Answer:
8cm and 9cm
Step-by-step explanation:
because for the triangle to work you need the other two other sides when added together needs to be greater then 13
Please help me with solving these. I’d really appreciate your help. Thank you very much.
Answer:
Problem 17)
[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]
Problem 18)
[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]
Step-by-step explanation:
Problem 17)
We have the curve represented by the equation:
[tex]\displaystyle 4x^2+2xy+y^2=7[/tex]
And we want to find the equation of the tangent line to the point (1, 1).
First, let's find the derivative dy/dx. Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[4x^2+2xy+y^2\right]=\frac{d}{dx}[7][/tex]
Simplify. Recall that the derivative of a constant is zero.
[tex]\displaystyle \frac{d}{dx}[4x^2]+\frac{d}{dx}[2xy]+\frac{d}{dx}[y^2]=0[/tex]
Differentiate. We can differentiate the first term normally. The second term will require the product rule. Hence:
[tex]\displaystyle 8x+\left(2y+2x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0[/tex]
Rewrite:
[tex]\displaystyle \frac{dy}{dx}\left(2x+2y\right)=-8x-2y[/tex]
Therefore:
[tex]\displaystyle \frac{dy}{dx}=\frac{-8x-2y}{2x+2y}=-\frac{4x+y}{x+y}[/tex]
So, the slope of the tangent line at the point (1, 1) is:
[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=-\frac{4(1)+(1)}{(1)+(1)}=-\frac{5}{2}[/tex]
And since we know that it passes through the point (1, 1), by the point-slope form:
[tex]\displaystyle y-1=-\frac{5}{2}(x-1)[/tex]
If desired, we can simplify this into slope-intercept form. Therefore, our equation is:
[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]
Problem 18)
We have the equation:
[tex]\displaystyle y=\tan^{-1}\left(x^3\right)[/tex]
And we want to find the equation of the tangent line to the graph at the point (1, π/4).
Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\tan^{-1}(x^3)][/tex]
We can use the chain rule:
[tex]\displaystyle \frac{d}{dx}[u(v(x))]=u'(v(x))\cdot v(x)[/tex]
Let u(x) = tan⁻¹(x) and let v(x) = x³. Thus:
(Recall that d/dx [arctan(x)] = 1 / (1 + x²).)
[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2[/tex]
Substitute and simplify. Hence:
[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2=\frac{3x^2}{1+x^6}[/tex]
Then the slope of the tangent line at the point (1, π/4) is:
[tex]\displaystyle \frac{dy}{dx}\Big|_{x=1}=\frac{3(1)^2}{1+(1)^6}=\frac{3}{2}[/tex]
Then by the point-slope form:
[tex]\displaystyle y-\frac{\pi}{4}=\frac{3}{2}(x-1)[/tex]
Or in slope-intercept form:
[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]
Situation:
You invest $4,000 in an account that
pays an interest rate of 5.5%,
compounded continuously.
Calculate the balance of your account after 15
years. Round your answer to the nearest
hundredth.
Answer:
[tex]{ \bf{A=(P + \frac{r}{100} ) {}^{n} }} \\ { \tt{ = (4000 + \frac{5.5}{100} ) {}^{15} }} \\ \\ { \tt{ = \: 1.074 \times {10}^{54} \: dollars}}[/tex]
Can any one you help me with this ?
NUE is 30° LUN is 60° EUS is 30° LUE is 90° LUS is 120°
Step-by-step explanation:
NUE is given
LUN was from the 90° angle LUE but just minus 30°
EUS is honestly a guess :/
LUE is obviously 90° as we used it earlier
LUS was the 90° plus the EUS
If a translation of T.3. - 8(x, y) is applied to square
ABCD, what is the y-coordinate of B'?
4
3
0-12
A
В
-8
-E
5
2
3
4
0
D
C
Answer:
Its C. -6
Step-by-step explanation:
The coordinates of point B after translation are (-2, -6).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation T(-3, -8) follows the rule:
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
(x, y)--->(x-3, y-8)
From the diagram you can see that point B has coordinates (1,2).
(1, 2)--->(1-3, 2-8)
(1, 2)--->(-2, -6)
According to the previous rule this point will transform in point B' with coordinates (-2,-6),
Hence, the coordinates of point B after translation are (-2, -6).
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
If the bearing of A from B is 125.Find the bearing of B from A
Answer:
305°
Step-by-step explanation:
The bearing in the reverse direction is 180° plus the bearing in the forward direction, that is
bearing of B from A = 180° + 125° = 305°
A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a negative constant. The mean life M of an atom in the substance is
[infinity]
M = âk â« te^kt dt.
0
For the radioactive carbon isotope, 14C, used in radiocarbon dating, the value of k is -0.000121. Find the mean life of a 14C atom.
Answer:
mean life = 8264.5 s
Step-by-step explanation:
k = - 0.000121
The relation is given by
[tex]m = mo e^{kt}[/tex]
Now, the mean life is the life time for which the sample retains.
The mean life is the reciprocal of the decay constant.
The relation between the mean life and the decay constant is
[tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]
need help asap!! (geometry)
Answer:
A. reflection.
Step-by-step explanation:
If you were to use the reflection rule, then your answer will be:
B' (Now D): (1 , 2)
A' (Now E): (4 , 2)
C' (Now F): (3 , 5)
In this case, the reflected triangle does not match the given points, therefore it cannot be reflection.
~
What is the mean of this data? 7,5,5,3,2,2
Answer:
4
Step-by-step explanation:
The mean is the average of a data set. It can be found by adding up all of the values in a data set and then dividing it by the number of values in the data set.
The values in this data set;
[tex]7,5,5,3,2,2[/tex]
The number of values in this data set,
[tex]6[/tex]
Find the mean;
[tex]\frac{sum\ of\ vlaues}{number\ of\ values}[/tex]
[tex]=\frac{7+5+5+3+2+2}{6}\\\\=\frac{24}{6}\\\\=4[/tex]
A basketball team is to play two games in a tournament. The probability of winning the first game is .10.1 the first game is won, the probability of winning the second game is 15. If the first game is lost, the probability of winning the second game is 25. What is the probability the first game was won if the second game is lost? Express the answer with FOUR decimal points.
Answer:
[tex]P(\frac{A}{B'})[/tex]=0.111
Step-by-step explanation:
Given:
The probability of winning the first game is 10.1
The first game is won
The probability of winning the second game is 15
If the first is lost, the probability of winning the second game is 25
Solution:
[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]
Answer:
[tex]P(W_1/W_2')=0.1110[/tex]
Step-by-step explanation:
Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]
Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:
[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]
[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]
[tex]P(W_2)=0.24[/tex]
Hence the probability of losing the second game:
[tex]P(W_2')=1-P(W_2)[/tex]
[tex]P(W_2')=0.76[/tex]
Probability of winning the first game when the second game is won:
[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]
[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]
[tex]P(W_1/W_2)=0.0625[/tex]
Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:
[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]
[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]
[tex]P(W_1/W_2')=0.1110[/tex]
An urn contains 2 small pink balls, 7 small purple balls, and 6 small white balls.
Three balls are selected, one after the other, without replacement.
Find the probability that all three balls are purple
Express your answer as a decimal, rounded to the nearest hundredth.
Answer:
The probability is P = 0.08
Step-by-step explanation:
We have:
2 pink balls
7 purple balls
6 white balls
So the total number of balls is just:
2 + 7 + 6 = 15
We want to find the probability of randomly picking 3 purple balls (without replacement).
For the first pick:
Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)
p₁ = 7/15
Second:
Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:
p₂ = 6/14
third:
Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:
p₃ = 5/13
The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:
P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13) = 0.08
Solve for x. The triangles are similar.
Need helpppppppppppppppppp
Answer:
-18
Step-by-step explanation:
B=-6 C=2 P.E.M.D.A.S.
b - 6(c)
-6 - 6(2)
-6 - 12 . The negatives cancel out, adding each other
-6 + -12
= -18 :)
Answer:
b - 6c
= -6 - 6x2
= -6 x( 1+2)
= -6x3
= -18
¿Pueden ayudarme por favor?
HELP ME FAST WILL GIVE BRAINLY
A bag contains 16 white marbles, 10 blue marbles and 12 red marbles. Give each ratio as a reduced fraction.
A) The ratio of white marbles to blue marbles.
B) The ratio of red marbles to total marbles.
the total of marbles = 16 + 10 +12 =38
A) white : blue = 16/10 = 8/5
B) red : total = 12/38 = 6/19
Step-by-step explanation:
1. find the total of marbles
Okay, let's calculate the year end adjustment for overhead. Based on the data below, determine the amount of the year end adjustment to cost of goods sold due to over or under allocated manufacturing overhead during the year
Answer:
the adjustment made to the cost of goods sold is -$2,014
Step-by-step explanation:
The computation of the adjustment made to the cost of goods sold is given below:
Total actual overhead expenses $110,822
Less: Total overheads allocated -$112,836
Adjustment made to the cost of goods sold -$2,014
Hence, the adjustment made to the cost of goods sold is -$2,014
The same should be considered
A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?
Answer:
20 mStep-by-step explanation:
We have similar triangles here.
BC║DE, AB║AD and AC║AE ⇒ ΔADE ~ ΔABCThe ratio of corresponding sides of similar triangles is same:
BC/DE = AC/AEBC / 2 = 30/3BC / 2 = 10BC = 2*10BC = 20 mTake the similar triangles,
→ ∆ADE ≈ ∆ABC
Now we can find,
The height of the tree in meters,
→ BC/DE = AC/AE
In this equation BC is the height of tree,
→ BC/2 = 30/3
→ BC/2 = 10
→ BC = 10 × 2
→ BC = 20
Hence, the height of the tree is 20 m.
you have to find ABC and I'm not sure how to any help is appreciated
Hello,
Since (BD) bissects angle ABC,
18-x=26-3x
2x=8
x=4
18-x=18-4=14
m angle ABC=14°*2=28°
PLEASE I NEED HELP!!!!!
Find the volume of this sphere.
Use 3 for TT.
L-r=3ft
V [?]ft3
V = Tr3
Answer:
113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1
1 1/3 bushels of seed are needed to plant 1 acre of wheat. How many bushels of seed would be required to plant 30 acres?
An acre requires 1.33 bushels of seed.
Thirty acres thusly require 30 times 1.33 bushels of seed.
So we have, [tex]1.33\cdot30=\boxed{39.9}[/tex] bushels of seed.
Hope this helps.
calculate the value of X in the diagram
Answer:
that is the answer
Step-by-step explanation:
use triangle RSQ
from pythogrus theorem
a² + b² = c²
4² + 5² = RQ²
16 + 25 = RQ²
41 = R
Write an addition or a subtraction equation (your choice!) to describe the diagram. Pls help
Answer:
Addition equation = -4-0) + [(-13)-(-4)]
Answer = -13
Step-by-step explanation:
For the small arrow in the diagram, the expression is (-4 - 0)
For the bog arrow, the expression will be -13 - (-4)
Adding both expressions
Addition = (-4-0) + [(-13)-(-4)]
Addition = (-4) + (-13+4)
Addition = -4 + (-9)
Addition = -4-9
Addition = -13
Divide: (2n3+4n−9)÷(n+2).
Answer:
2n+2
_____
9 2n
A study is done to determine the average salary for all Santa Clara County teachers. If we were to randomly pick 15 schools in Santa Clara County and average together the salaries of all teachers, would this be a good sampling technique or a bad sampling technique
Answer:
Good sampling technique
Step-by-step explanation:
In other to determine the mean value for a population, it may be necessary to make inference from the a small subset of the population, called the sample, if it is impossible, difficult or inefficient to get all population data. Hence, in other to select a subset of the population, then the sample must be selected at random, such that all elements of the population have equal chances of being selected and hence, be representative of the population. Since, the sampling technique adopted above is done at random, hence, it is a good sampling technique.
An experimental drug is administered to 130 randomly selected individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial experiment
Answer:
Yes, as for each trial there are only two possible outcomes, the trials are independent, and the number of trials is fixed.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they respond favorably, or they do not. The probability of a student responding favorably is independent of any other student, and the number of trials is fixed. Thus, this probability experiment represents a binomial experiment.
SHOW PROCESS!!!
Will mark brainly!!
Thank you!
Answer:
Step-by-step explanation:
By applying cosine rule in the given triangle,
c² = a² + b²-2abcosC
c² = (5.6)² + (10.7)² - 2(5.6)(10.7)cos(109.3°)
c² = 185.46
c = 13.6 km
By applying sine rule in the given triangle ABC,
[tex]\frac{\text{sin}A}{a}= \frac{\text{sin}B}{b}= \frac{\text{sin}C}{c}[/tex]
[tex]\frac{\text{sin}A}{5.6}=\frac{\text{sin}B}{10.7}=\frac{\text{sin}109.3}{13.6}[/tex]
[tex]\frac{\text{sin}B}{10.7}=\frac{\text{sin}109.3}{13.6}[/tex]
sin(B) = [tex]\frac{10.7\times \text{sin}(109.30)}{13.6}[/tex]
= 0.7425
B = [tex]\text{sin}^{-1}(0.7425)[/tex]
B = 48.0°
[tex]\frac{\text{sin}A}{5.6}=\frac{\text{sin}109.3}{13.6}[/tex]
sin(A) = [tex]\frac{[\text{sin}(109.3)]\times (5.6)}{13.6}[/tex]
= 0.3886
A = [tex]\text{sin}^{-1}(0.3886)[/tex]
A = 22.9°
15.18. Find the area of the region bounded by
TC
the curve y = cosx, x=0, x= pi/
2 and x-axis.
Answer:
please mark me brainlist
Step-by-step explanation:
If the actual price in this market were below
the equilibrium price, what would drive the
market toward the equilibrium?
Step-by-step explanation:
If the price is below the equilibrium level, then the quantity demanded will exceed the quantity supplied. Excess demand or a shortage will exist. If the price is above the equilibrium level, then the quantity supplied will exceed the quantity demanded. Excess supply or a surplus will exist.Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium. A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.
Pls solve the above question
Kindly don't spam+_+
Answer:
Step-by-step explanation:
Given expressions are,
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex] and [tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
Remove the radicals from the denominator from both the expressions.
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}} \times \frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{p}=\sqrt{\frac{(\sqrt{10}-\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{5}}[/tex]
[tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\times \frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{q}=\sqrt{\frac{(\sqrt{10}+\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}[/tex]
[tex]\sqrt{q}-\sqrt{p}-2\sqrt{pq}=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}-\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}}-2(\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}})(\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}})[/tex]
[tex]=\frac{1}{\sqrt{5}}(\sqrt{10}+\sqrt{5}-\sqrt{10}+\sqrt{5})-\frac{2}{5}[(\sqrt{10})^2-(\sqrt{5})^2)][/tex]
[tex]=\frac{1}{\sqrt{5}}(2\sqrt{5})-\frac{2}{5}(10-5)[/tex]
[tex]=2-2[/tex]
[tex]=0[/tex]
Use the graph to find the y-intercept and axis of symmetry
Answer:
axis of symmetry=-2
y intercept=(0,-1)
1.055.
Determine whether the statement is true or false. If the statement is false, give a reason.
{5, 6, 7} = {5, 5, 6, 7, 7}
Given:
The statement is:
{5, 6, 7} = {5, 5, 6, 7, 7}
To find:
Whether the given statement is true or false.
Solution:
Two sets are equal if they have exactly the same elements.
The given set {5, 6, 7} has three elements and the set {5, 5, 6, 7, 7} has five elements but we known that all the elements of a set are distinct. It means, it has no repeated element.
Set {5, 5, 6, 7, 7} has three distinct elements 5, 6, 7. So,
{5, 5, 6, 7, 7} = {5, 6, 7}
Therefore, the given statement is true.
