What's 24.67 to one significant figure?
Given sina=6/7 and cosb=-1/6, where a is in quadrant ii and b is in quadrant iii , find sin(a+b) , cos(a-b) and tan(a+b)
sin(a+b) = -1/7 +√455/42 = 0.8721804464845457
cos(a-b) = √13/42 - √35/7 = -0.7761476987942811
tan(a+b )= (6√13/13 + √35) / (1 - 6√455/13) = -0.525
Given sin(a) = 6/7 and cos(b) = -1/6, with a in quadrant II and b in quadrant III, we need to utilize trigonometric identities to find sin(a+b), cos(a-b), and tan(a+b).
Firstly, since a is in quadrant II, cos(a) is negative. We use the identity sin²(a) + cos²(a)=1 to find cos(a):
cos(a) = -√(1 - sin²(a)) = -√(1 - (6/7)²) = -√(1 - 36/49) = -√(13/49) = -√13/7Similarly, since b is in quadrant III, sin(b) is also negative. We use the identity sin²(b) + cos²(b)=1 to find sin(b):
sin(b) = -√(1 - cos²(b)) = -√(1 - (-1/6)²) = -√(1 - 1/36) = -√(35/36) = -√35/6Now we can use the angle addition and subtraction formulas:
1. sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin(a + b) = (6/7)(-1/6) + (-√13/7)(-√35/6) = -1/7 + √(13×35)/(7×6) = -1/7 + √455/42 = -1/7 +√455/422. cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
cos(a - b) = (-√13/7)(-1/6) + (6/7)(-√35/6) = √13/(7×6) - (6√35)/(7×6) = √13/42 - √35/73. tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
Using tan(a) = -sin(a)/cos(a) = -(6/7)/(-√13/7) = 6/√13 and tan(b) = sin(b)/cos(b) = (-√35/6)/(-1/6) = √35:tan(a + b) = (6/√13 + √35) / (1 - (6/√13)(√35)) = (6√13/13 + √35) / (1 - 6√455/13)Determine whether the function f : z × z → z is onto if
a.f(m,n)=m+n. b)f(m,n)=m2+n2.
c.f(m,n)=m.
d.f(m,n) = |n|.
e.f(m,n)=m−n.
Newton uses a credit card with a 18.6% APR, compounded monthly, to pay for a cruise totaling $1,920.96. He can pay $720 per month on the card. What will the total cost of this purchase be?
D is the midpoint of CE.E has coordinates (-3,-2), and D has coordinates (2 1/2, 1). Find the coordinate of C.
The coordinate of point C on line CE will be (8, 4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
D is the midpoint of CE.
E has coordinates (-3,-2), and D has coordinates (2 1/2, 1).
Now, By the definition of midpoint;
Let the coordinate of point C = (x, y)
Then,
((x + (-3))/2 , (y + (-2))/2) = (2 1/2, 1)
By comparison we get;
x + (-3) / 2= 2 1/2
x - 3 = 2 (5/2)
x - 3 = 5
x = 3 + 5
x = 8
And, (y + (-2))/2 = 1
y - 2 = 2
y = 2 + 2
y = 4
Thus, The coordinate of point C = (x, y) = (8, 4)
So, The coordinate of point C on line CE will be (8, 4).
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4 is to 5 as 10 is to a
A.8
B.12
C.12.5
D.20
A submarine dives 300 feet every 2 minutes,and 6750 feet every 45 minutes.Find the constant rate at which he submarine dives.Give your answer in feet per minute and in feet per hour.
How do you figure out what 1/10 of 1,7000.000 km squared is?
Scores on a certain test are normally distributed with a variance of 88. a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 3 units.
To solve for the problem, the formula is:
n = [z*s/E]^2
where:
z is the z value for the confidence interval
s is the standard deviation
E is the number of units
So plugging that in our equation, will give us:
= [1.96*9.38/3]^2
= (18.3848/3)^2
= 6.1284^2
= 37.5 or 38
Round 5836197 to the nearest hundred
Answer:
5836200.
Step-by-step explanation:
Given : 5836197 .
To find : Round 5836197 to the nearest hundred.
Solution : We have given 5836197
Step 1 : First, we look for the rounding place which is the hundreds place.
Step 2 : Rounding place is 97.
Step 3 : 97 is greater than 50 then it would be rounded up mean next number to 97 would be increase to 1 and 97 become 00.
Step 4 : 5836200.
Therefore, 5836200.
The five-number summary for scores on a statistics test is 11, 35, 61, 70, 79. in all, 380 students took the test. about how many scored between 35 and 61
Answer: There are 95 students who scored between 35 and 61.
Step-by-step explanation:
Since we have given that
The following data : 11,35,61,70,79.
So, the median of this data would be = 61
First two data belongs to "First Quartile " i.e. Q₁
and the second quartile is the median i.e. 61.
The last two quartile belongs to "Third Quartile" i.e. Q₃
And we know that each quartile is the 25th percentile.
And we need "Number of students who scored between 35 and 61."
So, between 35 and 61 is 25% of total number of students.
So, Number of students who scored between 35 and 61 is given by
[tex]\dfrac{25}{100}\times 380\\\\=\dfrac{1}{4}\times 380\\\\=95[/tex]
Hence, There are 95 students who scored between 35 and 61.
The number of students who scored between 35 and 61 is 95
The 5 number summary is the value of the ;
Minimum Lower quartile Median Upper quartile and Maximum values of a distribution.The total Number of students = 380
The lower quartile (Lower 25%) = 35
The median (50%) = 61
The Number of students who scored between 35 and 61 : 50% - 25% = 25%This means that 25% of the total students scored between 35 and 61.
25% of 380 = 0.25 × 380 = 95Hence, 95 students scored between 35 and 61.
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If I have a floor that is 100 3/4 feet by 75 1/2 what is the area
What is the unit rate for 822.6 km in 18 hours? Enter your answer, as a decimal, in the box. Please Help
15 children voted for their favorite color. The votes for red and blue together we're double the votes for green and yellow together. How did the children vote?
Use the chain rule to find dw/dt. w = xey/z, x = t7, y = 4 − t, z = 2 + 9t
The derivative[tex]\( \frac{dw}{dt} \) is \( \frac{7t^6 e^{4-t}}{2+9t} - \frac{t^7 e^{4-t}}{2+9t} - \frac{9t^7 e^{4-t}}{(2+9t)^2} \).[/tex]
To find [tex]\( \frac{dw}{dt} \)[/tex] using the chain rule for the given function[tex]\( w = \frac{x e^y}{z} \), where \( x = t^7 \), \( y = 4 - t \), and \( z = 2 + 9t \)[/tex], follow these steps:
1. **Express ( w ) in terms of ( t ):**
Substitute ( x ), ( y ), and ( z ) into ( w ):
[tex]\[ w = \frac{x e^y}{z} = \frac{(t^7) e^{(4 - t)}}{2 + 9t} \][/tex]
2. **Apply the chain rule:**
The chain rule states that for a function ( w(t) ) defined implicitly by ( w = f(x(t), y(t), z(t)) ), the derivative [tex]\( \frac{dw}{dt} \)[/tex] is given by:
[tex]\[ \frac{dw}{dt} = \frac{\partial w}{\partial x} \cdot \frac{dx}{dt} + \frac{\partial w}{\partial y} \cdot \frac{dy}{dt} + \frac{\partial w}{\partial z} \cdot \frac{dz}{dt} \][/tex]
3. **Compute partial derivatives of ( w ) with respect to ( x ), ( y ), and ( z ):**
[tex]\( \frac{\partial w}{\partial x} = \frac{e^y}{z} \)[/tex]
[tex]\( \frac{\partial w}{\partial y} = \frac{x e^y}{z} \)[/tex]
[tex]\( \frac{\partial w}{\partial z} = -\frac{x e^y}{z^2} \)[/tex]
4. **Compute [tex]\( \frac{dx}{dt} \), \( \frac{dy}{dt} \), and \( \frac{dz}{dt} \):**[/tex]
[tex]\( \frac{dx}{dt} = 7t^6 \)[/tex]
[tex]\( \frac{dy}{dt} = -1 \)[/tex]
[tex]\( \frac{dz}{dt} = 9 \)[/tex]
5. **Substitute these into the chain rule formula:**
[tex]\[ \frac{dw}{dt} = \frac{e^y}{z} \cdot 7t^6 + \frac{x e^y}{z} \cdot (-1) + \left(-\frac{x e^y}{z^2}\right) \cdot 9 \][/tex]
6. **Substitute[tex]\( x = t^7 \), \( y = 4 - t \), \( z = 2 + 9t \)[/tex] into the expression:**
[tex]\( e^y = e^{4 - t} \)[/tex]
Substitute these values into the formula for [tex]\( \frac{dw}{dt} \):[/tex]
[tex]\[ \frac{dw}{dt} = \frac{e^{4 - t}}{2 + 9t} \cdot 7t^6 - \frac{t^7 \cdot e^{4 - t}}{2 + 9t} - \frac{9t^7 \cdot e^{4 - t}}{(2 + 9t)^2} \][/tex]
Therefore, [tex]\( \frac{dw}{dt} \)[/tex] is:
[tex]{\frac{dw}{dt} = \frac{7t^6 e^{4 - t}}{2 + 9t} - \frac{t^7 e^{4 - t}}{2 + 9t} - \frac{9t^7 e^{4 - t}}{(2 + 9t)^2} } \][/tex]
A, B, and C are mutually exclusive. P(A) = .2, P(B) = .3, P(C) = .3. Find P(A ∪ B ∪ C). P(A ∪ B ∪ C) =
The function y = –3(x – 2)2 + 6 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the zeros of this tion
A. Zeros at x = 2 and x = 6
B. Zeros at
C. The zeros are the hot dog prices that give $0.00 profit (no profit).
D. The zeros are the hot dog prices at which they sell 0 hot dogs.
The zeros of the function y = -3(x - 2)² + 6 are x = 2 + √2 and x = 2 - √2, which represent the hot dog prices at which the hot dog stand makes $0.00 profit.
Explanation:The zeros of a function are the values of x that make the y-coordinate equal to zero. In this case, the function y = -3(x - 2)² + 6 represents the daily profit, and we need to find the x-values that result in a profit of $0.00. Setting the profit, y, to zero and solving for x, we get:
0 = -3(x - 2)² + 6
Adding 3(x - 2)² to both sides and simplifying the equation gives:
3(x - 2)² = 6
Dividing both sides by 3, we have:
(x - 2)² = 2
Take the square root of both sides, remembering to consider both the positive and negative square roots:
x - 2 = ±√2
Adding 2 to both sides gives us the final solutions:
x = 2 ± √2
So, the zeros of this function are x = 2 + √2 and x = 2 - √2. These are the hot dog prices at which the hot dog stand makes $0.00 profit.
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how can I adjust a quotient to solve a division problem
The perpendicular bisector of side AB of ∆ABC intersects side BC at point D. Find AB if the perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
Answer:
Hence, AB=12.
Step-by-step explanation:
We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.
this means that side AE=BE.
Also we could clear;ly observe that
ΔBED≅ΔAED
( since AE=BE, side ED common, ∠BED=∠AED
so by SAS congruency the two triangles are congruent)
Now we are given that:
the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.
i.e. AB+AC+BC=AC+AD+CD+12
AB+BC=AD+CD+12
as AD=BD
this means that AD+CD=BD+CD=BC
AB+BC=BC+12
AB=12
Hence AB=12
Answer:
The required length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
Step-by-step explanation:
Given: The perpendicular bisector of side [tex]AB[/tex] of [tex]\bigtriangleup{ABC}[/tex] intersects side [tex]BC[/tex] at point [tex]D[/tex] and the perimeter of [tex]\bigtriangleup{ACD}[/tex].
From the figure,
[tex]AE=BE[/tex] .......(1) (as [tex]DE[/tex] is perpendicular bisector of side [tex]AB[/tex])
Now, In [tex]\bigtriangleup{BED}[/tex] and [tex]\bigtriangleup{AED}[/tex]
[tex]AE=BE[/tex] ( from equation 1 )
[tex]\angle {BED} =\angle {AED}[/tex] ( Both [tex]90^\circ[/tex] )
[tex]ED=ED[/tex] ( Common side)
[tex]\bigtriangleup{BED}\cong\bigtriangleup{AED}[/tex] ( by SAS congruence rule)
[tex]BD=AD[/tex] .........(2) (by CPCT)
As per question,
The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
[tex]AB+BC+AC=AC+CD+AD+12[/tex]
[tex]AB+BC=AD+CD+12\\AD+CD=BD+CD\\AB+BC=BC+12\\[/tex]
[tex]AB=12\rm\;{cm}[/tex]
Hence, the length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
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what is the answer of 9X23+3X39-28=n
Answer: n=296
Step-by-step explanation: 9 x 23 + 3 x 39 - 28 + n = 296
Hope this helps! <3
605 mi in 11 hours at the same rate how many miles would he drive in 13 hours
Jonathan pays $1.90 per pound for potatoes. He buys 8.3 pounds of potatoes. He determines that he will pay $15.77, before tax, for the potatoes. Which best describes the reasonableness of Jonathan’s solution?
The correct answer is C.
Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77.
Hope this helps.
The diagram represents a reduction of a triangle by using a scale factor of 0.8.
What is the height of the reduced triangle?
4.0 inches
4.8 inches
5.2 inches
7.5 inches
The reduction factor of 0.8 means the lengths in the reduced triangle are 0.8 times those of the original.
Then the original 6 inch length is reduced to 0.8×6 inches = 4.8 inches in the reduced triangle.
Answer:
4.8 inches
Step-by-step explanation:
The scale factors are used to convert a figure into another one with similar characteristics but different lengths, in this example is a triangle, and in order to calculate the measure of the height you just have to multiply the original height by the scale factor:
6 inches * scale factor
6 inches* 0.8= 4.8 inches
So the resultant triangle will have a height of 4.8 inches.
During her first year of subscribing to a newspaper, Christie paid $48. During each subsequent year, the annual cost was 1.5 times the price paid the previous year. Which of the following equations may be used to calculate the total cost, C, of subscribing to the newspaper after n years?
Which fraction is less than 1/2 a.3/8 b.5/8 c.5/7 d.9/16
Suppose you have two credit cards. The first has a balance of $415 and a credit limit of $1,000. The second has a balance of $215 and a credit limit of $750. What is your overall credit utilization?
Compute for the total balance:
total balance = $415 + $215 = $630
Then we compute for the total credit limit:
total credit limit = $1,000 + $750 = $1,750
The credit utilization would simply be the percentage ratio of total balance over total credit limit. That is:
credit utilization = ($630 / $1,750) * 100%
credit utilization = 36%
30 POINTS: The art club had an election to select a president. 25% of the 76 members of the club voted in the election. How many members voted?
Answer:
19 members voted.
Step-by-step explanation:
Percentage problems can be solved by a rule of three.
25% of the 76 members of the club voted in the election. How many members voted?
So 76 is 100% = 1. How much is 0.25?
76 - 1
x - 0.25
[tex]x = 76*0.25[/tex]
[tex]x = 19[/tex]
19 members voted.
Mrs. Milleman looked at another hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent.
write a fraction less than 1 with a denominator of 6 that is greater than 3/4
Answer:= 5/6
Step-by-step explanation:hope this helps
Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(t) = at2 + bt + c, where a, b, and c are to be determined.
To find a, b, c for the solution:
Let's start by writing down the expression for the function x(t) and its derivative:
We have:
x(t) = at² + bt + c
and
x'(t) = 2at + b
Using x' and x into the differential equation x′ + 2x = t² + 4t + 7 gives us:
2at + b + 2*(at² + bt + c) = t² + 4t + 7
Expanding this gives:
2at² + 2bt + b + 4at + 2c = t² + 4t + 7
By equating the coefficients of equivalent powers of t on both sides, we get three equations:
For t² :
2a = 1
So, a = 1/2
For t:
2b + 4a = 4
Substitute a = 1/2 into the equation gives b = 1 - 2 = -1
For the constant term:
b + 2c = 7
Substituting b = -1 gives c = 4.
So the solution is a = 1/2, b = -1, c = 4.
So the specific solution of this differential equation is given by x(t) = (1/2)t² - t + 4.