A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall. What angle will a 35-ft. ladder make the horizontal if it reaches the sample spot?
Answers
The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is .
Given that,
A 30-ft. ladder makes an angle of 60 degrees with the horizontal.
We have to find,
The angle will a 35ft.ladder make the horizontal if it reaches the sample spot.
According to the question,
A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall.
h = 30sin60
Then, the angle will a 35-ft. ladder make the horizontal if it reaches the sample spot.
Hence, The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is
For more information about Trigonometry click the link given below.
sin60=h/30
h=30sin60
Now we can find the angle that the 35 ft ladder make when it touches the same spot.
sinα=h/35 and using h we found earlier...
sinα=(30sin60)/35
α=arcsin[(30sin60)/35]
α≈47.93 (α≈47º55'42")
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You need 2.5 pounds of potatoes. If each potato weighs 5 ounces, how many potatoes will you need?
Answers
Answer:
If six people all shake hands with each other, how many hand shakes were made in total?
Publish your book. Become an author in 15 days. Get published.
I assume that no two people shake hands if they've already shaken them earlier, irrespective of who initiated it.
In that case Guest 1 will shake hands with 5 others (Guest 2 to 6)
Guest 2 will shake hands with 4 others (Remember she's already shaken hands with Guest 1).
Guest 3 will shake hands with 3 others (having already shaken hands with Guest 1 and 2)
and so on.....
We end up with 5+4+3+2+1 handshakes or 15 handshakes in all!
Step-by-step explanation:
please mark me as a brainlist...
Answer:
15 handshakes
Step-by-step explanation:
the 1st person shakes hands with 5 people
the 2nd person shakes hands with 4 people
the 3rd person shakes hands with 3 people
the 4th person shakes hands with 2 people
the 5th person shakes hands with 1 person
the 6th person shakes hands with no one
5+4+3+2+1=15
Answers
Answer:
a) 0.2588
b) 0.044015
c) 0.12609
Step-by-step explanation:
Using the TI-84 PLUS calculator
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question, we know that:
μ = 119 inches
standard deviation σ = 17 inches
(a) What proportion of trees are more than 130 inches tall?
x = 130 inches
z = (130-119)/17
= 0.64706
Probabilty value from Z-Table:
P(x<130) = 0.7412
P(x>130) = 1 - P(x<130) = 0.2588
(b) What proportion of trees are less than 90 inches tall?
x = 90 inches
z = (90-119)/17
=-1.70588
Probability value from Z-Table:
P(x<90) = 0.044015
(c) What is the probability that a randomly chosen tree is between 95 and 105 inches tall?
For x = 95
z = (95-119)/17
= -1.41176
Probability value from Z-Table:
P(x = 95) = 0.07901
For x = 105
z = (105 -119)/17
=-0.82353
Probability value from Z-Table:
P(x<105) = 0.2051
The probability that a randomly chosen tree is between 95 and 105 inches tall
P(x = 105) - P(x = 95)
0.2051 - 0.07901
= 0.12609
4 sin^2 x - 4 sin x + 1 = 0
Answers
Answer:
friends, how far do you drive?
Answers
You drive a total distance of 49.4 kilometers when you travel 27.54 kilometers to school and then 21.86 kilometers to your friend's house.
When you drive 27.54 km to school and then 21.86 km to your friend's place, you are covering a total distance of 49.4 kilometers. To calculate this, you simply add the two distances together:
Distance to school: 27.54 km
Distance to friend's place: 21.86 km
Total distance = 27.54 km + 21.86 km = 49.4 km
So, you drive a total of 49.4 kilometers when you travel to both school and your friend's house. This cumulative distance is the sum of the individual distances you cover for each leg of your journey. It's important to keep track of such distances, especially if you want to estimate fuel consumption, plan your commute, or calculate travel time accurately. In this case, you've covered 49.4 kilometers in total, which is the combined distance for your trip.
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Answer:
49.4 km
Step-by-step explanation:
you add 27.54 plus 21.86 so 49.4 km total between school and to your friends house
Answers
The required sum of -3x, 5x + y, and 7x - 8 - 3y in descending order is 9x - 2y - 8.
What is simplification?
Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
To add -3x, 5x + y, and 7x - 8 - 3y, we can first combine like terms.
Group the x-terms together:
-3x + 5x + 7x = 9x
Group the y-terms together:
y - 3y = -2y
Group the constants together:
-8
Putting it all together, we get:
9x - 2y - 8
Therefore, the sum of -3x, 5x + y, and 7x - 8 - 3y in descending order is 9x - 2y - 8.
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F I N A L A N S W E R
66
32
29
43
Answers
Answer:
The correct answer is x = 32.
Step-by-step explanation:
To solve this problem, we must remember the concept of supplementary angles. Two angles that are supplementary together make an angle of 180 degrees (a straight line).
In this case, we can see that inside the triangle, we will have an angle of 80 degrees. We know this because the angle at the top of the triangle is supplementary with the angle measuring 100 degrees, so its measure should be 180-100 = 80 degrees.
On the lower right hand of the triangle, a similar rationale can be applied. The angle inside of the triangle must measure 68 degrees, since it is supplementary to an angle measuring 112 degrees, and 180-112=68.
Finally, to solve this problem, we must remember that the sum of the three interior angles of a triangle should be 180 degrees. This lets us set up the following equation:
80+68+x = 180
Now, we can solve this equation. Our first step is to simplify the left side of the equation by adding together the constant terms.
148 + x = 180
Next, we should subtract 148 from both sides of the equation.
x = 180-148
x = 32
Therefore, the correct answer is x = 32 degrees.
Hope this helps!