the length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58 degree to 36 degree calculate correct to three significant figure the height of the pole
Answers
Answer:
The height of the pole is 167 m
Step-by-step explanation:
The given parameters are;
Increase in the length of the shadow = 90 m
Initial angle of elevation of the Sun = 58°
Final angle of elevation of the Sun = 36°
We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase in the length of the shadow
We have by sin rule;
90/(sin (22°) = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)
Let the initial ray from the top of the pole to the end of the shadow's length = l₁
90/(sin (22°) = l₁/(sin(122°)
l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m
Therefore;
The height of the pole = 283.3 m × sin(36°) = 166.52 m
The height of the pole= 167 m to three significant figures.
Answer:
height of pole = 121 m (to 3 significant figures
Step-by-step explanation:
From the diagram attached to this solution:
Let the length of the shadow = b
Let the height of the triangle = h
[tex]Triangle\ 1\\\\Tan\ (58)\ =\ \frac{h}{b}\\1.60\ =\ \frac{h}{b} - - - - - -(1)\\\\[/tex]
[tex]Tan\ (36) = \frac{h}{b+90} \\0.73\ =\ \frac{h}{b+90} - - - - (2)[/tex]
[tex]From\ equation\ (1)\\1.60 = \frac{h}{b}\\ cross-multiplying\\1.60b = h - - - - - (3)\\\\\\from\ equation\ (2)\\0.73\ =\ \frac{h}{b+90}\\ corss-multiplying\\0.73b\ +\ 65.7 = h\\h\ =\ 0.73b\ +\ 65.7- - - - - -(4)\\[/tex]
Notice that equation (3) = equation (4) = h
[tex]1.60b = 0.73b\ + 65.7\\1.60b\ -\ 0.73b\ = 65.7\\0.87b\ =\ 65.7\\b\ =\ \frac{65.7}{0.87} = 75.52\ m\\[/tex]
Now let us find the height of pole from equation (3)
1.60b = h - - - - - - (3)
where b = 75.52
h = 1.60 × 75.52
h = 120.83 m
= 121 m (to three significant figure
Related Questions
A drive has a maximum speed of 10000 revolutions per minute. If a disc has a diameter of 12 cm what is the linear speed, in km/h, of a point 4cm from the center if the disc is spinning at a rate of 7000 revolutions per minute?
Answers
Answer:
10.8 km/hr
Step-by-step explanation:
Given that
radius of the diameter is 4 cm
Converting 4 cm to km, we have
4/100000 = 0.00004 km or 4*10^-5 km
Angular speed is given as
v = 2πr/T
Where T is, 1/n,and n is the number of revolutions
v = (2 * 3.142 * 0.00004) / (1/7000)
v = 0.00126 / 0.007
v = 0.18 km/min
This is in km/min, now we convert to km/hr as requested.
0.18 * 60 = 10.8 km/hr
0.138.2 + 0.0032 correct to 1 decimal place
Answers
Answer:
Exact: 0.1414
Rounded: 0.1
Step-by-step explanation:
I can’t figure this out pls help 17-2p=2p+5+2p
Answers
Answer:
p=2
Step-by-step explanation:
17-2p=2p+5+2p
17-2p=4p+5
17=6p+5
12=6p
2=p
The graph of f(t) = 6.2" shows the value of a rare coin in year t. What is the
meaning of the y-intercept?
fit
10
A. When it was purchased (year 0), the coin was worth $2
B. Every year the coin is worth 6 more dollars.
C. When it was purchased (year 0), the coin was worth $6.
D. In year 1, the coin was worth $12
Answers
Answer:
C. When it was purchased (year 0), the coin was worth $6.
Step-by-step explanation:
The y-intercept is 6, indicating the value of the rare coin was 6 in year zero.
The area of quadrilateral ABCD in the below figure is
(a) 57 cm
(b) 95 cm2
(c) 102 cm2
(d) 114 cm
Answers
Answer:
a)57
Step-by-step explanation:
3x-2=25 solve equation
Answers
Answer:
x=9
Step-by-step explanation:
3x-2=25
Add 2 to each side
3x-2+2=25+2
3x = 27
Divide by 3
3x/3 = 27/3
x = 9
Answer:
x=9
Step-by-step explanation:
3x-2=25
3x =25+2
3x =27
x =27/3
x =9
5{3c-[d-2(c+d)]}
PLS ANSWER WILL MARK BRAINLIEST
Answers
Answer:
25c+5d
Step-by-step explanation:
First, write out the equation as you have been given in the problem:
[tex]5(3c-[d-2(c+d)])\\[/tex]
Next, distribute the -2 to the set of parenthesis containing "c+d" and combine any like terms that you can:
[tex]5(3c-[d-2c-2d])\\5(3c-[-2c-d])[/tex]
Then, distribute the "-"to the "-2c-d" in the brackets and combine and like terms that you can:
[tex]5(3c+2c+d)\\5(5c+d)[/tex]
Finally, distribute the coefficient 5 to the terms inside the parenthesis:
[tex]25c+5d[/tex]
Therefore, 25c+5d is you simplified answer to the problem.
Evaluate 4-0.25g+0.5h when g=10 and h=5
Answers
Answer:
[tex]4[/tex]
Step-by-step explanation:
[tex]4 - 0.25g + 0.5h = 4 - 0.25(10) + 0.5(5) = 4 - 2.5 + 2.5 = 1.5 + 2.5 = 4[/tex]
Answer:
4Step-by-step explanation:
[tex]4-0.25g+0.5h\\g =10\\h=5\\\\4 -0.25(10)+0.5(5)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=4-0.25\times\:10+0.5\times\:5\\\\\mathrm{Multiply\:the\:numbers:}\:0.25\times\:10=2.5\\=4-2.5+5\times\:0.5\\\\\mathrm{Multiply\:the\:numbers:}\:0.5\times\:5=2.5\\=4-2.5+2.5\\\\\mathrm{Add/Subtract\:the\:numbers:}\:4-2.5+2.5\\=4[/tex]
[tex] \frac{ {x}^{3} }{x { }^{2} + 2x + 1} [/tex]
Hi! I need help with the problem above. I know the answer to it is x-2+((3x+2)/(x^2+2x+1)), but I need help knowing and understanding the process. I can usually divide polynomials with ease, but I have never had to divide when the divisor is larger than the dividend. Can you please show me how to solve this with long division? Also, if you still have time to help me, how would synthetic division work with this? Thank you in advance!
Answers
Since
[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^3}{(x+1)^2}[/tex]
we can perform synthetic division twice, first for
[tex]\dfrac{x^3}{x+1}[/tex]
then dividing the result by [tex]x+1[/tex] again.
... || 1 0 0 0
-1 || -1 1 -1
================
... || 1 -1 1 -1
This translates to
[tex]\dfrac{x^3}{x+1}=x^2-x+1-\dfrac1{x+1}[/tex]
Now divide [tex]x^2-x+1[/tex] by [tex]x+1[/tex]. (Dividing the remainder term by [tex]x+1[/tex] can wait until the end.)
... || 1 -1 1
-1 || -1 2
=============
... || 1 -2 3
or equivalently,
[tex]\dfrac{x^2-x+1}{x+1}=x-2+\dfrac3{x+1}[/tex]
Taking everything together, we have
[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^2-x+1}{x+1}-\dfrac1{(x+1)^2}[/tex]
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac3{x+1}-\dfrac1{(x+1)^2}[/tex]
Combine the last two fractions:
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3(x+1)-1}{(x+1)^2}[/tex]
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3x+2}{(x+1)^2}[/tex]
which agrees with the solution we found in your other question.
(There's a variant of synthetic division that works with directly dividing a polynomial by another one of any degree, but it's basically just a condensed version of applying the algorithm for dividing a polynomial twice by a linear one, like we've done here.)
What number needs to be eliminated to solve this equation? 3d = -81
Answers
Answer:
You must first divide 3 from both sides.
Step-by-step explanation:
Whenever you solve an equation such as this you are always trying to isolate the variable that is given. In this case we are arriving at the value of d alone.
3d = -81
d = -27
Hope this helps!
Answer:
i believe that 3 needs to be eliminated
Step-by-step explanation:
3d÷3=-81÷3
d=27
hope i helped :D
Which equation represents this proportional relationship
y=3x
y=1/6x
y=6x
y=1/3x
Answers
Answer:
I think that, please check it y=3x
what is a short introduction of the story happy prince?
Answers
Answer:
happy prince was born and one day he died
please help me with this
Answers
Answer:
14/18 =0.7778
Step-by-step explanation:
14/18 =0.7777.........=0.7778 rounded to the nearest thousandth
Solve for h.
-12h + 4 = 0
Answers
Answer:
[tex]h=1/3[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-12h+4=0[/tex]
Subtract 4 from both sides:
[tex](-12h+4)-4=(0)-4\\-12h=-4[/tex]
Divide both sides by -12:
[tex](-12h)/-12=(-4)/-12\\h=-4/-12[/tex]
Simplify and reduce:
[tex]h=1/3[/tex]
Answer:
h =1/3
Step-by-step explanation:
[tex]-12h + 4 = 0\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\-12h+4-4=0-4\\\\\mathrm{Simplify}\\-12h=-4\\\\\mathrm{Divide\:both\:sides\:by\:}-12\\\frac{-12h}{-12}=\frac{-4}{-12}\\\\Simplify\\h=\frac{1}{3}[/tex]
Please help me with my assignment. I need to past this tom :(
Answers
Answer:
Step-by-step explanation:
a. 128
b.148
c.178
d.167
e.295
Solve for x in the simplest form 11=1/2(x+8)
Answers
Answer:
[tex] \boxed{\sf x = 14} [/tex]
Step-by-step explanation:
Solve for x:
[tex] \sf \implies 11 = \frac{1}{2} (x + 8)[/tex]
[tex] \sf 11 = \frac{1}{2} (x + 8) \: is \: equivalent \: to \: \frac{1}{2} (x + 8) = 11 : [/tex]
[tex] \sf \implies \frac{1}{2} (x + 8) = 11[/tex]
[tex] \sf Multiply \: both \: sides \: of \: \frac{1}{2} (x + 8) = 11 \: by \: 2 : [/tex]
[tex] \sf \implies \frac{1}{ \cancel{2}} (x + 8) \times \cancel{2 }= 11 \times 2[/tex]
[tex] \sf \implies 1(x + 8) = 11 \times 2[/tex]
11 × 2 = 22:
[tex] \sf \implies x + 8 = 22[/tex]
Subtract 8 from both sides:
[tex] \sf \implies x + (8 - 8) = 22 - 8[/tex]
8 - 8 = 0:
[tex] \sf \implies x = 22 - 8[/tex]
22 - 8 = 14:
[tex] \sf \implies x = 14[/tex]
The value of x is 4, for the equation 11 = 1/2 (x + 8).
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
11 = 1/2 (x + 8)
Simplify the equation by multiplying 2 in both the sides,
11 × 2 =2 × 1/2 × (x + 8)
22 = x + 8
Subtract 8 from both the sides,
22 - 8 = x + 8 - 8
14 = x
or x = 14
The required value of x for the given equation is 14.
To know more about Equation on:
https://brainly.com/question/187506
#SPJ2
please help :) Evaluate the expression: 75+125÷25×5 A.1.6 B. 40 C. 100 D. 76
Answers
Answer:
C = 100
Step-by-step explanation:
PEMDAS
multiplication and division first from left to right so
125/25 = 5
5x5 = 25
25 + 75 = 100
Answer:
C. 100
Step-by-step explanation:
To complete this question you must use systems of equations.
First you must complete multiplication or division depending on which comes first in the left to right sequence. In this case it is 125/25 which equals 5. This now makes the equation 75+5 x 5
Next, you complete any other division or multiplication Which in this case is, 5x5. The answer to this is 25, making the new equation, 75+25 which when added together equals 100!
And that is how you use systems of equations. Hope it helps ;)
Expand and simplify 5(2x-1) -2(3x+2) First person to answer gets brainliest !!
Answers
Simplified: 4x-9
Answer:
[tex] \boxed{ \mathsf{ \bold{ \purple{ 4x - 9}}}}[/tex]Step-by-step explanation:
[tex] \mathsf{5(2x - 1) - 2(3x + 2)}[/tex]
Distribute 5 through the parentheses
[tex] \mathsf{10x - 5 - 2(3x + 2)}[/tex]
Distribute 2 through the parentheses
[tex] \mathsf{10x - 5 - 6x - 4}[/tex]
Collect like terms
[tex] \mathsf{4x - 5 - 4}[/tex]
Calculate
[tex] \mathsf{4x - 9}[/tex]
Hope I helped!
Best regards!
Jose Plans to make a down payment plus monthly payments in order to buy a Harley Davidson motorcycle. At one dealership, he would pay $8,000 down and pay $250 each month. At another dealership, he would pay $10,000 down and pay $125 each month. After how many months would the payment be the same for both dealers? What will that amount be?
Answers
a) 16 month
b) $12 000
Step-by-step explanation:$8000 + 250m = $10000 + 125m
250m - 125m = $10000 - $8000
125m = $2000
m = $2000 : 125
m = 16 months
After how many months would the payment be the same for both dealers ?16 months
What will that amount be ?$8000 + $250×16 =
= $8000 + $4000
= $12000
$10000 + $125×16 =
= $10000 + $2000
= $12000
What slope is parallel to m=3/4
Answers
Answer:
[tex]\large \boxed{{m= \frac{3}{4} }}[/tex]
Step-by-step explanation:
Parralel lines have the same slope.
The slope will be [tex]\frac{3}{4}[/tex]
The line with a slope m = 3/4, the slope of the line parallel to this line will also be 3/4
The slope is the measure of the steepness of a line. It is also known as the gradient of a line.
Two parallel lines are known to have equal slopes. For example;
The line y = 2x - 5 and y = 2x + 3 are parallel because they have the same slope which is 2.Therefore for the line with a slope m = 3/4, the slope of the line parallel to this line will also be 3/4
Learn more here: https://brainly.com/question/12557573
1. Three times the the difference between x and five?
2. One half times a number increased by six?
Answers
Answer:
Step-by-step explanation:
1. 3(x - 5)
2. 0.5x + 6.
Answer:
1) 3(x-5)
2) 1/2x+6
Step-by-step explanation:
Three times the difference between x and five.
Three times=3* or 3(
difference between x and five= x-5
Together it will be
3(x-5)
One half times a number increased by six
One half times a number= 1/2x
increased by six= +6
Together it will be
1/2x+6
Hope this helps ;) ❤❤❤
Help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
by the way and the answer is c for yhe reasin because the of tje by theand i thaith
-5-(-7)
Full work plz
Answers
Answer:
-5 - (-7) = 2Step-by-step explanation:
-5 - (-7) = -5 + 7 = (-5) + (7) = (7) + (-5) = 7 - 5 = 2
hii:) anyone able to help with practice 6? Thanks:)!
Answers
Answer:
The answer is
[tex]x = \frac{ {e}^{ \frac{3}{ ln(2) } } }{4} [/tex]Step-by-step explanation:
[tex] ln(2) \times ln(4x) = 3[/tex]Divide both sides of the equation by ln 2
That's
[tex] \frac{ ln(2) ln(4x) }{ ln(2) } = \frac{3}{ ln(2) } [/tex]We have
[tex] ln(4x) = \frac{3}{ ln(2) } [/tex]Covert the logarithm into exponential form using the property
[tex] ln(x) = b\: \: is \: \: \: the \: \: \: same \: \: \: as \: \: \: \:
x = {e}^{b} [/tex]Are all the same
So
[tex] ln(4x) = \frac{3}{ ln(2) } [/tex]is the same as
[tex]4x = {e}^{ \frac{3}{ ln(2) } } [/tex]Divide both sides by 4
We have the final answer as
[tex]x = \frac{ {e}^{ \frac{3}{ ln(2) } } }{4} [/tex]Hope this helps you
Enter the mixed number as an improper fraction. 2 3/8 =
Answers
Answer:
19/8
Step-by-step explanation:
To find the mixed number
Take the denominator times the whole number
8*2 = 16
Add the numerator
16+3 = 19
Put this over the denominator
19/8
Step by step please: x^3+2x^2-5x-6=0
Answers
Answer:
x=-1, x=2, x=3
Step-by-step explanation:
Factor the left side of the equation.
(x+1)(x^2+x-6)
(x+1)(x-2)(x-3)
Now set everything equal to 0
x+1=0
x-2=0
x-3=0
Now solve for x
therefore, the answer is x=-1, x=2, x=3
Rewrite 2/20 : 1/40 as a unit rate
Answers
Answer:
[tex]\frac{4}{1}[/tex]
Step-by-step explanation:
Given:
2/20 : 1/40
A). First re-write the ratio as follows;
(i) Change the ratio sign to division (÷). i.e
2/20 ÷ 1/40
(ii) Solve the expression by changing the division to multiplication(×). This also means you will need to swap the numerator and the denominator of the second term. i.e (1 / 40) becomes (40 / 1)
(2/20) × (40 / 1) = [tex]\frac{2}{20}[/tex] × [tex]\frac{40}{1}[/tex] = [tex]\frac{4}{1}[/tex]
B). Now convert the result from above to unit rate. A unit rate is a rate in which the denominator has a value of 1.
So to convert [tex]\frac{4}{1}[/tex] to unit rate, we keep simplifying until the denominator becomes 1.
And since the denominator is already 1, there is no need for further simplification.
Therefore, 2/20 : 1/40 to unit rate is [tex]\frac{4}{1}[/tex]
Answer:4/1
Step-by-step explanation:
I say this because you are supposed to divided it and the answer is 4 then you find the answer choice with a 1 as the denominator and it should say 4/1 and that is the correct answer.
2.67 (7 repeating) as a fraction
Answers
Answer:
241/90 or 2 61/90
Step-by-step explanation:
Let's call the given number 2.67(7) = x
Then use below steps:
10x = 26.7(7)100x = 267.7(7)100x - 10x = 241 ⇒ subtract to get rid of the repeated part90x=241 ⇒ solve to get fractionx= 241/90 = 2 61/90 ⇒ answer241/90
2 61/90
Step-by-step explanation:2.67(7) =
= (2677 - 267)/900
= 2410⁽¹⁰/900
= 241/90
= 2 61/90
Point c d and g lie on plane x. Point e and f lie on plane y. Which statements are true
Answers
The true statements are: 3, 4 and 5
Step-by-step explanation:
search it up
Answer:
2,3,and 4
Step-by-step explanation:
What is an equation of the line that passes through the points (6,2) and (-6, -8)?
Put your answer in fully reduced form.
Answers
Step-by-step explanation:
Hey, there!!
Let me simply clear you.
The given points are (6,2) and (-6,-8).
Remember if you are finding the equation of the line passing through point, you will get equation in slope intercept form.
If there is two point you simply use one point formula. {i.e (y-y1)= m(x-x1)} (as the slope will be given too).If you are finding the equation for two points then use double point formula for the equation. { i.e (y-y1) = (y2-y1/x2-x1) × (x-x1)}.As in your question there are two points we must use double point formula,
[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]
[tex]( y - 2) = \frac{ - 8 - 2}{ - 6 - 6} (x - 6)[/tex]
Simplifying them we get,
6(y-2)= 5(x-6)
6y - 12 = 5x -30
Therefore, 5x - 6y - 18 = 0 is the required equation.
Hope it helps.....