/12. What is the degree measure of an arc 4 ft. long in a circle of radius 10 ft.? 72°.
Step-by-step explanation:
PC=PD then (PA)PC)=(PB)(___)
Answers
Answer:
PD is the answer
Step-by-step explanation:
(PA) (PC) = (PB) (PD)
On a scale drawing, the height of a tree is 2.25 inches. If the scale drawing is 1 in. : 75ft, how tall is the tree?
Answers
Answer:
168.75ft
Step-by-step explanation:
We can just multiply by the scale
2.25*75=168.75
The actual height of the tree is 168.75 ft.
What is Height?The height is defined as the measurement of the distance of an object from the base to the top.
Here, Given
Height of tree (in drawing) = 2.25 inches
Scale is given ; 1 inch = 75 ft.
so, 2.25 inches = 2.25 X 75 ft.
≈ 168.75 ft.
Thus, the actual height of the tree is 168.75 ft.
Learn more about height from:
https://brainly.com/question/10726356
#SPJ2
[tex](\frac{15x^{2}y }{8x} )(\frac{4y}{9xy} )[/tex]
Answers
PLEASE HELP ITS FOR A TEST I WILL GIVE U BRAINLIEST
Danica and Darrelle have developed a lucrative business selling handmade silver bracelets. Darrelle makes the more complex bracelets and Danica makes the simpler ones. It takes Darrelle 4 hours to make 3 bracelets and Danica can make 5 bracelets every 2 hours.
a. Convert this scenario into linear equation(s); show both the standard form and the slope-intercept form of your equation(s).
b. Could any part of this scenario be graphed using any of the special functions discussed in the course text? Explain your answer.
c. Each bracelet Darrelle sells makes $10.50 in profit. Each bracelet Danica sells makes $3.50 in profit. If Darrelle and Danica work the same amount of time, explain each of the steps you will use and then calculate how many hours will it take for the whole business to make at least $500 profit?
Answers
Answer:
At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500. (30.075)
Step-by-step explanation:
a) It is not clear what linear equation is desired. We are given enough information to write an equation relating the number of bracelets produced by each worker to the time it takes.
Let n represent the number of bracelets Danica produces. Let r represent the number of bracelets Darrelle produces. Let h represent time in hours.
.. r/3 = h/4 ... Darrelle produces 3 bracelets in 4 hours
.. 4r - 3h = 0 ... equation in standard form
.. r = (3/4)h ... equation in slope-intercept form (the intercept is 0)
.. n/5 = h/2 ... Danica produces 5 bracelets in 2 hours
.. 2n - 5h = 0 ... equation in standard form
.. n = (5/2)h ... equation in slope-intercept form
b) We have no idea what special functions were discussed in the course. Of course these equations can be graphed. (2-dimensional equations are easily graphed.)
c) A profit function can be written in terms of the number of bracelets produced. Then it can be solved to find when (h=?) profit is equal to $500.
.. Let p represent the total profit from production of bracelets.
.. p = 10.50*r + 3.50*n ... profit in terms of bracelets produced
.. p = 10.50*((3/4)h) + 3.50*((5/2)h) ... profit in terms of hours, where both work the same hours
.. p = 16.625 h
.. 500 = 16.625 h ... we want to find hours until $500 profit
.. 500/16.625 = h ≈ 30.0752
At the average rate of making profit, it will take slightly more than 30 hours for the business to reach a profit goal of $500.
_____
If you work out the timing of when bracelets are finished, assuming they are made at a constant rate, you find that there will be 23 of Darrelle's bracelets and 76 of Danica's bracelets finished in 30 hours and 40 minutes. These will yield a profit of $507.50. After another 8 minutes, Danica will have finished bracelet 77 to add another $3.50 to the profit total.
What is the factored form of the polynomial?
x2 + 9x +20
1
(x - 4)(x - 5)
(x-2)(x - 10)
(x + 4)(x + 5)
(x + 2)(x + 10)
Answers
what is a cofunction
Answers
Answer:
A cofunction is whenever A and B are completmentary angles.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Pls help, I will mark brainlessly and give 5 stars
Answers
Answer:
1.C 2.D
Step-by-step explanation:
Answer:
1 is C and 2 is D
Step-by-step explanation:
A certain solution contains 4.3 grams of salt per liter.
How much salt is there in 11 liters of the solution?
Round your answer, if necessary, to the nearest tenth.
Answers
Answer:
47.3 grams
Step-by-step explanation:
Given: A solution contains 4.3 grams of salt per liter.
To find: Amount of salt in 11 liters of the solution
Solution:
Amount of salt in 1 liter of the solution = 4.3 grams
So, amount of salt in 11 liters of the solution = 11 × Amount of salt in 1 liter of the solution = 11 × 4.3 = 47.3 grams
Hence, 11 liters of the solution contains 47.3 grams of salt.
Answer: 47.3
Step-by-step explanation: Khan Academy
