A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answers
Answer:
(a) the new angle the ladder makes with the ground is [tex]32.7^o[/tex]
(b) the ladder slipped back about 5 meters
Step-by-step explanation:
Notice that the ladder doesn't change its length in the process.
So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:
[tex]sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m[/tex]
therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.
Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:
[tex]sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o[/tex]
To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:
[tex]cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m[/tex]
Now fro the new position of the bottom of the ladder relative to the wall:
[tex]cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m[/tex]
then the difference in between those two distances is what we need:
8.4 m - 3.4 m = 5 m
Related Questions
The linear function g(x) = -4.5x + 144 represents the amount of money,
g(x), Sara has on her lunch card, where x represents the number of days
since the beginning of each month. Which represents the amount of
money on Sara's lunch card at the beginning of each month?
Answers
Answer:
Sara has $144 at the beginning of the month.
Step-by-step explanation:
At the beginning of the month, x = 0 because no days have passed since the beginning of the month. When x = 0, g(0) = -4.5(0) + 144 = 144, therefore, we know that Sara has $144 on her card at the beginning of the month.
Perform 3ax (2x - ax + 5)
Answers
Answer:
Step-by-step explanation:
Multiply the monomial by each and every term of the polynomial
= (3ax) (2x) - (3ax) (ax) + (3ax) (5)
= 6ax^2 - 3a^2x^2 + 15ax
Which of the following are solutions to the equation below?
Check all that apply.
X^2+18=-9x
Answers
Answer:
The solution set is {-3, -6}.
Step-by-step explanation:
x^2 + 18 = -9x
x^2 + 9x + 18 = 0
(x + 3)(x + 6) = 0
x = -3, -6.
What is the measure of the complement?
Answers
Answer:
64°
Step-by-step explanation:
If two angles add up to give 90°, that are said to be complementary. One is a complement of the other.
Therefore, given that the measure of an angle, angle A = 26°, the measure of the complement of angle A = 90 - 26 = 64°.
The measure of the complement of angle A, is 64°.
b = 1/2 a - 3c rearrange to make a the subject
Answers
Answer:
[tex]\huge \boxed{a = 2b + 6c}[/tex]
Step-by-step explanation:
b = 1/2a - 3c
Add 3c to both sides of the equation.
b + 3c = 1/2a - 3c + 3c
b + 3c = 1/2a
Switch sides.
1/2a = b + 3c
Multiply both sides of the equation by 2.
2(1/2a) = 2(b + 3c)
a = 2b + 6c
Step-by-step explanation:
[tex]b = \frac{1}{2} a- 3c[/tex]
Multiply both sides ✖ of the equation by 2
[tex]2b = a - 6c[/tex]
Move the variable to the left-hand side and change its sign
[tex] - a + 2b = - 6c[/tex]
MOVE THE VARIABLE TO THE RIGHT-HAND SIDE AND CHANGE ITS SIGN
[tex] - a = - 6c - 2b[/tex]
Change the sign on both sides of the equation
[tex]a = 6c + 2b[/tex]
Therefore the answer is
[tex]a = 6c + 2b[/tex]
A company issues 10% Irredeemable preference shares. The face value per share is RO 10, but the issue price is RO 9.5. what is the cost of preference share?
Answers
Answer:
The answer of the question is 10.53%.
What does 5x evaluate to if x is equal to 2?
Answers
Answer: Hi!
Since 5 is being multiplied by x, and x is equal to 2, be would multiply 5 and 2. 5 * 2 is equal to 10.
Hope this helps!
Answer:
Step-by-step explanation:
Name the image of C after a rotation of 180° about the origin.
Answers
Answer:
C'(-5, 2)
Step-by-step explanation:
Rule to be followed for a point rotated 180° about the origin,
(x, y) → (-x, -y)
From the figure attached,
When ABCD is rotated 180° about the origin, the new points of the image will be
A(2, 0) → A'(-2, 0)
B(4, 0) → B'(-4, 0)
C(5, -2) → C'(-5, 2)
D(1, -2) → D'(-1, 2)
Therefore, image of C will be C'(-5, 2).
If a new movie is selling for $20, and the local city charges 8% sales tax, how much tax will be charged? $_____
Answers
Answer: $1.6
Step-by-step explanation:
price × percentage of tax=amount of tax
$20 × 8%=20 × 0.08= $1.6
Hope this helps!! :)
Distribute a negative -(5.5q+7)
Answers
Hi there! :)
Answer:
[tex]\huge\boxed{-5.5q - 7}[/tex]
-(5.5q + 7)
Distribute:
-(5.5q) -(7)
-5.5q - 7
Answer:
Z≥0 = {0, 1, 2, .
Step-by-step explanation:
Just took test
Find the indicated margin of error. In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confidence interval used to estimate the population proportion.
Answers
Answer:
The margin of error is [tex]E = 0.021[/tex]
Step-by-step explanation:
From the question we are told that
The population size is [tex]n = 2161[/tex]
The number that showed improvement is [tex]k = 1214[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{ 1214}{2161}[/tex]
=> [tex]\r p = 0.56[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha =(100-95) \%[/tex]
=> [tex]\alpha =0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{\frac{ 0.56(1 - 0.56 )}{2161} }[/tex]
=> [tex]E = 0.021[/tex]
After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The rat population on the island grows exponentially, and after 15 months, there are 280 rats on the island.
A. Find a function that models the population t months after the arrival of the rats.
B. What will the population be 3 years after the shipwreck?
C. When will the population reach 2000 rats?
Answers
Answer:
a. [tex]X(T) = 120 (1.058)^T[/tex]
b. Population after 3 years is 142
c. 50 years
Step-by-step explanation:
Given
Type of growth: Exponential
Initial number of rats = 120
Number of rats (15months) = 280
Solving (a)
Since the growth type is exponential, we make use of the following exponential progression
[tex]X_T = X_0 (1 + R)^T[/tex]
Where Xo is the initial population;
Xo = 125
[tex]X_T[/tex] is the current population at T month
So;
[tex]X_T = 280[/tex]; when [tex]T = 15[/tex]
Substitute these values in the above formula
[tex]280 =120 * (1 + R)^{15}[/tex]
Divide both sides by 120
[tex]\frac{280}{120} =(1 + R)^{15}[/tex]
[tex]2.3333 =(1 + R)^{15}[/tex]
Take 15th root of both sides
[tex]\sqrt[15]{2.3333} =1 + R[/tex]
[tex]1.05811235561 = 1 + R[/tex]
Subtract 1 from both sides
[tex]R = 1.05811235561 - 1[/tex]
[tex]R = 0.05811235561[/tex]
[tex]R = 0.058[/tex] (Approximated)
Plug in values of R and Xo in [tex]X_T = X_0 (1 + R)^T[/tex]
[tex]X_T = 120 (1 + 0.058)^T[/tex]
[tex]X_T = 120 (1.058)^T[/tex]
Write as a function
[tex]X(T) = 120 (1.058)^T[/tex]
Hence, the function is [tex]X(T) = 120 (1.058)^T[/tex]
Solving (b):
Population after 3 years
In this case, T = 3
So:
[tex]X(T) = 120 (1.058)^T[/tex]
[tex]X(3) = 120 (1.058)^3[/tex]
[tex]X(3) = 120 * 1.18466445254[/tex]
[tex]X(3) = 142.159734305[/tex]
[tex]X(3) = 142[/tex] (Approximated)
Solving (c): When population will reach 2000
Here: X(T) = 2000
So:
So:
[tex]2000 = 120 (1.058)^T[/tex]
Divide both sides by 120
[tex]\frac{2000}{120} = 1.058^T[/tex]
[tex]16.667 = 1.058^T[/tex]
Take Log of both sides
[tex]Log(16.667) = Log(1.058^T)[/tex]
Apply law of logarithm
[tex]Log(16.667) = TLog(1.058)[/tex]
Divide both sides by Log(1.058)
[tex]T = \frac{Log(16.667)}{Log(1.058)}[/tex]
[tex]T = 49.9009236926[/tex]
Approximate
[tex]T = 50\ years[/tex]
including a 8% sales tax an inn charges $140.40 per night find the inns nightly cost before tax is added
Answers
Answer:
129.168
Step-by-step explanation:
multiply- 140.40*0.08=11.232
subtract- 140.40-11.232= 129.168
02
Question 3 (2 points)
Find the estimate
At a certain university. It costs a student $689 per credit hour to attend. Estimate
the cost for a student to attend one semester if he registers for 9 credit hours.
Answers
Answer:
About $6000
Step-by-step explanation:
Multiply 689 × 9.
When you are estimating, you should round the numbers off to values that you can easily work in your head.
I would round 9 up to 10 and 689 down to 600 to compensate. Then,
10 credit hours × $600/credit hour ≈ $6000.
It should cost about $6000 to register for 9 credit hours.
Find the 4th term in the sequence with the following definition
Answers
Answer:
-37
Step-by-step explanation:
[tex]a_{1}=-2\\a_{n}=2a_{n-1}-3\\a_{2}=2a_{1}-3=2(-2)-3=-4-3=-7\\a_{3}=2a_{2}-3=2(-7)-3=-14-3=-17\\a_{4}=2a_{3}-3=2(-17)-3=-34-3=-37[/tex]
Simplify the following expression as much as possible.
4^10/4^10 x 7^O=?
Answers
Answer:
1
Step-by-step explanation:
4^10/4^10 x 7^O =
= 4^(10 - 10) * 1
= 4^0 * 1
= 1 * 1
= 1
Answer:
1
Step-by-step explanation:
4^10/4^10 = 1
7^0 = 1
1 x 1 = 1
If you throw a single die twice, what's the probability of first getting a 3 and then getting another odd number?
Answers
Answer:
the answer is one twelve 1/12
fling
Find the slope of the line passing through the points (1,5) and (4,-2).
Answers
CAN SOMEONE PLS HELP!!!
Answers
Answer:
[tex] 2ab^2 -d^3 + c [/tex]
Step-by-step explanation:
Given the expression [tex] 2ab^2 - (d^3 - c) [/tex], all you need to do to evaluate the expression is to open the bracket.
Use the negative sign to multiply all the terms within the bracket alongside the sign they carry.
Thus,
[tex] 2ab^2 - (d^3 - c) = 2ab^2 -d^3 + c [/tex] (negative sign multiplied by negative sign equal positive sign)
We cannot evaluate [tex] 2ab^2 -d^3 + c [/tex] further. The me three terms are different from one another. There are no like terms.
Solve for x. x/r-8 +1/8=x+1/8-r
Answers
Answer: x=16
Step-by-step explanation:
Eddie Lange earns $11.50 per hour. He worked 40 hours, plus time and a half
for 7 hours.
Answers
Answer:580
Step-by-step explanation:
Please please someone help me
Here is a graph of the function h
Use the graph to find the following
If there is more than one answer , separate them with commas
Answers
Answer:
minimum is -3,0
Step-by-step explanation:
PLEASE HELP ME!! 10 POINTS!
number 1: you make 35 bracelets in 5 hours. Find the unit rate.
Number 2:
Identify the terms, coefficients, and constants in the expression 14x + 19.
Answers
Answer: Number 1- you make 7 bracelets in 1 hour.
Step-by-step explanation:
Number 1- You divide 35 by 5 and get 7. The hour (5) goes at the denominator and the number of bracelets(35)goes on the numerator and you divide
A group of friends are going to see a movie the admission cost eight dollars per person the table below represents the number of friends on the total cost which set of ordered pairs can be written from the table
Answers
Answer:(2,16),(3,24),(4,32),(5,40)
Step-by-step explanation:
(-1 2/3) the power of 2 =
Answers
[tex]2\frac{7}9}[/tex]
Step-by-step explanation:[tex](-1\frac{2}{3})^{2}=(-\frac{5}{3})^{2}=\frac{-5^{2}}{3^{2}}=\frac{25}{9}=2\frac{7}9}[/tex]
Let p0, p1, and p2 be the orthogonal polynomials described below, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, 2. Find the othogonal projection of 3t^(3) onto Span{p0,p1,p2}.
p0(t) = 4
p1(t) = 3t
p2(t) = t^(2) -2
Answers
Answer:
[tex]$\frac{51}{5}t$[/tex]
Step-by-step explanation:
Let W = [tex]$(p_0, p_1, p_2)$[/tex] be orthogonal polynomials which is equal to [tex]$(4, 3t, t^2 -2)$[/tex], which defines the inner products as
[tex]$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$[/tex]
Now, we find the orthogonal projection of [tex]$p=3t^3$[/tex] on W.
So the projection is
[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]
[tex]$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$[/tex]
[tex]$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$[/tex]
[tex]$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$[/tex]
[tex]$=4(4)+4(4)+4(4)+4(4)+4(4)=80$[/tex]
[tex]$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$[/tex]
[tex]$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$[/tex]
[tex]$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$[/tex]
[tex]$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$[/tex]
[tex]$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$[/tex]
[tex]$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$[/tex]
[tex]$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$[/tex]
[tex]$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$[/tex]
Therefore,
[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]
[tex]$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$[/tex]
[tex]$=\frac{51}{5}t$[/tex]
a. y=sin(x²+3x-1), differentiate y
b. x³+sinx, find third derivative
c. y={x+(1÷x)}², differentiate y
d. y=(5x–2)-², differentiate y
Answers
A.
[tex]y=\sin(x^2+3x-1)[/tex]
[tex]\implies y'=\cos(x^2+3x-1)(x^2+3x-1)'=(2x+3)\cos(x^2+3x-1)[/tex]
B.
[tex]y=x^3+\sin x[/tex]
[tex]\implies y'=3x^2+\cos x[/tex]
[tex]\implies y''=6x-\sin x[/tex]
[tex]\implies y'''=6-\cos x[/tex]
C.
[tex]y=\left(x+\dfrac1x\right)^2[/tex]
[tex]\implies y'=2\left(x+\dfrac1x\right)\left(x+\dfrac1x\right)'=2\left(x+\dfrac1x\right)\left(1-\dfrac1{x^2}\right)=2\left(x-\dfrac1{x^3}\right)[/tex]
D.
[tex]y=(5x-2)^{-2}[/tex]
[tex]\implies y'=-2(5x-2)^{-3}(5x-2)'=-10(5x-2)^{-3}=\dfrac{10}{(2-5x)^3}[/tex]
Suzanne read 87 pages of her book in 3 hours. At this rate, how many pages can Suzanne read in 5 hours?
Answers
Answer:
145
Step-by-step explanation:
Rate (no. of pages per hour)
= 87 ÷ 3
= 29
5 hours
= no. of pages per hour × 5
= 29 × 5
= 145
hope it helps :))
If Q is inversely proportional to P and Q =0.25 when
P = 2,
(i) express Q in terms of P,
(ii) find the value of Q when P = 5,
(iii) calculate the value of P when Q = 0.2.
Answers
Step-by-step explanation:
i)Q is inversely proportional to P is written as
[tex]Q \: \: \alpha \: \frac{k}{P} [/tex]
where k is the constant of proportionality
we must first calculate the relationship between them
So we have
when Q = 0.25
P = 2
Substitute the values into the above equation
That's
[tex]0.25 = \frac{k}{2} [/tex]
Cross multiply
We have
k = 0.25 × 2 = 0.5
So the formula for the variation is
[tex]Q = \frac{0.5}{P} [/tex]
ii)when P = 5
We have
[tex]Q = \frac{0.5}{5} [/tex]
We have the answer as
Q =0.1iii)When Q = 0.2
We have
[tex]0.2 = \frac{0.5}{P} [/tex]
Cross multiply
That's
0.2P = 0.5
Divide both sides by 0.2
We have the answer as
P = 2.5Hope this helps you
Simplify the following polynomial, then evaluate for x = -2 . 2x^2-4x+3x^2+x-7
Answers
Answer:
19
Step-by-step explanation:
first you would combine like terms to get 5x^2-3x-7. plug in -2 into the x's and you will get 19!