==========================================================
Explanation:
The volume of the cone is...
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*(1.25)^2*2.75
V = 4.49739583333333
which is approximate.
-----------
The volume of the sphere is
V = (4/3)*pi*r^3
V = (4/3)*3.14*(0.25)^3 ... note the radius is half the diameter
V = 0.06541666666667
which is approximate as well
-----------
Subtract the two volumes to finish things up
4.49739583333333-0.06541666666667 = 4.43197916666667
The result 4.43197916666667 then rounds to 4.43
This is the approximate amount of empty space in the cone that isn't taken up by the spherical gum. The units are in "cubic inches" or "in^3" for short.
Which is the domain of the function f(x) =
12
- 2?
Vx+4
O A. x20
O
B. x>-4
o
C. x>-2
D. x>-4
E. all real numbers
The domain of the function is x> -4.
The correct option is B.
We have the function
f(x) = 12/ √(x+ 4) - 2
Now, putting f(x) = 0
12/ √(x+ 4) - 2 = 0
12 - 2√(x+ 4) = 0
-2√(x+ 4) = -12
√(x+ 4) = 6
Taking Square on both side we get
x+ 4 = ±36
x = ± 36 - 4
x = 32 or x= -40
Thus, the domain of the function is x> -4.
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Trigonometry, Law of Cosines.
Select the angle that correctly completes the law of cosines for this triangle.
Answer:
○ C. [tex]\displaystyle 74°[/tex]
Step-by-step explanation:
[tex]\displaystyle c^2 + b^2 - 2cb\:cos∠A = a^2[/tex]
In the EDGE formula of the Law of Cosines, whatever squared edge term is on the outside of the equivalence symbol, its angle measure is what you write next to the trigonometric function, if you understand the formula written above.
I am joyous to assist you at any time.
What are the roots of the equation x^2+8x+32=0 in simplest a+bi form?
Answer:
x = -4 ± i4
Step-by-step explanation:
This is a quadratic equation with coefficients {1, 8, 32}. We apply the quadratic formula to solve for x. The first step is to find the 'discriminant,' b^2 - 4 ac, which here is (8)^2 - 4(1)(32), or 64 - 128, or -64.
A negative discriminant indicates that this quadratic has two unequal complex roots.
-b ± √(b^2 - 4ac)
The formula is x = ----------------------------
2a
which, when evaluated at a = 1, b = 8 and c= 32, yields
-8 ± √(-64)
The formula is x = ----------------------------
2(1)
or:
-8 ± i√64
The formula is x = ----------------- = x = -4 ± i4
2
how do I multiply and divided exponent denominator and numerator
9. A building 62 feet tall casts a shadow 21 meters long. At what angle is the sun shining on the building?
A. 19.80
B. 18.71
C. 70.20
D. 71.29
First, we imagine a right triangle. Second, we are given that the building is 62 feet tall. Since the height of building is vertical straight - that means the height is opposite side of triangle. It also casts a shadow 21 meters long. Shadow should be the adjacent side because it casts on the ground and not on the air.
If we imagine the right triangle + the problem in our head, we'd get the triangle that the opposite side is 62 feet tall and the adjacent side is 21 meters long.
Use the tangent ratio to find the angle of sun shining.
[tex] \large \boxed{ \tan \theta = \frac{opposite}{adjacent} }[/tex]
Substitute adjacent = 21 and opposite = 62 in the ratio.
[tex] \large{tan \theta = \frac{62}{21} }[/tex]
For this part, you might need a calculator or trigonometric table because some values cannot be exactly found.
From the equation, we should get 71.288 which we round the answer to nearest hundreth and the answer would be 71.29
Answer
The answer is 71.29Answer:
71.29°
Step-by-step explanation:
By question its given that , a 62 feet tall tree cast a shadow of 21 m long. We need to find the angle at which the sun is shining on the building .
For this we gonna imagine a right angle triangle . Where , the length of the shadow will be the base of the triangle and the height of the building will be the perpendicular on the triangle .
Here since we have got perpendicular and base , we can use the ratio of tan . We know that tan is defined as perpendicular by base , that is ,
[tex]\implies tan \theta =\dfrac{perpendicular}{base}[/tex]
where theta is the angle between the Ray of the the sun and the the shadow of the building.Plug in the respective values , we have ,
[tex]\implies tan \theta =\dfrac{62}{21} \\\\\implies\theta = tan^{-1}\bigg( \dfrac{62}{21}\bigg) \\\\\implies \underline{\underline{\theta = 71.29^o }}[/tex]
Hence the required answer is 71.29° .
Find the circumference of a circle with diameter,
d
= 7.18m.
Give your answer rounded to 2 DP.
Answer:
C = 22.56
Step-by-step explanation:
The equation for the circumference of a circle is [tex]C=2\pi r[/tex].
The radius is half the diameter so [tex]r=\frac{7.18}{2}=3.59[/tex]
Plug the radius into the equation.
[tex]C=2*\pi *3.59[/tex]
[tex]C=22.55664[/tex]
Given:
Diameter of circle = 7.18 m
To find:
Circumference of the circle
Steps:
We know that radius is equal to half of the diameter
r = d/2
r = 7.18/2
r = 3.59 m
Now circumference is equal 2πr
Circumference = 2πr
Circumference = 2 × 3.14 × 3.59 (taking pi as 3.14)
Circumference = 6.28 × 3.59
Circumference = 22.5452
Circumference ≈ 22.55 meters
Therefore, the circumference of the circle is approximately 22.55 meters
HAPPY TO HELP :)
If you need any more help, feel free to ask
Which negative angle is equivalent to 285 degrees?
A.-85 degrees
B.-95 degrees
C.-65 degrees
D. -75 degrees
By definition of coterminal angles, the negative angle that is equivalent to an angle of 285° is equal to - 75° degrees. (Correct choice: D)
How to find a negative coterminal angle?
In this problem we must determine a negative angle coterminal to a given angle, two angles are coterminal when both have the same direction. Given that a complete revolution is done each 360°, we can derive an expression for angles coterminal to a given one:
θ' = θ + i · 360° (1)
Where i is the index of the coterminal angle.
If we know that θ = 285° and i = - 1, then the negative angle is:
θ' = 285° + (- 1) · 360°
θ' = - 75°
By definition of coterminal angles, the negative angle that is equivalent to an angle of 285° is equal to - 75° degrees. (Correct choice: D)
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pls help in the middle of my final lol
Answer:
b) 2
Step-by-step explanation:
both angles have the same values, they are technically opposites.
Set your formula up as
130 = 66x - 2
130 + 2 = 66x
132/66 = x
2 = x
I would really appreciate someone helping me with this one.
About 20,000 white and brown beans were mixed in a bag. You take out 400 beans randomly from the bag. Of these, 220 are brown and 180 are white. How many white beans should be in the bag from the beginning?
Answer:
9,000
Step-by-step explanation:
180/400 × 20,000 = 9,000
Answer:
9,000
Step-by-step explanation:
180÷400= 0.45
0.45×20,000= 9,000
Help me please I really need help
Answer:
[tex]17\sqrt{2}[/tex] ft
Step-by-step explanation:
take angle b as reference angle
using sin rule
sin 45 = opposite / hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] = 17 / BC
BC =17 / [tex]\frac{1}{\sqrt{2} }[/tex]
BC = 17 * [tex]\sqrt{2}[/tex]
BC = [tex]17\sqrt{2}[/tex] ft
Answer:
BC = 17[tex]\sqrt{2}[/tex] ft
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{17}{BC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
BC = 17[tex]\sqrt{2}[/tex] ft
PLEASE HELP ITS DUE TONIGHT, IM CONFUSED
Answer:
this may or may not help ya :/
perimeter of a rectangle = 2 × ( length + breadth)= 2 ×( x + 2 + x )
= 2 ( 2x + 2)
= 4x + 4 units
area of a rectangle = length × breadth= (x + 2) × x
= x² +2x Sq. units
The point D(-4,-2) Is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, D' ?
Answer:
Step-by-step explanation:
use formula
A(x,y)=A'(-x,-y)
D(-4,-2)=D'(4,2)
A tool box has the dimensions of 9 in by 3 in by 5 in. If Jesse plans to double all three dimensions to build a larger tool box, he believes he would double the volume of the tool box. Is he correct?
Answer:
No, the volume will be incresed by 8 times (2x2x2=8)
Step-by-step explanation:
[tex]Volume=3*5*9=135 in^{3} \\increased -Volume=6*10*18=1080 in^{3}\\\frac{1080}{135} =8[/tex]
Question 1 of 10
Classify the following triangle. Check all that apply.
60
60
60
O A. Isosceles
B. Equilateral
O C. Scalene
O D. Acute
E. Right
Answer:
A, B, & D
Step-by-step explanation:
A. isosceles - 2 sides equal (actually) all sides are equal
B. equilateral - all sides equal and all angles are equal too
D acute - all angles are less than 90 degrees
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 6
A. log(2) + log(1/6)
B. log 2
C.log(1/3)
D. log 3
Answer:
is there a picture or something i cant understand
Step-by-step explanation:
Answer:
C. log(1/3)
Step-by-step explanation:
log a - log b = log(a/b)
Write an equation for the nth term of the arithmetic sequence. -6,-9,-12,-15
Answer:
[tex]a_{n}[/tex] = - 3n - 3
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 6 and d = a₂ - a₁ = - 9 - (- 6) = - 9 + 6 = - 3 , then
[tex]a_{n}[/tex] = - 6 - 3(n - 1) = - 6 - 3n + 3 = - 3n - 3
2 x 12 divided by (2 + 6) +2^3
Answer:
11
Step-by-step explanation:
To add fractions, find the LCD and then combine or Pemdas
Answer:
Your answer should be 1.5
Step-by-step explanation:
Can I get brainliest
Which expression represents the series 1+5+25+125+625
Answer:
[tex]1 = {5}^{0} [/tex]
[tex]5 = {5}^{1} [/tex]
[tex]25 = {5}^{2} [/tex]
[tex]125 = {5}^{3} [/tex]
[tex]625 = {5}^{4} [/tex]
option A is correct, it starts with the power of zero (equals always one, see it as
[tex] \frac{5}{5} [/tex]
and it goes up to the power of 4
Letter D thanks for asking for help
How do I solve this. Please help!!
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then using the upper 45°
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 4[tex]\sqrt{2}[/tex]
Find the circumcenter of a triangle ABC with vertices at A(2, 2), B(0, -4), and C(7, -1)
20 POINTS PEOPLE
Answer:
just sum up the 3 sides.
quick side note: I lost my previews writing bc I waited too long too post it :(
but long story short: you get the length of, say, AB by using pythagoras theorem.
[tex] \sqrt{ {2}^{2} + {6}^{2} } [/tex]
do this with BC and CA too
the 2 is just the distance in x-direction and the 6 is just the distance in y-direction
and since a²+b²=c², we need to take the root to get the distance between 2 points
see screenshot for summing up the three distances. the part out of screen is written out above
the sum is 21.011 length units
hope it helps. have a nice day.
feel free to ask questions.
and maybe, if I'm feeling really nice and a lil bored, i leave greeting answers under yours to enable posters to give gives brainliests. if theres no 2and answer at least
The width of an extra large rectangle poster is 8 inches more than half its length.The area of this poster is 306 square inches
Answer:
a² + 16a - 612 = 0
Step-by-step explanation:
Here is the complete question :
The width of an extra large rectangle poster is 8 inches more than half its length. The area of this poster is 306 square inches
Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.
Area of a rectangle = length x width
Let length = a
width = 8 + 1/2a
Area = (8 + 1/2a) x a
306 = (8 + 1/2a) x a
multiply both sides of the equation by 2
612 = 16a + a²
a² + 16a - 612 = 0
the dimensions of the poster can be determined using quadratic formula
please help, i attached a photo.
Answer:
yes..
Step-by-step explanation:
what is 6t + 3t + 4 simplified?
Answer:
9t + 4
Step-by-step explanation:
6t + 3t + 4
= 9t +4
What is the inverse (opposite) of addition? *
pls i will give brainliest
Answer:
subtraction
Step-by-step explanation:
because if you add in addition you would take away when you subtract
Answer:
la inversa de la suma es la resta
Step-by-step explanation:
How are patterns applied in real – life situations? Cite an example.
Find the value of X and Y in the parallelogram
Answer:
[tex]Find~x:-[/tex]
[tex]4x-37=49[/tex]
[tex]4x=49+37[/tex]
[tex]x=21.5[/tex]
[tex]Find ~y:-[/tex]
[tex]y/5=4x-3[/tex]
[tex]y=5(4*21.5-3)[/tex]
[tex]y=415[/tex]
----------------------hope it helps...have a great day!!calculate the value of 3√12 ÷ 6√27
The ratio of positive reviews to negative reviews on David's customer feedback website is 3:5. There are 352 reviews on David's website Part A: What fraction of the reviews on David's website is positive? What fraction is negative? Explain your reasoning. Part B: How many positive reviews would need to be added to David's website to make the ratio of positive reviews to negative reviews equal to 1: 1? Explain your reasoning
Answer:
Part A
positive=132
negative=220
Part B=88
Step-by-step explanation:
Part A
3:5
positive: negative
3+5=8
352/8=44
3x44=132 positive or 3/8 of 352
5x44=220 negative 5/8 0f 352
Part B
220
-132
---------------
88
(ii) 3x - 5y - 4 = 0 and 9x = 2y +7
Step-by-step explanation:
3×‐9×-5y-2y =0-7
-6x-7y =-7
Answer:
[tex]x = \frac{9}{13} \ , \ y = - \frac{5}{13}[/tex]
Step-by-step explanation:
3x - 5y = 4 ----------- ( 1 )
9x - 2y = 7 -----------( 2 )
______________________
( 1 ) x 9 => 27x - 45y = 36 ----------------- ( 3 )
( 2) x 3 => 27x - 6y = 21 -------------------( 4 )
_____________________
( 3 ) => 27x - 45y = 36
- ( 4 ) => -27x + 6y = - 21
____________________
( 3 ) - ( 4 ) => 0x - 39y = 15
-39y = 15
[tex]y = \frac{15}{-39} = -\frac{5}{13}[/tex]
Substitute y in ( 1 ) :
[tex]3x - 5y = 4\\\\3x - ( 5 \times -\frac{5}{13}) = 4\\\\3x + \frac{25}{13} = 4\\\\3x = 4 - \frac{25}{13}\\\\3x = \frac{52 - 25}{13}\\\\3x = \frac{27}{13}\\\\x = \frac{27}{13 \times 3}\\\\x= \frac{9}{13}[/tex]
80 25 x pls help me with this one
Answer:
25
Step-by-step explanation:
Answer:
x = 25
Step-by-step explanation:
Okay so as you can see there is an x shape and whenever you have that it means they are verticle angles. So we can conclude that 25 is verticle to x and so x is equal to 25.
