Answers
v=D/(2z)
First option is correct i.e. [tex]v = \frac{D}{2z}[/tex] .
What is variable in an equation?Variable is a symbol( usually a letter) standing in for an unknown numerical value in an equation.
How to solve an equation for the variable?To solve or isolate a variable means to get the variable on one side of the equation by itself.
According to the given question
we have an equation
D = 2zv and to solve for variable v
For solving the above equation for the variable v, make the variable v on one side of the equation by itself.
⇒ [tex]\frac{D}{2z} = \frac{2zv}{2z}[/tex] ( dividing both the sides by 2z)
⇒ [tex]v = \frac{D}{2z}[/tex]
Hence, option first is correct.
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Related Questions
solve for m
2m = -6n -5; n = 1, 2 ,3
Answers
at n=1:
2m=-6(1)-5=-6-5=-11
m = -11/2
at n=2:
2m=-6(2)-5=-12-5=-17
m = -17/2
at n=3:
2m=-6(3)-5=-18-5=-23
m = -23/2
Two consecutive odd integers have a sum of 44 . Find the integers.
Answers
x + x + 2 = 44
2x + 2 = 44
2x = 44 - 2
2x = 42
x = 42/2
x = 21
x + 2 = 21 + 2 = 23
ur numbers are 21 and 23
2n+2=44 subtract 2 from both sides
2n=42 divide both sides by 2
n=21
So n and n+2 are 21 and 23.
A section of land has an area of 1 square mile and contains 640 acres. determine the number of square meters in an acre
Answers
1 squre mile = 1760^2 yd^2 = 3097600 yd^2
This means that
Each acre has (3097600 yd^2/ sq. mile ) / (640 acres/sq. mile(= 4840 yd^2 / acre
Also, we know that 1 inch = 2.54 cm exactly.
Therefore
1 yd = 3*12*2.54 cm = 91.44 cm = 0.9144 m
1 yd^2 = (0.9144 m)^2 = 0.83612736 m^2
Using the conversion from acre to sq yards,
1 acre=4840 yd^2
=4840 yd^2 * 0.83612736 m^2 / yd^2
= 4046.8564224 m^2
Answer: 1 acre = 4046.8564224 m^2
An acre, a unit of area commonly used in the Imperial and U.S. customary systems, is approximately 4047 square meters. This is calculable by using the known conversions between acres, square miles, and square meters.
Explanation:To determine the number of square meters in an acre, it's helpful to understand the relationship between these units. A square mile is equivalent to 640 acres. Therefore, the area of one acre is 1/640 of a square mile. However, these are both Imperial measurements, and we want to convert to a metric measurement - square meters.
To make this conversion, we need to identify the conversion factor between square miles and square meters. There are 2,589,988.11 square meters in a square mile.
Our starting point is that 1 acre = 1/640 square mile. Next, we substitute the number of square meters in a square mile:
1 acre = 1/640 x 2,589,988.11 square meters = 4046.86 square meters.
Therefore, there are approximately 4047 square meters in an acre.
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The price of an item has been reduced by 15% . The original price was $51 .
Answers
85 - (60/100)*85
= 85 - 0.6 *85
= 85 - 51
= $34
The question is about calculating the new price of an item after a discount. The original price of the item was $51.00, and it was reduced by 15%, making the new price $43.35.
Explanation:The subject of this question is Mathematics and it is looking for a solution to a percentage price reduction problem. The item had an original price of $51.00 and its price has been reduced by 15%. To find the new price after the discount, we have to calculate the amount of the reduction and subtract it from the original price.
First, let's calculate the amount of the discount: 15/100 * 51 = $7.65.}
Now, we subtract this amount from the original price: 51 - 7.65 = $43.35.
Therefore, the new price of the item after a 15% discount is $43.35.
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Evaluate the surface integral s f · ds for the given vector field f and the oriented surface s. in other words, find the flux of f across s. for closed surfaces, use the positive (outward) orientation. f(x, y, z) = x i + y j + 10 k s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2
Answers
[tex]\implies\nabla\cdot\mathbf f(x,y,z)=1+1+0=2[/tex]
By the divergence theorem, the surface integral along [tex]S[/tex] is equivalent to the triple integral over the region [tex]R[/tex] bounded by [tex]S[/tex]:
[tex]\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=2\iiint_R\mathrm dV[/tex]
Convert to cylindrical coordinates, setting
[tex]\begin{cases}x=r\cos\theta\\y=Y\\z=r\sin\theta\end{cases}\implies\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dY[/tex]
The triple integral is then equivalent to
[tex]=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{Y=0}^{Y=2-r\cos\theta}r\,\mathrm dY\,\mathrm dr\,\mathrm\theta[/tex]
[tex]=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r(2-r\cos\theta)\,\mathrm dr\,\mathrm\theta[/tex]
[tex]=\displaystyle\frac23\int_{\theta=0}^{\theta=2\pi}(3-\cos\theta)\,\mathrm dr\,\mathrm\theta[/tex]
[tex]=4\pi[/tex]
standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
Answers
Final Answer:
The standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15) is (x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1
Explanation:
To write the standard form of the equation of a hyperbola with the given vertices and a focus, we'll follow these steps:
1. Determine the center of the hyperbola.
2. Calculate the distance between the vertices and the center to find the length of the transverse axis (2a).
3. Calculate the distance between a focus and the center to find the focal distance (c).
4. Use the relationship c^2 = a^2 + b^2 to determine the length of the conjugate axis (2b).
5. Write the standard form equation based on the orientation of the hyperbola.
Step 1: Determine the center of the hyperbola.
The center of the hyperbola is the midpoint of the line segment joining the two vertices. Since the vertices are at (-10, -15) and (70, -15), the center (h, k) can be found as follows:
h = (-10 + 70) / 2 = 60 / 2 = 30
k = (-15 + (-15)) / 2 = -30 / 2 = -15
So, the center of the hyperbola is at (30, -15).
Step 2: Calculate the length of the transverse axis (2a).
The distance between the vertices is the length of the transverse axis. The vertices are 80 units apart because they are at (-10, -15) and (70, -15). This means:
2a = 80
a = 40
Therefore, the length of the semi-transverse axis a is 40 units.
Step 3: Calculate the focal distance (c).
The focal distance is the distance between the center and one of the foci. We were given one focus at (-11, -15). Since the center is at (30, -15), the focal distance c is:
c = |30 - (-11)| = |30 + 11| = 41
Step 4: Use the relationship c^2 = a^2 + b^2 to determine b.
We know that a = 40 and c = 41. Plugging these values into the relationship gives us:
41^2 = 40^2 + b^2
1681 = 1600 + b^2
b^2 = 1681 - 1600
b^2 = 81
b = 9
Therefore, the length of the semi-conjugate axis b is 9 units.
Step 5: Write the standard form equation.
Since the hyperbola is horizontal (the vertices have the same y-coordinate), the standard form of its equation is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
Plugging in the values for h, k, a, and b, we get:
(x - 30)^2 / 40^2 - (y + 15)^2 / 9^2 = 1
Simplify further by squaring the values of a and b:
(x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1
This is the standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
Select the correct inequality for the graph below: A solid line passing through points (1, 2) and (2, 5) has shading below. y < 3x − 1 y ≤ 3x − 1 y ≥ 3x − 1 y > 3x − 1
Answers
Here is your answer:
Solving the equation:
[tex] (5-2)\div(2-1)= 3 [/tex][tex] \frac{y - y1}{(x - x1) } [/tex][tex] y-5=3(x-2) [/tex][tex] y= 3x- 6+ 5 [/tex]" [tex] y= 3x-1 [/tex] " or option B.Hope this helps!
Step 1
Find the equation of the line that passes through points [tex](1, 2)[/tex] and [tex](2, 5)[/tex]
Find the slope of the line
The formula to calculate the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{5-2}{2-1}[/tex]
[tex]m=\frac{3}{1}[/tex]
[tex]m=3[/tex]
Find the equation of the line
The equation of the line into slope-point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3[/tex]
[tex](1, 2)[/tex]
substitutes
[tex]y-2=3(x-1)[/tex]
[tex]y=3x-3+2[/tex]
[tex]y=3x-1[/tex]
Step 2
Find the equation of the inequality
we know that
The solution is the shaded area below the solid line
therefore
the inequality is
[tex]y\leq 3x-1[/tex]
the answer is
[tex]y\leq 3x-1[/tex]
see the attached figure to better understand the problem
Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. How far will Jane walk?
Answers
Jane will walk 733.34 yards around the edge of the rectangular park after converting the width from feet to yards and calculating the perimeter.
Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. To determine how far Jane will walk, we need to calculate the perimeter of the rectangle. First, let's convert all measurements to the same unit. Since the length is given in yards and the width in feet, we can convert the width to yards (1 yard = 3 feet).
Width in yards: 200 feet \/ 3 feet per yard = 66.67 yards.
Now that both measurements are in yards, we can calculate the perimeter:
Perimeter = 2 ×(length + width) = 2 × (300 yards + 66.67 yards) = 2 ×366.67 yards = 733.34 yards.
Therefore, Jane will walk 733.34 yards around the edge of the park.
the longest runway at an airport has the shape of a rectangle with an area of 2181600sqft. this runway is 180 ft wide. how long is the runway
Answers
A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck is to be expanded by 6 feet, and the width by 2 feet. If the area of the new rectangular deck is 68 ft2 larger than the area of the original deck, find the dimensions of the original deck.
Answers
The area of the original deck is [tex]W*4W=4W^{2} [/tex]
The dimensions of the new deck are :
length = 4W+6
width=W+2
so the area of the new deck is :
[tex](4W+6)(W+2)= 4W^{2}+8W+6W+12= 4W^{2}+14W+12[/tex]
"the area of the new rectangular deck is 68 ft2 larger than the area of the original deck" means that we write the equation:
[tex]4W^{2}+14W+12=68+4W^{2}[/tex]
[tex]14W+12=68[/tex]
[tex]14W=68-12=56[/tex]
[tex]W= \frac{56}{14}= 4 [/tex]
the length is [tex]4W=4*4=16[/tex] ft
Answer: width: 4, length: 16
find the quotient of 0.34 and 0.2.
Answers
is the graph of y=sin(x^6) increasing or decreasing when x=12
Answers
y=sin(x^6)
is
y'=dy/dx=cos(x^6)*(6x^5)
Substitute x=12 (radians)
y'(12)=cos(12^6)*(6*12^5)
=1492992cos(2985984)
=1128592.5 >0
Therefore y(x) is increasing at x=12 (radians).
In the first 120 miles over 240 mile journey a truck driver maintained an average speed of 50 mph what was his average featuring the next 120 miles if the average speed of the entire trip with 60 mph
Answers
Next: determine the length of time required to drive the first 120 miles at 50 mph. It is (120 miles) / (50 mph), or 2.4 hours.
Next, find the length of time required to drive the second 120 miles. It is 4 hours less 2.4 hours, or 1.6 hours.
Lastly, find the average speed over which the second 120 miles were covered in 1.6 hours:
average speed (2nd 120 miles) = (120 miles) / (1.6 hours) = 75 mph.
What is greater: a half dozen dozen pair of shirts or a half of two dozen dozen shirts
Answers
A half dozen dozen pair of shirts is:
6 dozen pairs:
6 * 12 pairs
72 pairs
PAIRS.
So, for every 1 shirt in this group, there is another that goes with it. It must be multiplied by two.
72 * 2 = 144
There is a total of 144 shirts in this group.
Now, the second group...
Half of two dozen dozen shirts:
Half of two dozen = 12
12 dozen shirts.
12 * 12
144!
See? The amounts are exactly the same!
Sounds more like a riddle than math homework to me...
Hope I could help you out! If my math is incorrect, or I provided an answer you were not looking for, please let me know. However, if my math is explained well and correct, please consider marking my answer as Brainliest! :)
Have a good one.
God bless!
From the computation, a half of two dozen shirts will be greater.
A dozen = 12
It should be noted that a half dozen pair of shirts will be:
= 1/2 × 12
= 6 shirts
A half of two dozen shirts will be:
= 1/2 × (2 × 12)
= 12 shirts
Therefore, a half of two dozen shirts will be greater.
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If 5x=17, what is the value of 15x-11
Answers
5x=17
x=17/5 = 3.4
15x-11 =
15(3.4)-11 = 51-11 = 40
A package contains 3 cups of trail mix. A serving of trail mix is ⅓ cup. How many servings of trail mix is in the package?
Answers
3 * 3/1 =
9 <== the package contains 9 servings
The widrh of a rectangle is w yards and the length of a rectangle is (6w-4) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(6w-4). Simplify the algebraic expression 2w+2(6w-4) and determine the perimeter of a rectangle whose width w is 4 yards
Answers
p=2w+2(6w-4) can be simplified to:
p=2w+12w-8
p=14w-8
if w=4
p=14(4)-8
p=56-8 = 48 yards
check:
w = 4
length = 6w-4= 6(4)-4 = 24-4=20
perimeter = 4*2 + 20*2 = 8+40 = 48
it checks out, perimeter = 48 yards
A pizzeria owner wants to know which pizza topping is least liked by her customers so she can take it off the menu. She used four different methods to find this information.
Method 1: The owner asked every third customer to rate all the pizza toppings in order of preference.
Method 2: The owner gave all customers a toll-free telephone number and asked them to phone in their topping preferences.
Method 3: The owner asked the preferences of every other teenager who entered the pizzeria.
Method 4: The owner reviewed the pizzeria’s complaint cards and assessed all complaints related to pizza toppings.
Which method is most likely to give a valid generalization
Answers
The second method requires a lot on the initiatives of customers, and likely to have extreme cases only (liked very much or disliked very much).
The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas.
Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.
The valid method is the owner asked every third customer to rate all the pizza toppings in order of preference. The correct option is A.
What is feedback?information that is utilized as a foundation for improvement, such as data on how people react to a product or how well someone performs a task.
I suggest method 1 because it is unbiased and systematic. The second method requires a lot of the initiative of customers and is likely to have extreme cases only (liked very much or disliked very much).
The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas. Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.
Therefore, the valid method is for the owner to ask every third customer to rate all the pizza toppings in order of preference. The correct option is A.
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someone please help me to find the answer to this geography problem please explain
Answers
The M represents slope while the B represents the Y-intercept.
With that out of the way, take a look at your top equation, y = 3/2x + ?. If you noticed the question mark is in the spot of the B (Y-intercept), we can simply find this by finding where on the graph does the line intercept the Y-axis.
Triangle B shows the Y-intercept to be -7, this means that the hypotenuse intercepts the Y-axis at (0 , -7).
If we were to find the (what I like to call) the interception point of triangle A's hypotenuse and the Y-axis, we find our missing variable.
Just looking at the graph, we can count and visually determine that the Y-intercept of the hypotenuse is (0 , 1).
Therefore, we can say: The equation of A's hypotenuse is:
y = 3/2x + 1
Hope I could help you out!
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Derek and Mia place two green marbles and one yellow marble in a bag. Somebody picks a marble out of the bag without looking and records its color (G for green and Y for yellow). They replace the marble and then pick another marble. If the two marbles picked have the same color, Derek loses 1 point and Mia gains 1 point. If they are different colors, Mia loses 1 point and Derek gains 1 point. What is the expected value of the points for Derek and Mia?
Answers
Answer:
Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.
Step-by-step explanation:
Number of green marbles = 2 and Number of Yellow marbles = 1
Then, total number of marbles = 2+1 = 3
A person selects two marbles one after another after replacing them.
So, the probabilities of selecting different combinations of colors are,
[tex]1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}[/tex]
[tex]2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}[/tex]
[tex]3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}[/tex]
[tex]4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}[/tex]
Now, we have that,
If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.
If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.
Also, the expected value of a random variable X is [tex]E(X)=\sum_{i=1}^{n} x_i\times P(x_i)[/tex].Then, the expected value of points for Derek is,
[tex]E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}[/tex]
And the expected value of points for Mia is,
[tex]E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}[/tex].
Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.
Answer: P(GG)= 4/9
P(GY)= 2/9
P(YG)= 2/9
P(YY)= 1/9
Derek, E(X) = -1/9
Mia, E(X) = 1/9
Step-by-step explanation: just did it on edge
If 2^m = 4x and 2^w = 8x, what is m in terms of w?
Answers
The average winter snowfall in City A is 105 cm. City B usually gets 2.8 m of snow each winter. Compare the yearly snowfall in the two cities. Complete parts a and b. (A) the difference in one year is __ m. (B) the difference over two years is ___ cm
Answers
City A: 105 centimeters OR 1.05 meters
City B: 280 centimeters OR 2.8 meters
Now that we know the measurements, let's look at the first problem. (A) asks for the difference in one year in meters. The difference of course means subtraction. Now it's here where I personally am confused on what it asking for in terms of which city is it asking for us to subtract from, but using an educated guess, I'll say we're subtracting from city B because if we were to subtract from city A, we'd have a negative, and you can't have a negative amount of snow, only 0 snow.
So once again, for question (A), we subtract 1.05 from 2.8 (2.80 - 1.05) and we get 1.75 meters of snow.
Question (B) asks for the difference during two years in centimeters, so we multiply both measurements by 2 and use the centimeter measurements. (105 x 2 = 210) (280 x 2 = 560) Subtract 560 from 210 (560 - 210) and we get 350 centimeters.
So your answers are: (A) 1.75 meters (B) 350 centimeters
I hope this helps!
Definition 7.1.1 laplace transform let f be a function defined for t ≥ 0. then the integral {f(t)} = ∞ e−stf(t) dt 0 is said to be the laplace transform of f, provided that the integral converges. to find {f(t)}. f(t) = cos t, 0 ≤ t < π 0, t ≥ π
Answers
Given that
[tex]f(t)=\begin{cases}\cos t&\text{for }0\le t<\pi\\0&\text{for }t\ge\pi\end{cases}[/tex]
the Laplace transform of [tex]f(t)[/tex] is given by the definite integral
[tex]\displaystyle\int_{t=0}^{t\to\infty}f(t)e^{-st}\,\mathrm dt=\int_{t=0}^{t=\pi}\cos t\,e^{-st}\,\mathrm dt+\int_{t=\pi}^{t\to\infty}0\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^\pi\cos t\,e^{-st}\,\mathrm dt[/tex]
[tex]=\dfrac{(1-e^{-\pi s})s}{s^2+1}[/tex]
(which you can find by integrating by parts twice)
Show that the series is convergent. how many terms of the series do we need to add in order to find the sum to the indicated accuracy? sum_(n=1)^(infinity) (-1)^(n+1)/( n^7)text( ) \(|text(error)| < 0.00005 \)
Answers
[tex]|S-S_k|\le|a_{k+1}|[/tex]
We have
[tex]a_n=\dfrac1{n^7}[/tex]
so in order to have an error within 0.00005 of the sum's actual value, we need [tex]k[/tex] terms such that
[tex]\left|S-S_k\right|\le\left|\dfrac{(-1)^{k+2}}{(k+1)^7}\right|=\dfrac1{(k+1)^7}<0.00005[/tex]
[tex]\implies (k+1)^7<\dfrac1{0.00005}=20000[/tex]
[tex]\implies k+1<20000^{1/7}\approx4.1156[/tex]
[tex]\implies k<3.1156[/tex]
which suggests that we require [tex]k=4[/tex] terms at the least to approximate the series within the given accuracy.
The series is convergent, but the number of terms needed to find the sum to a specific accuracy cannot be determined.
Explanation:To determine the convergence of the series sum_(n=1)^(infinity) (-1)^(n+1)/( n^7), we can use the Alternating Series Test. The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In this case, the terms of the series alternate in sign and decrease as n increases, so the series is convergent.
To find the number of terms needed to achieve a sum with an error less than 0.00005, we need to use the Remainder Estimation Theorem. However, this theorem requires that the terms of the series decrease in absolute value, which is not the case in this series. Therefore, we cannot determine the number of terms needed to reach the desired accuracy.
Overall, the series is convergent, but we cannot determine the number of terms needed to reach a specific accuracy.
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What is the standard form of 8 hundreds + 2 hundreds
Answers
The standard form of 8 hundred + 2 hundred will be 1000.
What is the standard form of the number?A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.
Given that the number is 8 hundred + 2 hundred the standard form of the number will be:-
Standard form = 8 hundreds + 2 hundreds
Standard form = 800 + 200
Standard form = 1000
Therefore, the standard form of 8 hundred + 2 hundred will be 1000.
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The Center of the Circle is at the origin on a coordinate grid. The vertex of a Parabola that opens upward is at (0,9). If the Circle intersects the parabola at the parabola's vertex, which Statement must be true?
Answers
The parabola and the circle have the same axis of symmetry, and can intersect at one point only.
The statement that must be true is; The maximum number of solution is one
Reason:
The given parameters are;
Location of the center of the circle = The origin (0, 0)
Location of the vertex of the parabola opening upwards = (0, 9)
Point where the circle intersects the parabola = The vertex
Required:
The statement that must be true
Solution;
The equation of the circle is x² + y² = r²
The vertex (0, 9) is a point on the circle, therefore;
0² + 9² = r²
The radius, r = 9
The highest point on the circle is the point with the maximum vertical
distance from the center, which is the point (0, 9), which is also the lowest
point on the parabola.
Therefore, the parabola and the circle can intersect at only the point (0, 9),
which gives;
The maximum number of solution is one.
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Which of the following statements is true? A 6.75 < 6.759 < 6.751 < 6.85 B 5.55 < 5.559 < 5.65 < 5.69 C 4.11 < 4.12 < 4.17 < 4.15 D 7.42 < 7.41 < 7.40 < 7.39
Answers
The only sign used is "less than", so every consecutive number must be larger than the ones before it. Choice B is the only option that does not break this rule.
Find the area of a square with radius 17√2 in. Round to he nearest whole number. Please help me!!
Answers
The area of the square with radius 17√2 is 1156 square inches.
What is area?The area is the amount of space within the perimeter of a 2D shape
What is the formula for the area of square?The formula for the area of square is
[tex]A = \frac{1}{2} d^{2}[/tex]
Where, d is the length of the diagonal of the square.
According to the given question.
The radius of the square is [tex]17\sqrt{2}[/tex] in.
⇒ Diameter or the length of the square = 2 × 17 √2 = 34√2
Therefore,
The area of the square
= [tex]\frac{1}{2}( 34(\sqrt{2)} )^{2}[/tex]
= [tex]\frac{2312}{2}[/tex]
=[tex]1156\ in^{2}[/tex]
Hence, the area of the square with radius 17√2 is 1156 square inches.
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What is the area of parallelogram ABCD in square units
Answers
Use AB, BC, CD, DA to make the triangles.
The left-overs make up a rectangle that has the area of 2x3, which is 6.
Triangle AB and CD are equivalent, they are both (1/2)(1)(3)=1.5 each, which add up to 3.
Triangle AD and BC are equivalent, they are both (1/2)(1)(4)=2 each, which add up to 4.
So, just add up the 6 from the rectangle and the 3 & 4 and you get 13.
The area of that parallelogram is 13.
13 square units
Further explanationConsider attachment for details.
We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.
Let us take the following strategic steps:
Calculate the area of KLMN.Calculate the area of the triangles ABL, CDM, ADK, and BCN.Subtract the area of the KLMN rectangle with the area of all triangles.The difference in the area above is the area of the ABCD parallelogram.The Process:
The area of KLMN = 4 x 5 = [tex] \boxed{ \ 20 \ square \ units. \ }[/tex]The ADK triangle is congruent to the BCN triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 4 \times 1 = 2 \ square \ units. \ }[/tex] Thus the total area of ADK and BCN is [tex]\boxed{ \ 2 + 2 = 4 \ square \ units. \ }[/tex]The ABL triangle is congruent to the CDM triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 3 \times 1 = 1.5 \ square \ units \ }.[/tex] Thus, the combined area of ABL and CDM is [tex]\boxed{ \ 1.5 + 1.5 = 3 \ square \ units. \ }[/tex]Finally, the area of ABCD = 20 - 4 - 3 = 13.As a result, we get the area of the parallelogram ABCD is 13 square units.
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