Answer:
Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.
Step-by-step explanation:
Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.
Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.
We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.
So, 3V/2 = 2w² + 2(w - 2)²
= 2w² + 2(w² - 4w + 4)
= 2w² + 2w² - 8w + 8
= 4w² - 8w + 8
= 4(w² - 2w + 2) (1)
Also we want to know if V/2 is equal to the volume of the two top-most slabs.
So, V/2 = 2(w - 4)² + 2(w - 6)²
= 2(w² - 8w + 16) + 2(w² - 12w + 36)
= 2w² - 16w + 32 + 2w² - 24w + 72
= 4w² - 40w + 104
= 4(w² - 10w + 26)
From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)
Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.
2/5 + 2/5
Help my sister
Step-by-step explanation:
2/5+2/5(2+2)/54/50.8stay safe healthy and happy...Answer:
4/5
Step-by-step explanation:
2 + 2 = 4
5 + 5 = 5
4/5
Taylor invested $2500 in an account that pays 3.7% interest compounded monthly. If Taylor does not touch the money, what will the balance of the account be after 7 years?
Answer:
hehe
Step-by-step explanation:
what is the difference between 1089 and 4445
Answer:
If it is:
1,089-4,445= -3,356
but if it is the other way:
4,445-1,089= 3,356
Hope it helped!
Answer:
Its a Subtraction problem
4445-1089
=3356
6. Find the sum of the geometric series.
a1=-9 a5=-729 r=-3
Answer:
Sn = -9(1-(-3)^n)/4
Step-by-step explanation:
Since r < 1, the sum of nth term of a geometric sequence is expressed as;
Sn = a(1-r^n)/1-r
a is the first term
n is the number f terms
r is the common ratio
An = -9(1-(-3)^n)/1-(-3)
Sn = -9(1-(-3)^n)/4
Hence the sum of the nth term of the series is Sn = -9(1-(-3)^n)/4
What's the volume to this prism?
Answer:
36 cubic inch
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
[tex]V=whl[/tex]
----------------------------------------------------------------------------------------------------------------
So:
6 × 3 × 2 = 36
----------------------------------------------------------------------------------------------------------------
Have a good day :)
Solve the trigonometric equation over the interval [0, 2π)
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
Show your work, thanks!
Answer:
θ = 0° , 60°
Step-by-step explanation:
[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]
Substract both the sides from 1.[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex]
[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]
Rearrange the terms in L.H.S.[tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Replace the terms in brackets with '-sin²θ' by using the identity (sin²θ + cos²θ = 1).[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Take 'sinθ' common from the whole expression in L.H.S.[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]
Now solve each part separately :-
1) [tex]\sin \theta = 0[/tex]
[tex]=> \theta = \sin^{-1}0 = 0[/tex]
2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]
Divide both the sides by 'cosθ'.[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex]
[tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex]
[tex]=> -\tan \theta + \sqrt{3} = 0[/tex]
Add both the sides with 'tanθ'.[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex]
[tex]=> \tan \theta = \sqrt{3}[/tex]
[tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex]
∴ θ = 0° , 60°
Answer:
Solution given:
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
[tex] 1-sin^{2} \theta+\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] 1-1 +sin^{2}\theta=\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] Sin\theta(sin\theta -\sqrt{3}cos\theta)[/tex]
Either
[tex] sin\theta=\sqrt{3} cos \theta [/tex]
[tex] \sqrt{sin\theta}{cos \theta}=\sqrt{3} [/tex]
[tex] Tan \theta =\sqrt{3}[/tex]
[tex] Tan \theta =Tan 60,Tan(180+60),Tan (360+60)[/tex]
[tex] \theta =60°,240°,420°[/tex]
in terms of π is
[tex] \theta =⅓π,\frac{4}{3}π,[/tex]
Or
[tex] Sin\theta=1[/tex]
[tex]Sin\theta=Sin0° ,Sin180°[/tex]
In terms of π is
[tex]\theta=0π,π[/tex]
so
[tex]\theta=0π,⅓π,π,\frac{4}{3}π,[/tex]
please help! 20 points. if you guess or just comment to take my points i will make sure ur account gets banned. thanks! i want a simple explanation
Answer:
x = 9
Step-by-step explanation:
Of course I'll do very simple explanation!
every time you see a straight line (nondiagonal) it measures 180°.
so if we're trying to solve for x in this case, we'll subtract 180° - 40° = 140°.
Then use the statement to solve for x
[tex]10x+50=140[/tex]
[tex]10x-50[/tex] = - 50 Subtract 50 from both sides
[tex]10x[/tex] [tex]=[/tex] 90 Divide 10 from both sides
x = 9
Pleaseeeeeeeee helppppp someone pleaseeeeeee I’m begging uuuuuuuuuuuu
Answer:
x=6
ABC= 135 degrees
Step-by-step explanation:
ABE and CBD are congruent angles (don't remember the theorem)
therefore
3x+27=45
solve for x
x=6
ABC and CBD are supplementary (meaning they add to 180)
Answer:
6
Step-by-step explanation:
Find the midpoint
(1,-8) (-7,0)
Answer:
(-3, -4)
Step-by-step explanation:
Handy fact: the average of two numbers is exactly halfway between them.
To find the midpoint, average the x-coordinates; average the y-coordinates.
(1 + -7)/2 = -6/2 = -3
(-8 + 0)/2 = -8/2 = -4
The midpoint is (-3, -4).
Convert 3.12 mm into cm, m and km.
Answer:
3.12mm= 31,2cm
3.12= 0.312m
3.12 = 0.000312km
The graph of quadratic function is shown on the grid.
Which of these best represents the domain of f?
A.
[tex]y \geqslant 5.5[/tex]
B.
All real numbers
C.
All real numbers less than -3 or greater than 2
D.
[tex] - 3 \leqslant x \leqslant 2[/tex]
Help out on the bottom part
Answer:
x+2y=-3
x+2(-1)=-3
x-2=-3
x=-3+2
x=-1
Pleas help!
WILL THANKS YOUR ACCONT and MARK BRAINLIEST
zuma took a loan of 630 000 from the bank. he will repay the loan over 48 months at 9.5% per annum simple interest. how much interest will zuma pay on the loan
Answer:
Interest amount = 239400
Step-by-step explanation:
Below is the calculation of interest amount:
Given the loan amount or present value = 630000
Time period = 48 months or 4 years
Interest rate give = 9.5%
Total amount = P ( 1 + rt)
P = 630000
r = 9.5%
t = 4 years
Total amount = 630000 ( 1 + 9.5% x 4)
Total amount = 869,400
Interest amount = 869400 - 630000
Interest amount = 239400
Carlitos purchased $13.90 of roasted almonds to make his own almond milk.He purchased 5 pounds of almonds.Assuming the cost per pound is the same,what was the cost per pound of the almonds?
Helpppppp pleaseeeer
Answer:
D is the answer
Step-by-step explanation:
What is 1/3 minus 1/6
Answer:
Step-by-step explanation:
1/3 - 1/6
take the lcm of 3 and 6
lcm=6
=1*2-1/6
=2-1/6
=1/6
P L E A S E A N S W E R A S A P
P L E A S E E E E E E
Answer:
d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
like the guy above me said
What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?
Answer:
[tex]y=\frac{1}{2}x-5[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope and different y-intercepts1) Determine the slope (m)
[tex]x-2y=6[/tex]
Rearrange this equation into slope-intercept form (this will help us find the slope)
Subtract x from both sides
[tex]x-2y-x=6-x\\-2y=-x+6[/tex]
Divide both sides by -2
[tex]y=\frac{1}{2} x-3[/tex]
Now, we can identify clearly that the slope of the given line is [tex]\frac{1}{2}[/tex] since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of [tex]\frac{1}{2}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (-6,-8)
[tex]-8=\frac{1}{2}(-6)+b\\-8=-3+b[/tex]
Add 3 to both sides to isolate b
[tex]-8+3=-3+b+3\\-5=b[/tex]
Therefore, the y-intercept is -5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x-5[/tex]
I hope this helps!
PLEASE I NEEED HELP!!! YOU DONT HAVE TO AWNSER NUMBER 6
Answer:
6942-8.7 or 26/3-3.5 or -7/2Find the surface area. 10 ft 3 ft 5ft
Answer:
5.7 feet i think
Step-by-step explanation:
is "6x – (3x + 8) = 16x" a no solution
Answer:
no x = -8/13
Step-by-step explanation:
6x – (3x + 8) = 16x
Combine like terms
6x -3x -8 = 16
3x-8 = 16
Subtract 3x from each side
3x-8-3x = 16-3x
-8 = 13x
Divide by 13
-8/13 = 13x/13
-8/13 =x
Answer:
No, the answer would be -8/13
Step-by-step explanation:
6x-(3x+8)=16x
6x-3x-8=16x
3x-16x=8
-13x=8
x=-8/13
I keep getting the wrong answers someone help please.
Answer:
1. 8.9
2. 14.5
3. 10.3
4. 18.8
5. 8.0
6. 15.0
(All to the nearest tenth)
The code is the sum of all missing sides
So adding all
=75.5
Simplify the following expression completely.
{x^2+11x+28}
{x^2+x-12}
wrote like division
Answer:
[tex] \frac{x + 7 }{x - 3} [/tex]
Step-by-step explanation:
First factorize both expressions
[tex] \frac{ {x }^{2} + 11x + 28 }{x { }^{2} + x - 12} \\ \frac{x {}^{2 } + 7x + 4x + 28 }{x { }^{2} + 4x - 3x - 12 } \\ \frac{x(x + 7) + 4(x + 7)}{x(x + 4) - 3(x + 4) } \\ \frac{(x + 7)(x + 4)}{(x + 4)(x - 3)} [/tex]
Now you can cross out x+4
and you'll be left with
[tex] \frac{x + 7}{x - 3} [/tex]
atus
view
The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given cos 0 = Ź, find sin 0.
sin 0 =
V 역
Simplify the fraction.
Enter
Answer:
√7 / 4
Step-by-step explanation:
Trigonometrical identity are used to show the relationship between the sides and angles of a right angled triangle. Some trigonometric identities are:
sinΘ = opposite / hypotenuse, cosΘ = adjacent / hypotenuse, tanΘ = opposite / adjacent.
Given that cosΘ = 3 / 4
Therefore, cosΘ = adjacent / hypotenuse = 3 / 4
adjacent = 3, hypotenuse = 4. Let x be the opposite side, to get the opposite side, we use Pythagoras theorem:
opposite² + adjacent² = hypotenuse²
x² + 3² = 4²
x² + 9 = 16
x² = 7
x = √7
sinΘ = opposite/hypotenuse = √7 / 4
what is the shape called??
Answer:
This is called a Trapezoidal prism
Number of faces: 5
Number of edges: 9
Number of vertices: 6
Hope this helps!!
The bear moves closer, so Rick decides to go to the other side of the lake. Since there is a forest, he can only spotpoint A when angle C measures 50'. What trigonometric function would Rick
use to find AB if he knows the measure of BC ?
Answer:
Tangent
Step-by-step explanation:
Given
[tex]\angle C = 50[/tex]
See attachment for complete question
Required
Function to calculate BC
If AB is known, BC is calculated as:
[tex]\tan(C) = \frac{AB}{BC}[/tex]
Substitute d for AB and 50 for C
[tex]\tan(50) = \frac{d}{BC}[/tex]
Make BC the subject
[tex]BC = d * \tan(50)[/tex]
Hence, BC can be found using tangent
1 2/3 -2/9st step by step
Answer:
stay safe healthy and happy...Can someone help me with this ?
You bought a new water glass. The glass is cone-shaped and has a circular base. It has a
diameter of 3 inches and a height of 7.5 inches. What is the volume of the glass? Use 3.14 to
approximate pi. Round your answer to the nearest tenth.
Answer:
TO find the answer, first you have to find the formula for volume of a cone-
The formula is
V= 1/3 times base times height
So V= (1/3) (pi3^2) (12)
V= 113.04
By the way for the base you have to find the volume of a circle. I divided the diameter by 2 to find the radius.
and pi is 3.14