The angle of depression of the top and the foot of a flagpole as seen from the top of a building 145 metres away are 26° and 34° respectively. Find the heights of the pole and the building.
The height of the pole and the building are 27.1 meters and 97.8 meters respectively.
How to find the height of the pole and the building?The situation forms a right angle triangle. The height of the building can be found using trigonometric ratios,
Therefore,
tan 34 = opposite / adjacent
tan 34 = h / 145
h = 145 tan 34
h = 145 × 0.67450851684
h = 97.8037349422
Therefore,
height of the building = 97.8 meters
tan 26 = x / 145
x = 145 tan 26
x = 70.721225342 meters
Therefore,
height of the flagpole = 97.8 - 70.7 = 27.1 meters
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please answer this question
[tex] \bold{\underline{\underline{\underbrace{Answer}}}} [/tex]
x = p and y = -q
Step-by-step explanation:
To findThe value of x and y
Givenpx + qy = p² - q²(equation 1)
qx - py = 2py
Solution{Taking equation 2}
[tex] \sf qx - py = 2py[/tex]
{Taking py on RHS}
[tex] \sf qx = 2py \ + py [/tex]
{Dividing both sides by q
[tex] \sf x = \frac{2pq}{q} + \frac{py}{q} \\ \\ \sf x = 2p + \frac{py}{q} (equation \: 3)[/tex]
{Now substituting the value of equation 3 in equation 1}
[tex] \sf p(2p + \frac{py}{q} ) + qy = {p}^{2} - {q}^{2} \\ \\ \sf 2 {p}^{2} + \frac{ {p}^{2}y }{q} + qy = {p}^{2} - {q}^{2} [/tex]
{Taking 2p² on RHS and taking LCM on LHS}
[tex] \sf \frac{ {p}^{2}y + {q}^{2} y }{q} = {p}^{2} - {q}^{2} - 2 {p}^{2} \\ \\ \sf \frac{y( {p}^{2} + {q}^{2} ) }{q} = - ( {p}^{2} + {q}^{2} )[/tex]
{Dividing (p² + q²) both sides}
[tex] \sf \frac{y}{q} = - 1 \\ \\ \red{ \boxed {\bold{y = - q}} }[/tex]
{Now using value of y in equation 3}
[tex] \sf x = 2p - \frac{pq}{q} \\ \\ \sf x = 2p - p \\ \\ \red{ \boxed{ \bold{ x = p}}}[/tex]
The beginning balance in a person's checking account was -10 dollars. After writing three checks for 8, 10 and 17 dollars and making a deposit of 90 dollars, what was the new balance in the account?
Answer:
45
Step-by-step explanation:
he have -10$ that means he have loan
he withdraw 8,10and 17 dollars
now his balance is -45$
now he deposited 90 dollars
now
=90-45$
=45$
If a bag of marbles contains 10 blue and 30 green, what is the complement for the probability of choosing a green marble.
Answer:3/4
Step-by-step explanation:there are 30+10=40 marble
you choose 30 green. 30/40=3/4
What is the equation of the line?
Answer:
y=1/2x+2
Step-by-step explanation:
I found this out just by looking at the line
Find the slope.
y= X/3 + 4
M= ?/?
Answer:
m=1/7
Step-by-step explanation:
The slope of y=x/3 + 4 is 1/7.
x/3+4 = x/7 so m = 1/7.
Answer:
m = 1/3
Step-by-step explanation:
The equation given is in slope-intercept form, which has the basic structure:
y = mx + b
In this equation, "m" is the slope and "b" is the y-intercept.
The value of "b" is 4.
The value of "m" is 1/3. This is because (x/3) is the same as (1/3 times x).
find the value of x. cos(67°) = 1/x
[tex]~~~~~\cos 67^{\circ} = \dfrac 1x\\\\\\\implies x = \dfrac 1{\cos 67^{\circ}}\\\\\\\implies x = 2.55[/tex]
A borrower has been approved for a loan of $5,000 at 8% interest. The loan will be repaid in nine months. What amount will be repaid at that time?
Answer:
Just multiply 5000 * 0.08, which equals 400.
400 + 5000 = 5400
The borrower will repay $5400 at the end of nine months.
Step-by-step explanation:
Need help thank you
A group of friends were working on a student film that had a budget of $1200. They used 62% of their budget on props. How much money did they spend on props?
ANSWER ASSAP PLEASE
Answer:
helloo!!!!
first up first.... i love your profile pic....
oh and the answer is 744..
please read the explanation... it always helps!!
Step-by-step explanation:
alrighty..
so the total budget is 1200, and we want to know how much is 62% of that
so you follow the percent formula as follows:
1200/100= 12 --> 12 x 62= 744 (which is the answer!)
Using the table below, what is the probability of selecting a girl or someone who likes Michigan?
Ohio State
Michigan
NC State
Total
Boys
56
14
20
90
Girls
50
22
38
110
Total
106
36
58
200
Using the table of values, the probability of selecting a girl that likes Michigan is 0.11
How to determine the probability?The table is given as:
Ohio State Michigan NC State Total
Boys 56 14 20 90
Girls 50 22 38 110
Total 106 36 58 200
In the above table, 22 girls out of the total sample size of 200 like Michigan.
This means that the required probability is:
P = 22/200
Evaluate the quotient
P = 0.11
Hence, the probability of selecting a girl that likes Michigan is 0.11
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due to inflatation, the cost of harys hot wings grows by 4% every year. this year a dozen hot wings cost 5.99
part a. how much will a dozen hot wings cost next year
part b. how much will a dozen hot wings cost in 2 years
Answer:
Part A : $6.23
Part B : $6.48
Step-by-step explanation:
Let's apply the Simple Interest Formula, which is :
Simple Interest = Principal Amount x Interest rate x Time Period
In one year :
I = 5.99 x 4% x 1I = $0.24Cost = $5.99 + $0.24Cost = $6.23In 2 years :
I = $6.23 x 4% x 1I = $0.25Cost = $6.23 + $0.25Cost = $6.48Lillian and Mackenzie clean rooms at a hotel. Today, they cleaned the same number of rooms, but Mackenzie worked fewer hours. Tomorrow, their shifts are the same length. Who will likely clean more rooms?
Answer:Mackenzie
Step-by-step explanation:
Answer:
Step-by-step explanation:
Mackenzie
10.4 sides polygon with 2 sides of parallel sides. What type of polygon is it?
Answer:
Here is the answer:
Step-by-step explanation:
An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent. A kite is a quadrilateral with exactly two pairs of adjacent congruent sides.
Match the numbers with the correct label.
Answer:
a = 1/7b = 0.2c = 3/9Step-by-step explanation:
Converting all fractions to decimal (for easier comparison) :
0.21/7 = 0.143/9 = 0.33Hence,
First point (a) = 1/7Second point (b) = 0.2Third point (c) = 3/9If Mrs. Hamm divides 7 pounds of potting soil equally into three flower pots, what is the weight of potting soil in one flower pot? A) 3 7 pound B) 7 3 pounds C) 3 1 7 pounds D) 7 1 3 pounds
The weight of potting soil in one flower pot is 7/3 pounds or 2.34 pounds option (B) is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have total weight of the potting soil = 7 pounds
It is divided equally into three flower pots.
So each pot contains = 7/3 potting soil
Thus, the weight of potting soil in one flower pot is 7/3 pounds or 2.34 pounds option (B) is correct.
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look at the image and please help
A solid aluminum sculpture in the shape of a rectangular prism has a mass of 129, 600 kilograms. The length of the sculpture is 6 meters, the width is 2 meters, and the height is 4 meters. What is the density of aluminum?
If the volume of the aluminum will be 48 cubic m. Then the density of the aluminum will be 2700 kg per cubic m.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
Density = mass/volume
A solid aluminum sculpture in the shape of a rectangular prism has a mass of 129,600 kilograms.
The length of the sculpture is 6 meters, the width is 2 meters, and the height is 4 meters.
Then the density of the aluminum will be
The volume of the aluminum brick will be
V = 6 x 2 x 4
V = 48 cubic m
Then the density will be
D = 129600/48
D = 2700 kg per cubic m
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Directions: Write your answers on your paper.Show your solutions with checking.
#1. Convert the decimal number 10 to a binary digit.
#2.Give the types of Mult-meter (VOM) and differential each function.
Nonsense = Reported!!
Answer:
1010See below ~Step-by-step explanation:
Q1
Decimal number 10 written in binary terms is 1010Q2
There are different types of multimeters like Analog, Digital, and Fluke multimetersFunctions :Resistance in OhmsCapacity in FaradsThe temperature in Fahrenheit/ CelsiusAC Voltage & AmperageInductance HenrysDC Voltage & AmperageFrequency in HzConductance in SiemensDecibelsDuty Cyclehope it helps you
# 1
Conversion of decimal number 10 into binary is:
10 / 2 = 5 with remainder 0
5 / 2 = 2 with remainder 1
2 / 2 = 1 with remainder 0
1 / 2 = 0 with remainder 1
Therefore, the 10 in decimal is equal to 1010 in binary.
# 2
Analog multimeters are multifunction electrical measuring instruments with indicationby means of an arrow (analog) scale.
Modern analog multimeter
Advantages of analog multimeters:
Possibility to carry out measurements at low temperatures down to -30 ° С.Fast operation with a large amount of measurements, when high precision is not required.Do not require power consumption from the built-in power supply in the mode of voltage and current measurement.Instant display of the dynamics of the signal change.
Disadvantages and features:
Non-linear scale and setting zero before starting measurements.Absence of automatic detection of voltage polarity.A small set of functions: most models can measure only DC and AC voltage, DC current and resistance.Low input resistance and, consequently, a high error in low-voltage measurements.Sensitivity to mechanical damage, vibration.
Digital multimeters are modern, reliable measuring devices characterized by high measurement accuracy and various functional capabilities. Digital devices have replaced analogue in connection with the possibility of wide application of semiconductor technologies. Today most of the produced multimeters are digital. Specialists working with electrical equipment, if necessary, can choose among the digital multimeters a model focused on a specific task.
Advantages of digital multimeters:
Maximum possible measurement accuracy.Automatic polarity detection: If the probes are connected incorrectly, the correct values with a minus sign appear on the screen.Possibility of automatic and manual selection of measuring ranges.Multifunctionality.Does not require mandatory zero adjustment.The accuracy of the meter reading does not depend on the battery charge.Resistance to mechanical damage.The ability to record measurement results in memory and synchronize with a PC.
I need to solve for X
Check the picture below.
Which expression best represents the areas of this square with sides in the photo below?
Answer: 9x⁴y⁶
Step-by-step explanation:
[tex](3x^{2}y^{3})(3x^{2}y^{3}) = 9x^{4}y^{6}[/tex]
Basically, when multiplied, integers multiply, and exponents add.Translate the problem into a mathematical sentence, using c as your variable
name. Do not use spaces in your answer.
Tom bought 13 CDs in December. Of those, 5 were jazz, the rest were
classical music. How many classical music discs did he buy?
Answer here
SUBMIT
c=8
Step-by-step explanation:
13-5=c, c=8
Molly gives 3% of her paycheck to a charity. If she makes $350 per week, how much goes to the charity?
Answer:
$10.50
trust me
answer:
342$
Step-by-step explanation:
Think about it........................ 77 + 33 =100
Between which two consecutive numbers does the root of 90 lie
Answer:
[tex]9 < \sqrt{90} < 10[/tex]
Step-by-step explanation:
Since [tex]9^2=81 < 90[/tex] and [tex]10^2=100 > 90[/tex], then [tex]9 < \sqrt{90} < 10[/tex]
There are 6 blue chips for every 4 green chips. How many green chips will there be with 15 blue chips?
Answer:
6
Step-by-step explanation:
Its simple,
first you find the multiplier, to do this you do:
6/4 which is 2.5
then we do 15 / 2.5
which is 6
what is the name of the first female mathematician?
Answer:
Hypatia was the first female mathmatican
Answer:
Hypatia, (born c. 355 ce—died March 415, Alexandria), mathematician, astronomer, and philosopher who lived in a very turbulent era in Alexandria's history. She is the earliest female mathematician of whose life and work reasonably detailed knowledge exists.
Step-by-step explanation:
verify the identity algebraically. Start on one side of the equation and manipulate using techniques to arrive at the other side
sin^2 − sin^4 = cos^2 − cos^4
Answer:
Step-by-step explanation:
sin^2 − sin^4 = cos^2 − cos^4
sin^2 (1-sin^2) = cos^2 − cos^4
sin^2 (cos^2) = cos^2 − cos^4
(1-cos^2) (cos^2) = cos^2 − cos^4
cos^2 − cos^4 = cos^2 − cos^4
Which is True :33 Send love
Please help me guys
a) If 2 Tan a = 3 Tan B, then show that Tan (a-B) =5 sin2b/5Cos 2B-1
Given that :-
2 tan A = 3 tan BProve that :-
Tan (a-B) = [ sin 2B/(5 – cos 2B)]Taking RHS :-
= sin 2B/(5 – cos 2B)] = [(2 tan B)/(1 + tan2B)]/ [5 – {(1 – tan2B)/(1 + tan2B)}]
= (2 tan B)/ [5(1 + tan2B) – 1 + tan2B]
= (2 tan B)/[5 + 5 tan2B – 1 + tan2B)
= (2 tan B)/(4 + 6 tan2B)
= (2 tan B)/[2(2 + 3 tan2B)]
= tan B/(2 + 3 tan B tan B)
Dividing the numerator and denominator by 2,
= [(1/2) tan B]/ [1 + (3/2) tan B tan B]
= [(3/2) tan B – tan B]/[1 + tan A tan B] {from (i)}
= (tan A – tan B)/(1 + tan A tan B)
= tan(A – B) = LHS
Write .0043 as a percentage
Answer:
0.43%
Step-by-step explanation:
In order to change a decimal to a percentage, you multiply it by 100. You can also move the decimal point to the right two times. By doing so, you get 0.43%. Someone tell me if I did it wrong please.
NEED HELP PLEASE!!!!!!
Answer:
i wish i knew im in the same situwantion
Step-by-step explanation: