A flagpole casts a 40-foot shadow. The angle of elevation from the tip of the
shadow to the tip of the flagpole is 34. How tall is the flagpole? Round your
answer to the nearest foot.
A. 29 feet
B. 22 feet
C. 27 feet
D. 33 feet
Answers
Answer:
27 Feet is the answer. Option C.
The flagpole is 27 feet tall.
What is right triangle?"It is a triangle whose one of the angle measures 90° "
What is tangent of angle?For angle [tex]\theta[/tex], [tex]tan(\theta)=\frac{opposite ~side~of~angle~\theta}{adjecent~side~of~angle~\theta}[/tex]
What is angle of elevation?"An angle that is formed between the horizontal line and the line of sight. "
For given question,
Consider the following diagram.
Here, AB = the flagpole,
A flagpole casts a 40-foot shadow.
so, BC = 40 foot
The angle of elevation from the tip of the shadow to the tip of the flagpole is 34°.
⇒ ∠ACB = 34°
We need to find the height of the flagpole.
We find the tan of angle 34°
[tex]\Rightarrow tan(34)=\frac{AB}{BC}\\\\ \Rightarrow 0.6745=\frac{AB}{40}\\\\\Rightarrow AB=0.6745\times 40\\\\\Rightarrow AB = 26.98\\\\\Rightarrow AB\approx 27~feet[/tex]
Therefore, the flagpole is 27 feet tall.
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Integrate the following:
[tex]\displaystyle \int \frac{x^2}{x^2+x+3}\, dx[/tex]
Answers
Answer:
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx = - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Completing the SquareRearranging VariablesAlgebra II
Long DivisionCalculus
U-Substitution[Integration Trick 1] Numerator Split[Integration Trick 2] Completing the SquareIntegration Rule 1: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Rule 2: [tex]\int {f(x)+g(x)} \, dx =\int {f(x)} \, dx + \int {g(x)} \, dx[/tex]Integration 1: [tex]\int {\frac{1}{u} } \, du =ln|u| + C[/tex]Integration 2: [tex]\int {\frac{du}{u^2+a^2} } = \frac{1}{a} arctan(\frac{u}{a} )+C[/tex]Integration 3: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} +C[/tex]Step-by-step explanation:
Step 1: Define
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx[/tex]
Step 2: Simplify Function
We do long division to simplify the function inside the function.
See Attachment for Long Division Work.
Once we do long division, our function becomes [tex]1-\frac{x+3}{x^2+x+3}[/tex]
Now we rewrite our Integral: [tex]\int ({1-\frac{x+3}{x^2+x+3} }) \, dx[/tex]
Step 3: Integrate Pt. 1
Distributive Integral [Int Rule 1]: [tex]\int {1} \, dx - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Integrate 1st Integral [Int 3]: [tex]x - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Step 4: Identify Variables Pt.1
Set variables for u-substitution.
u = x² + x + 3
du = (2x + 1)dx
Step 5: Integrate Pt. 2
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Set variables for u-substitution for 2nd integral.
z = x + 1/2
dz = dx
a = √(11/4)
Step 7: Integrate Pt. 3
[Integrate] U-Substitution: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + \int {\frac{5}{z^2 + (\sqrt{\frac{11}{4}})^2} } \, dz ][/tex]Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 1st Integral [Int 1]: [tex]x - \frac{1}{2} [ln|u| + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 2nd Integral [Int 2]: [tex]x - \frac{1}{2} [ln|u| + 5(\frac{1}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ) ][/tex]Distribute 5 [Alg]: [tex]x - \frac{1}{2} [ln|u| + \frac{5}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ][/tex]Distribute -1/2 [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5}{2\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Rationalize [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5\sqrt{11} }{11}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Resubstitute variables [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{x+\frac{1}{2} }{\sqrt{\frac{11}{4} } } )[/tex]Simplify/Rationalize [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} )[/tex]Rewrite [Alg]: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x[/tex]Integration Constant: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]And we have our final answer! Hope this helped you on your Calculus Journey!
hope this will help you........
I need help please!!!!!
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The Reiter family uses three different-sized scoops to serve mashed potatoes : blobs, globs and gobs (these names are so weird aren't they). 2 blobs are equal to 1 glob, and 5 globs equal 3 gobs of mashed potatoes. A bowl holds 12 gobs of potatoes. How many blobs are there in the bowl? RATIO PROBLEM!!! DUH, DUH, DUHHHHHHH.
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Answer: 30 blobs
Step-by-step explanation:
The ratios are:
2 blobs: 1 glob
5 globs: 3 gobs
If the bowl can hold 12 gobs, then we can multiply the 5:3 ratio by 4, to make solving easier. We get the ratio 15:12 and then we need to multiply the 2:1 ratio by 15 to get the answer 30 blobs
Write the rate below in simplest form?
12: 144
A.3:36
B.4:48
C.1:12
D.6:72
Answers
Answer:
C. 1:12Step-by-step explanation:
12 : 144 = 1 : 12 divide both numbers by 12Correct option is C
Core Algebra
Englis
Solving for an Unknown Using the Distributive Property
180(n-2)
The equation a = represents the angle measuresya, in a regular n-sided polygon. When the equation is
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Answer:
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Step-by-step explanation:
I got it right
Find the slope between the points: (3,4) and (-1,-2)
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Answer:
3/2 hope this helps hqhahjajja
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Answer:
(-1,-2)
Step-by-step explanation:
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You basically take the point D and keep your y coordinate, -2, the same /constant and change your x coordinate (flip the sign)
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So.. D's location reflected on the y axis is (-1,-2)
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So...
D's location reflected on the x-axis is (1,2)
Determine the area of the rectangle
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Answers
Answer:
Step-by-step explanation:
multiply the two expressions
(6x + 3)(x + 5)
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simplify if needed
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The box plots below show the miles per gallon (mpg) ratings distribution for three types of cars.
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can yall do the work of the answer 95 to this
Answers
9514 1404 393
Answer:
? = 95°
Step-by-step explanation:
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K=4.29
The value of k is 4.29. Hope this help
Which expression is equivalent to (4 + x) + 12?
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A water tank fills through two pipes. Water flows in
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and in through the other pipe at a rate of 45,000
gallons per hour. Water leaves the system at a rate of
60,000 gallons per hour.
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Answer:
130,000
Step-by-step explanation:
Answer:oh hey yulissa ✌️
Step-by-step explanation:
The vertical cross-sectional shapes of this prism are all congruent triangles.
A. True
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Answer:
false
Step-by-step explanation:
I hope i helped :)
The vertical cross-sectional of a triangular prism gives a quadrilateral shape.
What is a three dimensional shape?A three dimensional shape is a shape that have length, width and height. Example of three dimensional shapes are prism, pyramid, cone, cylinder and so on.
A triangular prism have two triangular bases and three quadrilateral lateral faces
The vertical cross-sectional of a triangular prism gives a quadrilateral shape.
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Plz help me get the right answer
Answers
This is because have of 10 is 5
And you would only fill in half a circle after that
Hope this helps
Answer: Choice H (upper right corner)
====================================================
Explanation:
Refer to the diagram below.
I started with the set of five circles you were given. Then I cut each of them in half. This results in 2*5 = 10 sections (each section is numbered in blue). If you shade 9 of those 10 sections, then you'll represent the fraction 9/10. This is what choice H represents, so that's why it's the answer
9/10 = 0.90 in decimal form
0.90 = 90% in percent form
need help ASAP mid term .
- 60 points
Answers
the metal bar/random line is almost the same size as the other two sides of the triangle. if one side is 32ft, then the opposite side is 32ft also. the bottom is 100ft, so we could eliminate C. because it couldnt be that number. now the bottom triangle, one side is 40ft so the other side has to be 40ft as well. its asking about the metal bar.
its either:
A. 53.2ft or
B. 44.4
because the line is almost the same size as 32ft. its almost a equallateral triangle. i would go with A. though because if you imagine the line at the bottom of the line (100ft.) the line would go over half of it (and 53.2 is over half of 100) so i would say
A.53.2
if this didnt help let me know. and i will delete this (if i can-)
5. Evaluate 13 + 6 + 7 + 4.
b. 29
a. 2184
c. 20
d. 30
Answers
Answer:
D is the answer for the question
Answer:
30/D
Step-by-step explanation:
just add the numbers :)
50 points.
Record the simplified expression
Answers
Answer:
-4x+5
Step-by-step explanation:
-(4x-2) change sign of each in parenthesis so they are now -4+2
now you have -4x+2+3 add like terms
now you have -4x+5
[tex]\sf \longmapsto−4x+2+3[/tex]
Combine like terms[tex]\sf \longmapsto−4x+2+3[/tex]
[tex]\sf \longmapsto(−4x)+(2+3)[/tex]
[tex]\sf \longmapsto−4x+5[/tex]
cuánto es 120 por 12
Answers
Answer:
120 x 12 = 1440
Step-by-step explanation:
Answer:
es 1440
Step-by-step explanation:
solo pones 120
x12
help please I will give brainiest
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If not I’m sorry
Donna wants to calculate the height of a tree. She finds the length of the tree's shadow is 25 meters and the angle of elevation from the ground to the top of the tree is 30°. Find the height of the tree to the nearest whole number.
Answers
Answer:55
Step-by-step explanation:
a plank is 6.7 feet long. Arachna wants to cut the plank into 0.8-foot pieces. how many 0.8-foot pieces can she get?
Please help- i need this urgently
Answers
Answer: 8
Step-by-step explanation:
You have to divide 6.7/0.8 and you'll get your answer. She'll be able to use 8 full pieces.
Ms. Guthrie spent 80% of her cash on gifts.
What fraction of her cash did she spend on gifts?
She spent type your answer...
of her cash on gift.
Answers
Answer:
She spend (8/10) or (4/5) of her cash on gift.
Step-by-step explanation:
4/5 is simplified.
but not simplified its 8/10
Explain how you know when 2 ratios are proportional.
Answers
Answer:
Ratios are proportional when they represent the same relationship.
Step-by-step explanation:
Such as: finding equivalent fractions
Answer:
Ratios are proportional if they represent the same relationship.
Step-by-step explanation
One good way to tell is to make them fractions and then reduce them. If the reduced fractions are the same, you ratio is proportional! Good luck !
Can somebody help please
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What is the question?
someone please help!! 60 points!!
Answers
Answer:
It C am sure it correct....
Answer:
I think the answer would be C.
