De l'Hospital rule applies to undetermined forms like
[tex]\dfrac{0}{0},\quad\dfrac{\infty}{\infty}[/tex]
If we evaluate your limit directly, we have
[tex]\displaystyle \lim_{x\to 0}(1+2x)^{-\frac{3}{x}} = 1^\infty[/tex]
which is neither of the two forms covered by the theorem.
So, in order to apply it, we need to write the limit as follows: we start with
[tex]f(x)=(1+2x)^{-\frac{3}{x}}[/tex]
Using the identity [tex]e^{\log(x)}=x[/tex], we can rewrite the function as
[tex]f(x)=e^{\log\left((1+2x)^{-\frac{3}{x}}\right)}[/tex]
Using the rule [tex]\log(a^b)=b\log(a)[/tex], we have
[tex]f(x)=e^{-\frac{3}{x}\log(1+2x)}[/tex]
Since the exponential function [tex]e^x[/tex] is continuous, we have
[tex]\displaystyle \lim_{x\to 0} e^{f(x)} = e^{\lim_{x\to 0} f(x)}[/tex]
In other words, we can focus on the exponent alone to solve the limit. So, we're focusing on
[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) [/tex]
Which we can rewrite as
[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) = -3\lim_{x\to 0}\frac{\log(1+2x)}{x}[/tex]
Now the limit comes in the form 0/0, so we can apply the theorem: we derive both numerator and denominator to get
[tex]\displaystyle -3\lim_{x\to 0}\frac{\log(1+2x)}{x} = -3 \lim_{x\to 0}\dfrac{\frac{2}{1+2x}}{1} = -3\cdot 2 = -6[/tex]
So, the limit of the exponent is -6, which implies that the whole expression tends to
[tex]e^{-6}=\dfrac{1}{e^6}[/tex]
By applying L'Hospital's rule to the given expression, the limit is found to be 1 as x approaches 0.
L'Hospital's rule can be applied to find the limit of the expression (1+2x)^(-3/x) as x approaches 0. This rule states that if we have an indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.
Take the derivative of the numerator: -3(1+2x)^(-3/x-1) * (2).Take the derivative of the denominator: -3/x^2 * (1+2x)^(-3/x).Now evaluate the limit by substituting x = 0 into the derivatives obtained.After simplifying the expressions and substituting x = 0, we find that the limit is equal to 1.
which is equivalent to "12 chars for every 3 tables"?
Is it 12 chairs per three tables? I might be wrong..
Answer: 12 chairs per 3 tables
Step-by-step explanation:
A crane lifts 50 Newtons 2 meters. How much work is done?
50 Nm
100 Nm
200 ft-lbs
2 Nm
Answer:
Step-by-step explanation:
2 meter is like 6.4 yards
so i would say B is the answer
Final answer:
The work done by the crane in lifting 50 Newtons over a distance of 2 meters is 100 Nm.
Explanation:
The work done by a crane can be calculated by multiplying the force applied by the distance over which the force is applied. In this case, the crane is lifting 50 Newtons over a distance of 2 meters. Therefore, the work done is:
Work = Force x Distance
Work = 50 N x 2 m = 100 Nm
So, the correct answer is 100 Nm.
which fraction is closer to 1/2 than to 0 or 1
A fraction is closer to 1/2 than to 0 or 1 if its numerator is more than half of 0 and less than half of the denominator. For instance, 3/5 is closer to 1/2 than to 0 or 1 because its numerator is more than half of 0 and less than half of 5.
Explanation:To determine which fraction is closer to 1/2 than to 0 or 1, consider the numerical value of the fractions in relation to 1/2. As a rule of thumb, if a fraction has a numerator that is half the denominator, it equals 1/2. When the numerator is less than half the denominator, the value is less than 1/2; when the numerator is over half the denominator, the value is greater than 1/2.
For example, if we take 1/3, it is clear that this value is less than 1/2 because the numerator, 1, is less than half of the denominator, 3. Comparatively, the fraction 2/3 is closer to 1 than to 1/2 since the numerator, 2, is greater than half of the denominator, 3.
Another example would be comparing 3/5 and 4/5 to 1/2. The fraction 3/5 has a numerator that is more than half of the denominator, making it closer to 1/2 than to 0 or 1, while 4/5 is closer to 1. Therefore, 3/5 is the fraction that is closer to 1/2 than to 0 or 1.
A fraction closer to 1/2 than to 0 or 1 falls in the range (> 1/3 but < 2/3); 5/8 is an example of such a fraction. An intuitive understanding and the use of a common denominator can aid in identifying and comparing these fractions.
Explanation:Determining which fraction is closer to 1/2 than to 0 or 1 involves understanding the number line and how fractions fall on it.
To identify such a fraction, it should be evident that any fraction greater than 1/2 will naturally be closer to 1, while any fraction less than 1/2 is closer to 0.
Therefore, we look for a fraction in the range (> 1/3 but < 2/3) to ensure it is closer to 1/2.
By using the intuitive sense of fractions, which is like having an understanding of fractions through visualization or practical examples, we can gauge the closeness to 1/2.
For instance, we know that 1/3 is less than 1/2, and similarly, 2/3 is more than 1/2.
Following this line of reasoning, the addition of fractions (1/3 + 1/6 = 1/2) indicates that 1/6 is the gap needed to reach from 1/3 to 1/2.
A fraction such as 5/8 would be a good example of a fraction closer to 1/2.
This fraction is more than 1/2 (4/8) but less than 3/4 (6/8), placing it comfortably closer to 1/2 on the number line.
Employing the common denominator strategy also helps to compare fractions effectively, by aligning them to a unifying reference point.
Please help me with this. Thank you!
Answer:
First choice listed
Step-by-step explanation:
Pick 2 points from the table and find the slope between them. I chose (30,12) and (20,8). Apply the slope formula to find the cost per CD:
[tex]\frac{Cost}{CD}= \frac{30-20}{12-8}=\frac{5}{2}[/tex]
The function then is C = 5/2d. or C = 2.5d, first choice
C = 2.5d. Plugging in for d and C we get the same solution on each side
Evaluate the surface integraliintegral.gifSF � dSfor 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) = xy i + yz j + zx kS is the part of the paraboloidz = 2 ? x2 ? y2 that lies above the square 0 ? x ? 1, 0 ? y ? 1,and has upward orientation
Looks like the paraboloid has equation
[tex]z=2-x^2-y^2[/tex]
and [tex]S[/tex] is the part of this surface with [tex]0\le x\le1[/tex] and [tex]0\le y\le1[/tex]. Parameterize [tex]S[/tex] by
[tex]\vec s(u,v)=u\,\vec\imath+v\,\vec\jmath+(2-u^2-v^2)\,\vec k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Take the normal vector to [tex]S[/tex] to be
[tex]\vec s_u\times\vec s_v=2u\,\vec\imath+2v\,\vec\jmath+\vec k[/tex]
Then the flux of [tex]\vec F[/tex] across [tex]S[/tex] is
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S[/tex]
[tex]\displaystyle=\int_0^1\int_0^1(uv\,\vec\imath+v(2-u^2-v^2)\,\vec\jmath+u(2-u^2-v^2)\,\vec k)\cdot(2u\,\vec\imath+2v\,\vec\jmath+\vec k)\,\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle=\int_0^1\int_0^1(2u^2v+(2v+1)u(2-u^2-v^2))\,\mathrm du\,\mathrm dv=\boxed{\frac{293}{180}}[/tex]
math question, help. I got two different answers for this and I don’t know which one is correct. please include steps
Answer:
16/(3(x+1))
Step-by-step explanation:
We can factor the denominator of the second term, which lets us see how to combine terms:
[tex]\displaystyle\frac{7}{x+1}-\frac{5}{3x+3}=\frac{7}{x+1}-\frac{5}{3(x+1)}\\\\=\frac{3\cdot 7}{3(x+1)}-\frac{5}{3x+3}=\frac{21-5}{3(x+1)}=\frac{16}{3(x+1)}[/tex]
Taylor took 6 hours to drive home from college for Thanksgiving break, a total distance of 290 miles. She was able to average 50 miles per hour for part of the trip but had to slow down to 45 miles per hour for the rest of the time due to poor weather. How many hours did she drive each speed.
PLEASE SHOW WORK/HOW TO SOLVE IT :)
Answer:
50 mph: 4 h45 mph: 2 hStep-by-step explanation:
Let t represent the time driving at 50 mi/h. Then her total distance driven (in miles) is ...
distance = speed · time
290 = 50t + 45(6-t)
20 = 5t . . . . . . . . . . . subtract 270, collect terms
4 = t . . . . . . divide by the coefficient of t
Taylor drove 4 hours at 50 miles per hour, then 2 hours at 45 miles per hour.
The vertices of a triangle are A(−6, −3), B(0, 3), and C(−6, 0). Draw its image after a dilation with respect to the origin using a scale factor of 1/3. All I need to know is the points of the new triangle.
Thanks!
Answer:
A'(-2, -1), B'(0, 1), C'(-2, 0)
Step-by-step explanation:
When dilation is about the origin, the scale factor multiplies each individual coordinate.
A' = (1/3)A = (-6/3, -3/3) = (-2, -1) . . . . for example
The rest is mental arithmetic, since all given coordinate values are divisible by 3.
surface area is measured in cubic units or units3? true or false
Answer:
FALSE
Step-by-step explanation:
Area is a two-dimensional measure, so is measured in linear units that have a power of 2 (not 3).
_____
Please note that the exponent applies to linear units, such as meters or inches. Area can also be measured in area units with no exponent, such as barns or acres. (A "barn" is equal to 10^-28 m^2. It is used in nuclear physics to measure cross sectional areas of atomic particles. I think of it as one of the jokes built into modern physics, having its origins in the saying "can't hit the broad side of a barn.")
Final answer:
The statement that surface area is measured in cubic units is false. Surface area is measured in square units, whereas cubic units are used for volume. For example, the surface area of a cube is calculated as 6 times the area of one face, whereas volume is the cube of the side length.
Explanation:
The statement that surface area is measured in cubic units or units³ is false. Surface area is actually measured in square units (units²), not cubic units. Cubic units are used to measure volume, not surface area.
For example, the surface area of a cube that has a side length of 4 units would be 6(4x4) = 96 units², because a cube has 6 sides and each side would be a square with an area of 4x4.
On the other hand, the volume of the same cube would be 43 = 64 units³, because volume is calculated by multiplying length by width by height.
For example, if you take a large cube with a side length of 3 units, its total surface area would be 3 x 3 x 6 = 54 units² and the volume would be 33 = 27 units³.
However, if this cube is replaced with 27 small cubes, each with a side length of 1 unit, the combined surface area becomes much larger at 162 units², while the total volume remains the same at 27 units³.
can someone please help me with this problem
Answer:
294.5 sq meters
Step-by-step explanation:
I found the area of the circle, subtracted away the area of the sector, then had to add back in the area of the triangle. The areas for each is as follows:
[tex]A_{c}=\pi (11.1)^2[/tex]
A = 387.0756 sq m
[tex]A_{s}=\frac{130}{360}*\pi (11.1)^2[/tex]
A = 139.7773
[tex]A_{t}=\frac{1}{2}(11.1)(11.1)sin(130)[/tex]
A = 47.1922
Now taking the area of the circle - area of sector + area of triangle:
387.0756 - 139.7773 + 47.1922 = 294.5 sq m
Answer:
294.5
Step-by-step explanation:
Starting from the entrance of her school, Alyssa walked 400 feet due north, then 300 feet due east, and ended up at the entrance of a running track. Miki walked directly from the entrance of the school to the entrance of the running track. How many more feet did Alyssa walk than Miki?
Answer:
Alyssa walked 200 ft more than Miki.
Step-by-step explanation:
According to the Pythagorean theorem formula if we square the a(400) and b(300) and add them both we would get 250,000. From then you square root it to 500. So Miki walked 500ft and Alyssa walked 700ft (400+300). Subtract 500 from 700 and you would get 200ft.
Consider the given quadratic equations. Equation A Equation B Equation C Equation D y = 3x2 − 6x + 21 y = 3x2 − 6x + 18 y = 3(x − 1)2 + 18 y = 3(x − 1)2 + 21 Complete the following statement. Equations are equivalent, and of those, equation is in the form most useful for identifying the extreme value of the function it defines.
Answer:
Equations A and C are equivalent, and of those, equation C is in the form most useful ...
Step-by-step explanation:
In standard form, the equations are ...
Equation A: y = 3x² -6x +21
Equation B: y = 3x² -6x +18
Equation C: y = 3x² -6x +21 . . . . equivalent to A
Equation D: y = 3x² -6x +24
__
Equation C is in vertex form, so the vertex (extreme value) can be read directly from the equation. It is (x, y) = (1, 18).
Equations A and C are equivalent; equation C is most useful for finding the vertex.
Answer with explanation:
→→Two equations or two polynomials are said to be equivalent, if written in distinct ways, and real value of variables is substituted in both equivalent and Original Polynomial, the numerical value of both the polynomials are Same.
→→The four Quadratic Polynomials are:
[tex]1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\2.\text{Equation} B: y = 3x^2 - 6 x + 18\\\\3.\text{Equation} C: y = 3(x-1)^2 +18=3(x^2-2 x +1)+18\\\\y=3x^2 - 6 x +18+3\\\\y=3x^2 - 6 x +21\\\\3.\text{Equation} C: y = 3(x-1)^2 +21[/tex]
→→If you will look at Equation A and Equation C, both the equation are Quadratic, Coefficient of x², Coefficient of x, as well as , constant term is same in both the equation.So, Equation A, and Equation C, are equivalent.
→→If you will look at the function,
[tex]y=3\times (x-1)^2+18\\\\y-18=3\times(x-1)^2[/tex]
at, x=1, y=18, which is extreme value of the function, as at vertex of the parabola , Parabola attains it's Maximum value.
⇒⇒Equations A and C,
[[tex]1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\3.\text{Equation} C: y = 3(x-1)^2 +18[/tex]]
are equivalent, and of those, equation is in the form most useful for identifying the extreme value is [tex]3.\text{Equation} C: y = 3(x-1)^2 +18[/tex]] function it defines.
Which is the correct answer a,b,c, or d. Need to now ASAP!
Answer:
I think C
Step-by-step explanation:
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation
4.5x+3y=2:
A(...,1/3)
B(2/3,...)
Answer:
A(2/9, 1/3)
B(2/3, -1/3)
slope = -1.5
Step-by-step explanation:
A graph can show the coordinates of interest: A(2/9, 1/3); B(2/3, -1/3).
Rearranging the equation to slope-intercept form, we have ...
3y = -4.5x +2
y = -1.5x +2/3
The slope is -1.5.
Final answer:
After solving for the missing coordinates, point A is (2/9, 1/3), and point B is (2/3, -1/3). Calculating the slope using these two points gives us a slope (m) of -3/2 for the line.
Explanation:
To find the missing coordinates for point A, we plug y=1/3 into the equation 4.5x+3y=2 and solve for x. Here is how:
4.5x + 3(1/3) = 2
4.5x + 1 = 2
4.5x = 1
x = 1 / 4.5
x = 2/9
Therefore, A(2/9, 1/3)
To find the missing coordinate for point B, we plug x=2/3 into the equation 4.5x+3y=2 and solve for y. Here is how:
4.5(2/3) + 3y = 2
3 + 3y = 2
3y = -1
y = -1/3
Therefore, B(2/3, -1/3)
To find the slope of the line, we use the two points A(2/9, 1/3) and B(2/3, -1/3). The slope formula is (y2 - y1) / (x2 - x1), which gives:
m = (-1/3 - 1/3) / (2/3 - 2/9)
m = (-2/3) / (4/9)
m = (-2/3) * (9/4)
m = -3/2, which is the slope of the line.
What is the area of the base of the cone below? Round the answer to the nearest tenth if necessary.
Answer:
19.5
Step-by-step explanation:
Answer:
Area of the base is 19.5 unit square.
Step-by-step explanation:
The volume of the cone is given as = 52 cubic inches
Height or h = 8 inches
Volume of the cone is given as : [tex]\pi r^{2} \frac{h}{3}[/tex]
[tex]52=3.14\times r^{2} \times\frac{8}{3}[/tex]
[tex]52= r^{2} \times 8.37[/tex]
[tex]r^{2} =6.212[/tex]
r = 2.492 inches
Now, area of the base is given as [tex]\pi r^{2}[/tex] because it is a circle.
Area = [tex]3.14\times2.492\times2.492[/tex]
= 19.499 ≈ 19.5 unit square.
Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class. Kendra wanted to know if it is plausible that 50% of the entire population of gym members had taken a yoga class. Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class. The dot plot shows the results of the simulations. What is the best conclusion for Kendra to make based on the data?
A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
B. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is likely.
C. It is plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
D. It is plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is likely.
Answer: A, it is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
Answer:
Option A is correct.
Step-by-step explanation:
Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class.
Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class.
The best conclusion based on the plot is - A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
The ratio of the radio of sphere A and sphere B is Ra\Rb =2/5. The volume of sphere b is 64 pied cu ft. What is the volume of sphere A
The volume of a sphere with radius [tex]r[/tex] is [tex]V=\dfrac43\pi r^3[/tex]. Sphere B has a volume of [tex]64\pi[/tex], so
[tex]V_B=\dfrac43\pi{r_B}^3\implies r_B=\sqrt[3]{\dfrac{64\pi}{\frac43\pi}}=\sqrt[3]{48}[/tex]
Now,
[tex]\dfrac{r_A}{r_B}=\dfrac25\implies r_A=\dfrac{2r_B}5[/tex]
so sphere A has volume
[tex]V_A=\dfrac43\pi\left(\dfrac{2r_B}5\right)^3=\dfrac{512}{125}\pi[/tex]
whast is the value of -3/4-(-3/8)?
Answer:
- 3/8
Step-by-step explanation:
- 3/4 - (-3/8)
= -3/4 + 3/8
= -6/8 + 3/8
= - 3/8
Yannick and Jean are playing a guessing game with integers. Yannick wrote these clues to help Jean guess the unknown integer. n+6 greater than or equal to 15 and n+5<15 What is the value of the unknown integer, n?
Answer:
9
Step-by-step explanation:
The solution to ...
n +6 ≥ 15
is found by subtracting 6:
n ≥ 9
__
The solution to ...
n +5 < 15
is found by subtracting 5:
n < 10
__
The only integer that is at least 9 and less than 10 is 9.
The value of the unknown integer, n, is 9.
A traffic light near a museum is green for 30 seconds, yellow for 5 seconds, and red for 15 seconds. If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is .
Answer:
about 0.254
Step-by-step explanation:
The light is red for 0.3 of the period, so that is the probability one car is stopped. Probability 3 cars are stopped and 5 are not is 0.3^3·0.7^5, about 0.004538. In the group of 8 cars, there are 56 different ways 3 of the cars can be stopped, so your overall probability could be 56·0.004538 ≈ 0.254.
_____
Comment on the question
Many factors go into a driver's decision to stop at a light. Many factors go into the distribution of arrival times at a light. Here, the problem is only tractable if we assume that cars arrive at the light individually and at random times with respect to the light's fixed 50-second cycle. (This is possibly the case only early in the morning hours when traffic is at its lightest (not associated with bar closings or night shift changes).)
What is the solution to the inequality below? 12x > 6(x - 2)
Answer:
x > -2
Step-by-step explanation:
12x > 6 (x - 2)
12x > 6x - 12
6x > - 12
x > - 2
I need help from question 11- 16! Please help!
Answer: D) 0, one real solution
A quadratic function is given of the form:
[tex]ax^2+bx+c=[/tex]
We can find the roots of this equation using the quadratic formula:
[tex]x_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Where [tex]\Delta=b^2-4ac[/tex] is named the discriminant. This gives us information about the roots without computing them. So, arranging our equation we have:
[tex]4a^2-4a-6=-7 \\ \\ Adding \ 7 \ to \ both \ sides \ of \ the \ equation: \\ \\ 4a^2-4a-6+7=-7+7 \\ \\ 4a^2-4a+1=0 \\ \\ Then \ the \ discriminant: \\ \\ \Delta=(-4)^2-4(4)(1) \\ \\ \Delta=16-16 \\ \\ \boxed{Delta=0}[/tex]
Since the discriminant equals zero, then we just have one real solution.
12. Find discriminant.Answer: D) -220, no real solution
In this exercise, we have the following equation:
[tex]-r^2-2r+14=-8r^2+6[/tex]
So we need to arrange this equation in the form:
[tex]ax^2+bx+c=[/tex]
Thus:
[tex]-r^2-2r+14=-8r^2+6 \\ \\ Adding \ 8r^2 \ to \ both \ sides \ of \ the \ equation: \\ \\ -r^2-2r+14+8r^2=-8r^2+6+8r^2 \\ \\ Associative \ Property: \\ \\ (-r^2+8r^2)-2r+14=(-8r^2+8r^2)+6 \\ \\ 7r^2-2r+14=6 \\ \\ Subtracting \ 6 \ from \ both \ sides: \\ \\ 7r^2-2r+14-6=6-6 \\ \\ 7r^2-2r+8=0[/tex]
So the discriminant is:
[tex]\Delta=(-2)^2-4(7)(8) \\ \\ \Delta=4-224 \\ \\ \boxed{\Delta=-220}[/tex]
Since the discriminant is less than one, then there is no any real solution
13. Value that completes the squaresAnswer: C) 144
What we need to find is the value of [tex]c[/tex] such that:
[tex]x^2+24x+c=0[/tex]
is a perfect square trinomial, that are given of the form:
[tex]a^2x^2\pm 2axb+b^2[/tex]
and can be expressed in squared-binomial form as:
[tex](ax\pm b)^2[/tex]
So we can write our quadratic equation as follows:
[tex]x^2+2(12)x+c \\ \\ So: \\ \\ a=1 \\ \\ b=12 \\ \\ c=b^2 \therefore c=12^2 \therefore \boxed{c=144}[/tex]
Finally, the value of [tex]c[/tex] that completes the square is 144 because:
[tex]x^2+24x+144=(x+12)^2[/tex]
14. Value that completes the square.Answer: C) [tex]\frac{121}{4}[/tex]
What we need to find is the value of [tex]c[/tex] such that:
[tex]z^2+11z+c=0[/tex]
So we can write our quadratic equation as follows:
[tex]z^2+2\frac{11}{2}z+c \\ \\ So: \\ \\ a=1 \\ \\ b=\frac{11}{2} \\ \\ c=b^2 \therefore c=\left(\frac{11}{2}\left)^2 \therefore \boxed{c=\frac{121}{4}}[/tex]
Finally, the value of [tex]c[/tex] that completes the square is [tex]\frac{121}{4}[/tex] because:
[tex]z^2+11z+\frac{121}{4}=(x+\frac{11}{2})^2[/tex]
15. Rectangle.In this problem, we need to find the length and width of a rectangle. We are given the area of the rectangle, which is 45 square inches. We know that the formula of the area of a rectangle is:
[tex]A=L\times W[/tex]
From the statement we know that the length of the rectangle is is one inch less than twice the width, this can be written as:
[tex]L=2W-1[/tex]
So we can introduce this into the equation of the area, hence:
[tex]A=L\times W \\ \\ \\ Where: \\ \\ W:Width \\ \\ L:Length[/tex]
[tex]A=(2W-1)(W) \\ \\ But \ A=45: \\ \\ 45=(2W-1)(W) \\ \\ Distributive \ Property:\\ \\ 45=2W^2-W \\ \\ 2W^2-W-45=0 \\ \\ Quadratic \ Formula: \\ \\ x_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{1}=\frac{-(-1)+ \sqrt{(-1)^2-4(2)(-45)}}{2(2)} \\ \\ W_{1}=\frac{1+ \sqrt{1+360}}{4} \therefore W_{1}=5 \\ \\ W_{2}=\frac{-(-1)- \sqrt{(-1)^2-4(2)(-45)}}{2(2)} \\ \\ W_{2}=\frac{1- \sqrt{1+360}}{4} \therefore W_{2}=-\frac{9}{2}[/tex]
The only valid option is [tex]W_{1}[/tex] because is greater than zero. Recall that we can't have a negative value of the width. For the length we have:
[tex]L=2(5)-1 \\ \\ L=9[/tex]
Finally:
[tex]The \ length \ is \ 9 \ inches \\ \\ The \ width \ is \ 5 \ inches[/tex]
16. SatelliteThe distance in miles between mars and a satellite is given by the equation:
[tex]d=-9t^2+776[/tex]
where [tex]t[/tex] is the number of hours it has fallen. So we need to find when the satellite will be 452 miles away from mars, that is, [tex]d=452[/tex]:
[tex]d=-9t^2+776 \\ \\ 452=-9t^2+776 \\ \\ 9t^2=776-452 \\ \\ 9t^2=324 \\ \\ t^2=\frac{324}{9} \\ \\ t^2=36 \\ \\ t=\sqrt{36} \\ \\ \boxed{t=6h}[/tex]
Finally, the satellite will be 452 miles away from mars in 6 hours.
I really need help. Thanks in advance
Answer:
D
Step-by-step explanation:
9.6 is a floating-point number, therefore, not a integer.
Answer:
d
Step-by-step explanation:
What is 144 in exponential form? A) 212 B) 27 C) 43 D) 122
Answer:
D
12²
Step-by-step explanation:
Given in the question, an integer = 144
To find the exponential form 144 we will do factorisation
The prime factorisation of 144 is
2 × 2 × 2 × 2 × 3 × 3
So the exponential form is 2[tex]^{4}[/tex] × 3²
The other way is
√144 = 12
which means
12² = 144
Answer: 12^2=144
Step-by-step explanation:
Which means (12)(12)=144
Which figures demonstrate a single reflection?
Select each correct answer.
Answer:
Please see the attached image below, to find more information about the graph
The figures that are obtained by a single reflection are shown in the image inside a red rectangle.
The axis of reflection is shown with a black line.
- The figure from the left shows horizontal reflection
- The figure from the right shows vertical reflection
simply
[tex]\sqrt[4 ]{162 {b}^{8} } [/tex]
Answer:
see below
Step-by-step explanation:
[tex]\sqrt[4]{162b^8}=\sqrt[4]{2\cdot 3^4b^8}=\sqrt[4]{2(3b^2)^4}\\\\=3b^2\sqrt[4]{2}[/tex]
number 7 and 8 and explain pls
Answer:
7. x=8
8. x=7
Step-by-step explanation:
7. The segment marked 30 is bisected by the segment marked x. So, you have a right triangle with legs x and 15 and hypotenuse 17. The Pythagorean theorem applies:
x^2 + 15^2 = 17^2
x^2 = 289 -225 = 64
x = √64 = 8
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8. The arc subtended by the chord x is 360° -230° -65° = 65°. Since this is the same measure as the arc subtended by the chord of length 7, x will also be of length 7.
___
In fact, this geometry is impossible. The combination of circle radius, arc measure, and chord length cannot be obtained all in the same circle. The answer you get will depend on how you work the problem.
!PLEASE HELP! WILL GIVE BRAINLIEST!!
A projectile launched straight up into the air with an initial velocity of 20 meters per second from a height of 10 meters. How long will it take for the projectile to hit the ground?
please solve and show your work!!
Can someone please just make some equations for me? I would be so grateful. Look at the graph.
3) For Zach, if his heart beats 15 times in 10 seconds, his heart beats 1.5 times in 1 second. Multiply this by 25 to get the number of times his heart will beat in 25 seconds → 1.5 * 25 = 27.5 times per 25 seconds. 1.5 * 60 = 90 times per minute. 1.5 * 120 = 180 times per two minutes. Do the same for your heart beats. 14 beats per 10 seconds is 1.4 beats per second. 1.4 * 25 = 35 times per 25 seconds. 1.4 * 60 = 84 times a minute. 1.4 * 120 = 168 times per two minutes.
4) Zach's equation would be H = 1.5n and yours would be H = 1.4n
5) Your heat beats just a little bit slower than Zachs. Everyone is different and there are many different things that can affect heart rate. Maybe he walked a little more than you did or maybe he was stressing about something which made his heart beat a little faster.
I hope this helps you!
WRITE THE EQUATION OF THE PARABOLA with a directrix of y=1 and a focus of (0,-1).
Answer:
-4y = x², or y = - x²/4, or y = -(1/4)x²
Step-by-step explanation:
Because the focus is beneath the directrix, this vertical parabola opens down. The general formula is 4py = x².
Because the distance between focus and directrix is 2 units, p = -1 here. The negative sign shows that the parabola opens down.
4py = x² becomes 4(-1)y = x², or -4y = x², or y = - x²/4