Answer:
Part 1
[tex]\boxed{r = 8.9 \;cm}[/tex]
Part 2
[tex]\boxed{SA=995.4\;cm^2}[/tex]
Step-by-step explanation:
If r is the radius of a sphere
Volume of a sphere:
[tex]V = \dfrac{4}{3}\pi r^2[/tex]
Surface Area
[tex]SA = 4\pi r^2[/tex]
Part 1
We are given volume = 3,000 cm³
Setting this to volume to the equation for volume gives
[tex]3000 = \dfrac{4}{3} \pi r^3\\\\[/tex]
Multiplying both sides by 3/4 yields
[tex]\dfrac{3}{4}\cdot 3000 = \pi r^3\\\\2250 = \pi r^3\\\\r^3 = \dfrac{2250}{\pi}\\\\r^3 \approx 716.1972\\\\\\r = \sqrt[3]{716.1972} \\\\r = 8.947\\\\\\\textrm{Rounded to the nearest tenth:}\\\\\boxed{r = 8.9 \;cm}\\\\\text{(Answer\;Part 1)}\\[/tex]
Part 2
Using r = 8.9 cm we can compute the surface area SA using the formula for surface area
[tex]SA = 4\pi r^2\\\\SA = 4\pi (8.9)^2\\\\SA = 995.38\;cm^2\\\\\textrm{Rounded to the nearest tenth:}\\\\\boxed{SA=995.4\;cm^2}\\\\\textrm{(Answer Part 2)}[/tex]
When is the graph of f (x) = 2x2 – 5x – 3 negative?
9514 1404 393
Answer:
-1/2 < x < 3
Step-by-step explanation:
First you need to find the x-intercepts. Since the leading coefficient is positive, you know the graph is decreasing through the left x-intercept, so will be negative between the x-intercept values.
f(x) = 2x^2 -5x -3
f(x) = 2x^2 -6x +x -3
f(x) = 2x(x -3) +1(x -3)
f(x) = (2x +1)(x -3)
The x-intercepts are the values of x that make these factors zero:
2x +1 = 0 ⇒ x = -1/2
x -3 = 0 ⇒ x = 3
The graph of f(x) is negative on the interval ...
-1/2 < x < 3
P = 100 - 20 cos (8πt/3) That's (8 pi t /3) where t is the time (in seconds). What is the period of the model? Discuss what the period represents in the context of this model.
Answer:
The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.
Step-by-step explanation:
Cosine is a trigonometric function and trigonometric functions are characterized by having a periodical behavior. The period is the time needed for the function to cover an angle of [tex]2\pi[/tex] radians. By this approach we find that:
[tex]\frac{8\pi\cdot t}{3} = \frac{2\pi\cdot t}{T}[/tex] (1)
Where:
[tex]t[/tex] - Time, measured in seconds.
[tex]T[/tex] - Period, measured in seconds.
Then, we solve (1) for [tex]T[/tex]:
[tex]\frac{8}{3} = \frac{2\pi}{T}[/tex]
[tex]T = \frac{6\pi}{8}\,s[/tex]
[tex]T = \frac{3\pi}{4}\,s[/tex]
The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.
What is the value of x in the equation 6x + 3 + 4x =
(9 + 10x)?
Enter your answer in the box.
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Answer:
x = 3/10
Step-by-step explanation:
Given
6x +3 +4x = 1/2(9 +10x)
We can collect term, then multiply by 2.
10x + 3 = (1/2)(9 +10x)
20x + 6 = 10x + 9 . . . . . . . multiply by 2
10x = 3 . . . . . . . . . . . . . . . . subtract (6+10x)
x = 3/10 . . . . . . . . . . . . . . . divide by 10
_____
Check
6(3/10) +3 +4(3/10) = (1/2)(9 + 10(3/10))
1.8 + 3 + 1.2 = 1/2(9 +3)
6 = 6 . . . . . solution checks OK
What is the missing angle
120°
70°
Answer:
the measure of angle B is 50
Step-by-step explanation:
the measure on the other side of the 120 is 60
hope this helps!!
In the figure above, PQRS is a circle. If PQT and SRT
are straight lines, find the value of x.
Given:
PQRS is a circle, PQT and SRT are straight lines.
To find:
The value of x.
Solution:
Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.
We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.
[tex]m\angle SPQ+m\angle QRS=180^\circ[/tex]
[tex]81^\circ+m\angle QRS=180^\circ[/tex]
[tex]m\angle QRS=180^\circ-81^\circ[/tex]
[tex]m\angle QRS=99^\circ[/tex]
Now, SRT is a straight line.
[tex]m\angle QRT+m\angle QRS=180^\circ[/tex] (Linear pair)
[tex]m\angle QRT+99^\circ=180^\circ[/tex]
[tex]m\angle QRT=180^\circ-99^\circ[/tex]
[tex]m\angle QRT=81^\circ[/tex] ...(i)
According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.
Using exterior angle theorem in triangle QRT, we get
[tex]m\angle PQR=m\angle QRT+m\angle QTR[/tex]
[tex]x=81^\circ+22^\circ[/tex]
[tex]x=103^\circ[/tex]
Therefore, the value of x is 103 degrees.
I need help with B. Do you I think this will mean the end of life on earth?
Please answer ASAP
Answer:
yes
Step-by-step explanation:
Sara was cliff jumping. She was on a cliff 25 feet above sea level. She jumped into the sea and descended a total of 37 feet. How many feet below sea level did she travel? Justify your reasoning.
Answer:
12 feets below sea level
Step-by-step explanation:
Initial height = 25 feets above sea levwl
Total descent = 37 feets
Distance traveled below sea level = 37 feets - 25 feets = 12 feets
Hence, Sarah traveled 12 feets below sea level
What is the difference between the profits Mr. Brown's store earned in the first quarter and the third quarter?
Answer:
Hi we need a picture or a chart.
Step-by-step explanation:
Answer:
2,411.44
Step-by-step explanation:
Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days?
Answer:
48.72 km in 3 days.
Step-by-step explanation:
Given that,
A one-way trip is 8.12 kilometers.
We need to find the distance he travel in 3 days.
The distance traveled by Jim in one day to the bus and from school = 2(8.12) = 16.24 km
Distance traveled in 3 days = 3(16.24)
= 48.72 km
Hence, he will cover 48.72 km in 3 days.
me Digão qual e a resposta
Answer:
As somas estão abaixo
Step-by-step explanation:
a) 158
b) 2095
c) 2819
d) 9082
Eu espero que isso ajude :)
PLEASE HELP,, A home decorator is adding new flooring to a living room using the blueprint shown.
image
What are the actual length and width of the living room? Show your work.
A.
7ft, 6ft
B.
14 ft, 10ft
C.
10ft, 8ft
D.
20ft, 16ft
Answer: 20ft, 16ft
Step-by-step explanation:
Because 0.5in=2ft, you would divide the length (5in) and the width (4) both by 0.5. Which give you 10 for the length and 8 for the width. Then you multiply both of those products by 2 and that gives you your answer. 20ft and 16ft. Hope this helps. :)
8 students in Mr. Webb's class got an A on the exit ticket. There are 25
students in his class total. What percent of students got an A?*
Answer:
32%
Step-by-step explanation:
To find the percentage, we have to multiply 25 and 8 by 4.
25x4 = 100
8x4 = 32
So, 8 out of 25 is 32%.
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Answer:
25.12 inches
Step-by-step explanation:
Find the missing length?
A. 18in
B. 6in
C. 2in
D. 36in
Answer:
B. 6in
Step-by-step explanation:
We can use the Pythagorean theorem [ a² + b² = c² ] to find the missing side.
8² + b² = 10²
64 + b² = 100
b² = 36
b = 6
Best of Luck!
What is the radius of a circle with a circumference of 81.64 feet.
Answer:
Step-by-step explanation:
Your answer
Circumference = 2 * π* r = 81.64
r = 12.99 → 13
Mark it as Brainlist answer. Follow me.
select the correct choice and fill in the box to complete your choice. pls help!!!
Can you see the image I’m not sure if you can please let me know
Answer:
you can't sorry
Step-by-step explanation:
ycucycycufycycycyc
Answer:
no I can't see
Step-by-step explanation:
please mark me as brainlist
What is the solution to the equation sqrt 2x+3 minus sqrt x+2=2? x =
Answer:
x= 1/4 or 0.25
Answer:
23
Step-by-step explanation:
on edg
Find the value of x.
Answer:
x=7
Step-by-step explanation:
Since the two lines, the transversal intersects are parallel we know that the angles are same-side interior. This means they are supplementary or add up to 180. Therefore, to solve add the two expressions and set them equal to 180, then solve with properties of equality.
14x+7+10x+5=180
First, add like terms
24x+12=180
Then, subtract 12 from both sides
24x=168
Next, divide both sides by 24
x=7
Which of the following is a situation in which an equation cannot be solved
using the quadratic formula?
A. The coefficient of the x-term is zero.
B. One term of the polynomial has a degree of 3.
C. The right-hand side of the equation is zero.
D. The coefficient of the XP-term is 1.
Answer:
B One term of the polynomial has a degree of 3
Cash loan $100 20.0% 3 years $6 (100 x .2 x .3) $106 ($100 + $6) Big-screen TV $500 9.0% 4 years $ (500x $ College loan $13,000 4.5% 15 years $ $
Answer:
Cash loan = $160
Big screen TV = $680
College loan = $$21775
Step-by-step explanation:
Cash loan :
Loan amount or principal = $100
Interest rate, r = 20.0%
Time, t = 3 years
Using the relation :
Simple interest = Principal * rate * time
$100 * 0.2 * 3 = $60
Final amount = loan amount + interest on loan
Final amount = $100 + $60 = $160
Big Screen TV:
Principal = $500
Rate, r = 9.0%
Time, t = 4 years
Interest amount = (500 * 0.09 * 4)
Interest amount = $180
Final amount = principal amount + interest on loan
Final amount = $500 + $180 = $680
College loan
Principal, = $13,000
Rate, r = 4.5%
Time, t = 15 years
Interest amount = (13000 * 0.045 * 15)
Interest amount = $8775
Final amount = principal amount + interest on loan
Final amount = $13000 + $8775 = $21775
Solve: -2x - 5 = -3
plz help me hurry
Answer:
x=-1
Step-by-step explanation:
-2x - 5 = -3
add 5 to both sides
-2x = 2
divide both sides by -2
x = -1
Answer:
x = -1
Step-by-step explanation:
-2x - 5 = -3
Same to both sides:
-2x = -3 + 5
Simplify:
-2x = 2
Divide by -2 on each side to isolate x:
x = -1
Let me know if you have any questions
Carl is deriving the quadratic equation by completing the square. His work at one of the steps is shown. x + b/na = + or - b^2-4ac. Carl is not sure what the value of n is. What value should he use to continue deriving the quadratic equation correctly? A. 1 B. 2 C. 3 D. 4
Answer:
the correct option is B. 2
Step-by-step explanation:
As given,
x + [tex]\frac{b}{na}[/tex] = ± √b²-4ac
⇒x = -[tex]\frac{b}{na}[/tex] ± √b²-4ac
As e know that the quadratic formula is
x = [tex]\frac{-b + or - \sqrt{b^{2} - 4ac } }{2a}[/tex]
So , by comparing with the formula
we get
n = 2
So, the correct option is B. 2
Determine the slope of the line
Answer:
2 !!
Step-by-step explanation:
use RISE/RUN !! you would go up from the 1 point, on the y axis !! from there, ud go up 2, then to the right 1, so ur slope is 2/1 .... which is 2 !!
i hope this helped !
funny corona-virus meme
Answer:
lol thats funny
Step-by-step explanation:
hahahahahahahahahahahahahahahahahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! That is funny;)
Find the area of the regular octagon.
Answer:
3*4
=12 sq. cm
= 12 cm²
Answer:
48cm^{2}
Step-by-step explanation:
[tex]A=4ah=4*4*3=48 cm^{2}[/tex]
I NEED THIS RN AS FAST AS POSSIBLE! Your teacher decides to split the class into four equal groups with no more than five students in each group. that represents the number of students in the class.
Answer:
option 1 i think
Step-by-step explanation:
imma just take these 5 points back
1. In Mr. B's classroom, there are 20 students.
Twelve students got a B, one student got a C, and
the rest received an A. What percent of the class
received an'A?
Help please
Answer:
1.5%
Step-by-step explanation:
x2 + 3x + 2 by x + 1
Answer:
x²+3x+3
Step-by-step explanation:
hope it helps you
please mark me as brainlist
SMART PEOPLE PLEASE TAKE THE TIME TO ANSWER THIS!!!!!!!!!
Answer:
40% ⋅ x = 35
x = 87.5
Step-by-step explanation:
To write an equation representing this situation, use the key words. 40% stays 40%. "Of" is the same as multiplication. "X" remains "x". "Is" is the same as equal to. 35 remains 35. So, the new equation you get is: 40% ⋅ x = 35.
To solve for "x", first turn the 40% into a decimal: 0.4. Now divide 0.4 from both sides to get: x = 87.5.
Note:
The dot "⋅", stands for the multiplication sign. I'm not using the "x" symbol for it because there is a variable x in the equation already.
Hope it helps!