The surface area of the sphere is SA = 324π cm².
Calculate the surface area of the sphere by using the formula: SA = 4πr².
To find the value of r, substitute SA = 324π in the above formula.
324π = 4πr²
81 = r²
r = ± 9.
The measurements of the sphere cannot be expressed in negative sign.
The radius of the sphere is r = 9 cm.
Calculate the surface area of the sphere by using the formula: V = (4/3)πr³.
Substitute r = 9 in the above formula
V = (4/3)π 9³ = 972π cm³.
Which number line represents all of the values of x for the equation x2 = 36?
yes thats the corrects answer -6 and 6 on the number line.
A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amount of material used.
A cell phone company charges a basic rate of $19.99 per month for 300 minutes of local usage. Any local usage over 300 minutes is charged at $.10 per minute. All long distance calls are charged at $.25 per minute. Write and simplify an expression that gives the total monthly bill if x is the number of local minutes and y is the number of long distance minutes. Evaluate the expression if local usage totals 375 minutes and long distance usage totals 54 minutes.
total = 19.99 + 0.10(x-300) + 0.25y
x = 375
y=54
total = 19.99 +0.10(375-300) +0.25(54)
total = 19.99 + 0.10(75) + 0.25(54)
total = 19.99 + 7.50 + 13.50
total = $40.99
The total monthly bill is $40.99 for 375 local minutes and 54 long distance minutes, given the cell phone company's rates.
The total monthly bill can be expressed as the sum of the basic rate, the extra charge for local minutes beyond the included 300, and the charge for all long distance minutes. The expression can be written as:
Total Monthly Bill = Basic Rate + (Local Extra Charge x Extra Local Minutes) + (Long Distance Rate x Long Distance Minutes)
Where:
Basic Rate = $19.99Local Extra Charge = $0.10 per minuteExtra Local Minutes = x - 300 (only if x > 300)Long Distance Rate = $0.25 per minuteLong Distance Minutes = yFor x = 375 local minutes and y = 54 long distance minutes, the total monthly bill is calculated as follows:
Total Monthly Bill = $19.99 + ($0.10 x (375 - 300)) + ($0.25 x 54)
Total Monthly Bill = $19.99 + $7.50 + $13.50
Total Monthly Bill = $40.99
Conjectures can always be proven true.
True or False
James is four years younger than Austin. If 2 times James age is increased by the square of austins age, the result is 28. Find the 2 ages. Use an algebraic solution
Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = eight divided by square root of quantity two x plus four.
The book Kathy is reading is 540 pages long. So far, she has read 405 pages. What percent of the book does she have left to read?
Answer: b
Step-by-step explanation: i got it right
The distance of saturn from the sun is 1507 million kilometers express this distance in standard form
A rectangular patio is 9 ft by 6 ft. When the length amd width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6+x)(9+x)= 88. What do her solutions represent?
The solutions represent the additional length and width that need to be added to the original dimensions to achieve the desired area of 88 sq ft.
Explanation:The equation is: (6+x)(9+x) = 88. Ginger is using the zero product property to solve for x. The solutions she finds represent the value of x that, when added to both the length and width of the original patio, will result in a patio with an area of 88 sq ft.
By solving the equation, Ginger will find the possible values of x that will make the area of the new patio equal to 88 sq ft. These values represent the additional length and width that need to be added to the original dimensions to achieve the desired area.
For example, if Ginger finds that x = 2, then the new patio dimensions would be 9+2 = 11 ft by 6+2 = 8 ft, resulting in an area of 11 * 8 = 88 sq ft.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ12
How do you simplify this problem?
1+tan^2(x) = sec^2(x)
sec^2(x) = 1/cos^2(x)
csc(-x) / 1/cos^2(x) =
cos^2(x) csc(-x)
Which is a factor of 54xy + 45x + 18y + 15?
Please Help!! Find the measure of angle 2. Image Attached
Check all that apply: If cos theta = 15/17 then:
A. Sec theta = 17/15
B. Tan theta = 8/15
C. Sin theta = 15/8
D. Csc theta = 17/15
The options (A) and (B) are correct.
What is trigonometric Ratios?"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".
For the given situation,
Cos θ = 15/17
By using Pythagoras theorem,
We know Cos θ = [tex]\frac{base}{hypotenuse}[/tex]
Sine θ = [tex]\frac{perpendicular}{hypotenuse}[/tex]
tan θ = [tex]\frac{perpendicular}{base}[/tex]
By Pythagoras theorem, [tex]Hypotenuse^{2}= base^{2}+perpendicular^{2}[/tex]
⇒[tex]17^{2}=15^{2}+perpendicular^{2}[/tex]
⇒[tex]perpendicular^{2}= 289-225[/tex]
⇒[tex]perpendicular=\sqrt{64}[/tex]
⇒[tex]perpendicular=8[/tex]
Thus, Sec θ = 17/15
Tan θ = 8/15
Sine θ = 8/17
Cosec θ = 17/8.
Hence we can conclude that the options (A) and (B) are correct.
Learn more about trigonometric ratios here
https://brainly.com/question/9085166
#SPJ2
Answer:
tan and sec
Step-by-step explanation:
A amd B
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the
transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
The value of y varies jointly with the values of x and z. When x=4 and z=9, the value of y is 360. What is the value of y when x=5 and z=12?
.help me with this please
Brian is waiting at a park across the street from the hockey arena for his dad to pick him up. It rained most of the morning, and the streets still have puddles. At which point should Brian stand to be as far as possible from each street to avoid getting splashed? Explain your answer.
To avoid getting splashed from puddles on the street, Brian should stand in the middle of the park. This would distance him completely from the immediate spray zone of passing vehicles, like being further away from the shore reduces the impact of sprays from waves.
Explanation:To avoid getting splashed by cars driving through the puddles, Brian should stand in the middle of the park. By doing so, he establishes the maximum possible distance between himself and any part of the street. Staying as far away from the streets reduces the risk of any water reaching him when cars pass by.
Think of it like Jill delivering her flyers and retracing her steps: the farthest spot from her house during her journey was at the midpoint of her travel route.
Also consider Peter's driving scenario: The farther he is from other cars, the less likely he is to get affected by their maneuvers. In a similar way, Brian, being in the middle of the park would keep him away from the splash zone of passing cars.
Lastly, akin to Julian and his father on their surfboards, being away from the impact point of the waves (which is near the shore) they get least affected by the spray. This analogy can be compared to Brian's situation with the puddles.
Learn more about Maximizing Distance here:https://brainly.com/question/32250758
#SPJ11
A cylindrical metal can is to have no lid. it is to have a volume of 8Ï in3. what height minimizes the amount of metal used?
To solve this problem let us say that,
h = height of the can
r = radius of the can
We try to minimize the amount of metal used which is the surface area (SA), and the equation for a cylinder is:
SA = 2πrh + πr^2
To get the minima, we take the derivative of this function and set it equal to 0. But first, the function is in two variables so we must eliminate one of them. We use the extra information given in the problem which is volume:
V = 8π = πr^2 h
Therefore,
h = 8/r^2
Plug this into the SA function to have it in terms of one variable only:
SA = 2πrh + πr^2
SA = 2πr(8/r^2) + πr^2
SA = 16π/r + πr^2
Taking the 1st derivative of the function:
0 = −16π r^−2 + 2πr
0 = −16π/r^2 + 2πr
16π/r^2 = 2πr
r^3 = 8
r = 2 in
By obtaining r, we calculate for h:
h = 8/r^2
h = 8/(2)^2
h = 8 / 4
h = 2 in (ANSWER)
Vanessa typically works 8 hours per day in a normal 5 day work week. last week, however, vanessa had to take 90 minutes off on tuesday, 45 minutes off on thursday, and she left two and a half hours early on friday. how many hours did vanessa work last week?
The total number of hours Vanessa work in a week is:
total work hours = (8 hours / day) * 5 day / week
total work hours = 40 hours per week
The total number of hours she did not work:
total hours did not work = (90 minutes)(1 hour / 60 minutes) + (45 minutes)(1 hour / 60 minutes) + 2.5 hours
total hours did not work = 4.75 hours
The amount of hours Vanessa work last week can be calculated using the formula:
work hours = total work hours - total hours did not work
work hours = 40 hours – 4.75 hours
work hours = 35.25 hours
Solve 2x2 + 20x = −38.
a. −5 ± square root 14
b.−5 ± square root 51
c. −5 ±square root 6
d.−5 ± square root 13
Answer:
c
Step-by-step explanation:
−5 ±square root 6
(30 points) Enter numbers to write 0.000328 in scientific notation.
In which expression should the exponents be multiplied?
a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2
Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.
The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.
Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).
(6.04)The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
What is the y-intercept of the line of best fit and what does it represent?
1 minute; the number of minutes students stretch when they do not jog
1 hour; the number of hours students jog when they do not stretch
4 hours; the number of hours students jog when they do not stretch
4 minutes; the number of minutes students stretch when they do not jog
What is the value of x in the equation 2(x – 3) + 9 = 3(x + 1) + x?
x =
How many roots does y+x^2-6x+9 have?
A. One
B. Two
C. Zero
D. Three
The equation sec^2x-1=tan^2x is an identity true or false
A point where two or more rays or "arms" of an angle meet
Final answer:
The point where two or more rays meet in optics is known as the focal point, which is crucial in geometric optics. For a converging lens or mirror, it's where light rays converge, while for a diverging lens or mirror, it's where light rays appear to originate.
Explanation:
The point where two or more rays or 'arms' of an angle meet in the context of geometrical optics is known as the focal point. In terms of a converging lens or mirror, the focal point is where converging light rays intersect after passing through the lens or reflecting off the mirror surface. This is a fundamental concept in the study of geometrical optics, which deals with the ray aspect of light. A ray is a straight line that originates at a point and is used in geometric optics to represent the path along which light travels.
For a converging lens, which is also known as a convex lens, parallel light rays entering the lens will refract and converge at a single point on the opposite side of the lens. This single point is the focal point. Similarly, in concave mirrors, ray diagrams show the focal point as the point where reflected rays converge or appear to converge. The distance from the focal point to the mirror along the central axis is referred to as the focal length. Conversely, for a diverging lens or mirror, the focal point is the point from which diverging light rays appear to originate.
Which lines can you conclude are parallel given that m14 + m2 = 180? Justify your conclusion with a theorem.
Answer:
Option 2 is correct.
Step-by-step explanation:
Given the diagram and also the condition m∠14 + m∠2 = 180°
we have to tell which lines are parallel.
By the theorem of exterior angles
Same-side exterior angles which are formed outside of the parallel lines and on same side of transversal line.
The theorem states that when parallel lines are cut by a transversal line, the sum of the same-side exterior angles is 180° i.e these are supplementary.
∴ Lines a and b are are parallel by converse of same side exterior angle theorem.
every evening jenna empties her pockets and puts the changein a jar. at the end of the week she had 50 coins, all of them dimes and quarters. when she added them up, she had a totals of $10.25
d=number of dimes q=number of quarters
how many dimes did jenna have?
Let $s$ be the set of points with polar coordinates $(r,\theta)$ such that $ 2 \le r \le 6$ and $\frac{\pi}{3} \le \theta \le \frac{5 \pi}{6} $. find the area of $s$.