Answers
9) Volume of the cone: [tex]9152 mm^3[/tex]
10) New volume of the cone: [tex]339 mm^3[/tex]
11) The volume of the cone shrinks by a factor of [tex]3^3=27[/tex]
12) Volume of the composite figure: [tex]15 ft^3[/tex]
Step-by-step explanation:
9)
The volume of a cone is given by the equation
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
where
[tex]\pi r^2[/tex] is the area of the base, where
r is the radius of the cone
h is the height of the cone
For the cone in this problem, we have:
r = 18 mm (radius)
h = 27 mm (height)
Therefore, the volume of this cone is
[tex]V=\frac{1}{3}\pi (18)^2 (27)=9152 mm^3[/tex]
10)
In this second exercise, the radius and the height of the cone are divided by 3. Therefore we have:
[tex]r'=\frac{r}{3}=\frac{18}{3}=6 mm[/tex] is the new radius of the cone
[tex]h'=\frac{27}{3}=9 mm[/tex] is the new height of the cone
Therefore, the new volume of the cone is
[tex]V=\frac{1}{3}\pi r'^2 h'[/tex]
And substituting, we find
[tex]V=\frac{1}{3}\pi (6)^2 (9)=339 mm^3[/tex]
11)
We can understand what happened to the volume of the cone after dividing its dimensions by 3 by calculating the ratio of the original volume to the new volume:
[tex]\frac{V}{V'}=\frac{9152}{339}=27[/tex]
This means that the new volume of the cone is 27 times smaller than the original volume.
We see that this "factor of shrinking" corresponds to the total factor of shrinking ofits dimensions, to the power of 3. In fact:
- Each the radius and the height of the cone has shrunk by a factor of 3
- However, the cone is a figure in 3 dimensions, so the total factor of shrinking of its volume is [tex]3^3 = 27[/tex]
12)
The composite figure consists of a squared pyramid + a parallelepiped.
The volume of the square pyramid is given by:
[tex]V_1 = \frac{1}{3}Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 6 ft is the height of the pyramid
Substituting,
[tex]V_1 = \frac{1}{3}(5)(1)(6)=10 ft^3[/tex]
The volume of the parallelepiped is given by
[tex]V_2=Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 1 ft is the height
Substituting,
[tex]V_2 = (5)(1)(1)=5 ft^3[/tex]
So, the total volume of the composite figure is
[tex]V=V_1+V_2=10+5=15 ft^3[/tex]
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Answer:
9) Volume of the cone: 9152 mm^3
10) New volume of the cone: 339 mm^3
11) The volume of the cone shrinks by a factor of 3^3=27
12) Volume of the composite figure: 15 ft^3
Step-by-step explanation:
Related Questions
I need help please and thank you
Answers
Answer: [tex]Perimeter= 71.75[/tex]
The parameter of a 2-D figure is the total length of its boundaries.
Step-by-step explanation:
In the given figure a hexagon is given with the length of its sides given in mixed fraction.
A mixed fraction can be solved by [tex]p\frac{x}{y} =\frac{(p*y)+x}{y}[/tex]
So adding the given sides in the figure:
[tex]Perimeter=14\frac{3}{4}+ 4\frac{1}{2}+ 8\frac{1}{2}+10 \frac{2}{5}+10 \frac{2}{5}+12 \frac{4}{5}[/tex]
[tex]=\frac{(14*4)+3}{4} +\frac{(4*2)+1}{2} +\frac{(8*2)+1}{2} +\frac{(10*5)+2}{5}+ \frac{(10*5)+2}{5} +\frac{(12*5)+4}{5}[/tex]
[tex]=\frac{59}{4}+ \frac{9}{2}+ \frac{17}{2}+ \frac{52}{5}+ \frac{52}{5}+ \frac{64}{5}[/tex]
[tex]=14.75+4.5+8.5+10.4+10.4+12.8[/tex]
[tex]Perimeter= 71.75[/tex]
The perimeter of the given figure is 71.75
What's 0 divided by 0?
Answers
Answer:
Nothing
Step-by-step explanation:
You can't divide by zero
Answer:
ANYTHING DIVIDED BY 0 IS ALWAYS ZERO
Step-by-step explanation:
PLEASE MARK BRAINLIEST
Which summation formula represents the series below? 1 + 2 + 6 + 24
Answers
Question:
Which summation formula represents the series below? 1 + 2 + 6 + 24
(a) [tex]\sum_{n=2}^{5}(n-1) ![/tex]
(b) [tex]\sum_{n=0}^{3} n ![/tex]
(c) [tex]\sum_{n=1}^{4}(n+1) ![/tex]
(d) [tex]\sum_{n=2}^{5} n ![/tex]
Answer:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex] is the correct answer.
Explanation:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](2-1) !+(3-1) !+(4-1) !+(5-1) ![/tex]
Subtracting, we have,
[tex]1 !+2!+3 !+4 ![/tex]
Expanding the factorial,
[tex]1+(2*1)+(3*2*1)+(4*3*2*1)[/tex]
Simplifying, we get,
[tex]1+2+6+24[/tex]
Thus, the summation [tex]\sum_{n=2}^{5}(n-1) ![/tex] represents the series [tex]1+2+6+24[/tex]
Hence, Option a is the correct answer.
Option b: [tex]\sum_{n=0}^{3} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]0!+1!+2!+3![/tex]
Expanding the factorial,
[tex]0+1+(2*1)+(3*2*1)[/tex]
Simplifying, we get,
[tex]0+1+2+6[/tex]
Thus, the summation [tex]\sum_{n=0}^{3} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option b is not the correct answer.
Option c: [tex]\sum_{n=1}^{4}(n+1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](1+1) !+(2+1) !+(3+1) !+(4+1) ![/tex]
Adding, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=1}^{4}(n+1) ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option c is not the correct answer.
Option d: [tex]\sum_{n=2}^{5} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=2}^{5} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option d is not the correct answer.
Hence, the correct answer is Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
Answer: A
Step-by-step explanation:
What is this (20+25)/3
Answers
Answer:
78 witch is 15%
Step-by-step explanation:
Clare has $150 in her bank account. She buys a bike for $200. What is Claire's account balance now?
Cooldown
unit 5, lesson 4
4.4
Answers
Answer:
-50
Step-by-step explanation:
she only had 150, but spent 200 she overdrew
she has an overdraft of $50
Answer:-50
Step-by-step explanation:150-200=-50
A steel ball is traveling through water with a speed of x meters per second, where x is positive the drag force, F
At what speed in meters per second does the ball have a force of 0.5 N on it
Answers
the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.
To find the speed at which the drag force F on the steel ball is 0.5 N, we need to solve the equation:
[tex]\[ F = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]
Given that [tex]\( F = 0.5 \)[/tex], we can substitute this value into the equation and solve for x:
[tex]\[ 0.5 = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]
Subtracting \( 0.5 \) from both sides, we get:
[tex]\[ 0 = 0.004(x + 50)(x - 2.5) \][/tex]
Now, since the product of two factors is equal to zero, at least one of the factors must be zero. So we have:
[tex]\[ x + 50 = 0 \][/tex] or [tex]\[ x - 2.5 = 0 \][/tex]
Solving these equations:
1. [tex]\( x + 50 = 0 \)[/tex]
[tex]\[ x = -50 \][/tex]
2. [tex]\( x - 2.5 = 0 \)[/tex]
[tex]\[ x = 2.5 \][/tex]
Since the speed cannot be negative, the only valid solution is [tex]\( x = 2.5 \)[/tex] meters per second.
Therefore, the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.
The complete Question is given below:
A steel ball is traveling through water with a speed of x meters per second, where x is positive. The drag force, F , in newtons (N) is: F=0.5+0.004(x+50)(x-2.5) At what speed in meters per second does the ball have a force of 0.5N on it?
brand A granola is 25% nuts and dried fruit and brand B granola is 10% nuts and dried fruit. how much of sweet item A and sweet item B should be mixed to form a 30-lb batch of sweets that is 22% nuts and dried fruit?
Answers
y = lbs of B
---
x + y = 10
25x + 20y = 21*10
---
put the system of linear equations into standard form
---
x + y = 10
25x + 20y = 210
lbs of A = 2
y = lbs of B = 8
To create a 30-lb batch of sweets that is 22% nuts and dried fruit, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B.
To find the solution, we can set up a system of equations based on the percentages of nuts and dried fruit in each brand of granola and the desired final percentage.
Let x represent the amount of sweet item A (in pounds) and y represent the amount of sweet item B (in pounds) to be mixed.
The total weight of the mixture is x + y = 30 lbs.
The percentage of nuts and dried fruit in brand A is 25%, so the amount of nuts and dried fruit from A is 0.25x lbs.
The percentage of nuts and dried fruit in brand B is 10%, so the amount of nuts and dried fruit from B is 0.10y lbs.
The desired final percentage in the mixture is 22%, so we have the equation: (0.25x + 0.10y) / 30 = 0.22.
Now, we can solve this system of equations to find x and y.
First, we'll multiply the last equation by 30 to get 0.25x + 0.10y = 6.6.
Then, we can use substitution or elimination to solve for x and y.
In this case, it's simpler to use elimination, and we find that x = 12 lbs and y = 18 lbs.
Therefore, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B to create the desired 30-lb batch with 22% nuts and dried fruit.
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Please Help Me!
A sphere's center is located at (0,0,0). The point (4,9,-5) is located on the surface of the sphere. Find the length of the radius of the sphere. Round to the nearest tenth.
Answers
Answer:
The length of the radius of the sphere is 11.0 units
Step-by-step explanation:
we know that
To calculate the radius of the sphere, we can use the distance formula
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}[/tex]
where
d is the length of the radius
(x_1,y_1,z_1) is the center of the sphere
and
(x_2,y_2,z_2) is one point on the surface of the sphere
we have
[tex](x_1,y_1,z_1)=(0,0,0)[/tex]
[tex](x_2,y_2,z_2)=(4,9,-5)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-0)^{2}+(9-0)^{2}+(-5-0)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(9)^{2}+(-5)^{2}}[/tex]
[tex]d=\sqrt{122}[/tex]
[tex]d=11.0\ units[/tex]
therefore
The length of the radius of the sphere is 11.0 units
Joe tracked the height of his Dalmatian puppy from age 13 weeks to 25 weeks. He graphed the data and determined the line of best fit is y = 1.12x + 28.78 where x is the age in weeks and y is the height in centimeters. How old was the puppy when he was 54 centimeters tall? Round to the nearest tenth.
a. 22.5 weeks
b. 28.2
c. 73.9
d. 89.3
Answers
Answer:
22.5 weeks
Step-by-step explanation:
y = 1.12x + 28.78 represents the height of the puppy. Here that height is 54 cm:
Then 54 = y = 1.12x + 28.78
Combining the constants, we get 1.12x = 25.22. Dividing both sides by 1.12, x turns out to be 22.5 weeks.
Claire is that in the first five years between 1977 in 1980 to the hospital about $12 per year are in the second five years between 1983 in 1888 the causal only by about two dollars a year show that Claire is correct
Answers
Answer:
Step-by-step explanation:
Does Y+7=2x and
2y=4x-14 have a solution?
Answers
Answer: It has no exact solution
A certain drink is made by adding 4 parts water to 2.5 part drink mix. What percent of the mixture is water? Omit % sign in your answer. Round your answer to the nearest tenth.
Answers
The mixture contains 61.5% of water.
Step-by-step explanation:
Total parts = 4+ 2.5 = 6.5
Parts of water =4
parts of drink = 2.5
Percent of water in the mixture = 4 × 100/ 6.5
= 400/6.5
= 61.53%
It is rounded to the nearest tenth as 61.5%.
To find the percentage of water in the mix, we calculate the proportion of water (4 parts) to the total mixture (6.5 parts) and multiply by 100%, resulting in approximately 61.5%.
To determine what percent of the mixture is water when a drink is made with 4 parts water and 2.5 parts drink mix, we add together the parts of water and drink mix to find the total parts of the mixture. Then, we calculate the fraction of the mixture that is water and convert that to a percentage.
First, we find the total parts of the mixture:
Water: 4 parts
Drink mix: 2.5 parts
Total parts: 4 + 2.5 = 6.5 parts
Next, we calculate the percentage of the mixture that is water:
(Parts of water / Total parts) × 100%
(4 parts / 6.5 parts) × 100% \approximately 61.5%
Rounding to the nearest tenth, we get:
61.5
what property can be used to solve x-3= -5
Answers
Answer:
-2
Step-by-step explanation:
x-3=-5
x=-5+3
x=-2
Which graph represents the solution for the equation -5/2x -1 = 4x + 2?
Answers
Answer:
D would be the best choice.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Did the test
V=15.81 V, P = 500 mW, I=
Answers
Answer:
0.032 Amperes
Step-by-step explanation:
in this question We are given;
Voltage, V =15.81 VPower, P = 500 mW (Milli-watts)We are required to determine the current, I
We need to know that power, P is given by the product of current and voltage.
That is;
Power = VI
But; 1 mW = 0.001 Watts
Thus, 500 mW = 0.5 watts
Rearranging the formula;
I = Power ÷ V
= 0.5 watts ÷ 15.81 V
= 0.0316 Amperes
= 0.032 A
Thus, the current, I is 0.032 Amperes
Anusha needs to find a rectangular container large enough to hold a volume of 130 in.3. Which container should she use?
A. a container with the dimensions 2 by 5 by 10 inches
B. a container with the dimensions 3 by 4 by 10 inches
C. a container with the dimensions 3 by 5 by 10 inches
D. a container with the dimensions 4 by 2 by 10 inches
PLEASE HELP!!
Answers
Option C
Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Solution:
Anusha needs to find a rectangular container large enough to hold a volume of 130 cubic inches
The volume of rectangular container is:
[tex]volume = length \times width \times height[/tex]
Option A
Container with the dimensions 2 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 2 \times 5 \times 10 = 100[/tex]
Thus volume is 100 cubic inches
Option B
Container with the dimensions 3 by 4 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 4 \times 10 = 120[/tex]
Thus volume is 120 cubic inches
Option C
Container with the dimensions 3 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 5 \times 10 = 150[/tex]
Thus volume is 150 cubic inches
Option D
Container with the dimensions 4 by 2 by 10 inches
Therefore, volume is given as:
[tex]Volume= 4 \times 2 \times 10 = 80[/tex]
Thus volume is 80 cubic inches
Thus Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Answer:C. a container with the dimensions by 5 by 10 inches
lonnie bought 6 pieces of ribbon. Each ribbon was 2 and 3/4 yards long. How much ribbon did Lonnie buy in all
Answers
Answer:
14.04
Step-by-step explanation:
you mupltiy
Answer:
b
Step-by-step explanation:
2.34 x 6 = 14.04
so it would total up to 14.12
On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
Answers
127 children and 264 adults swam at the public pool that day
Solution:
Let "c" be the number of children swam
Let "a" be the number of adult swam
Cost for each children = $ 1.25
Cost for each adult = $ 2.25
391 people used the public swimming pool
Therefore,
c + a = 391
a = 391 - c ------- eqn 1
The receipts for admission totaled $752.75
Therefore, we frame a equation as:
number of children swam x Cost for each children + number of adult swam x Cost for each adult = 752.75
[tex]c \times 1.25 + a \times 2.25 = 752.75[/tex]
1.25c + 2.25a = 752.75 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
1.25c + 2.25(391 - c) = 752.75
1.25c + 879.75 - 2.25c = 752.75
c = 879.75 - 752.75
c = 127
Substitute c = 127 in eqn 1
a = 391 - 127
a = 264
Thus 127 children and 264 adults swam at the public pool that day
Which inequality is equivalent to
6. X+7
5x+3?
Answers
Step-by-step explanation:
(1/2x)+7 is a equation
Answer:
on edgenuit it's c
Step-by-step explanation:
-15x-53/x^2+8x+15
BRAINLIEST 60 POINTS!! PLEASE HELP ITS DUE TODAY
First image is for question 1, and second image is for question 2
1. Remember what we know about vertical angles and solve for x.
2. Use the figure to answer the questions.
(a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain.
Answers
Answer:
1.[tex]x^\circ= 7^\circ[/tex]
2.(a)Therefore , Side LJ =side CA
(b) BC = KL
Step-by-step explanation:
1.
we know that, vertically opposite angles are congruent .
[tex]\therefore (x+16)^\circ= (4x-5)^\circ[/tex]
[tex]\Leftrightarrow 4x^\circ-x^\circ= 5^\circ+16^\circ[/tex]
[tex]\Leftrightarrow 3x^\circ= 21^\circ[/tex]
[tex]\Leftrightarrow x^\circ= 7^\circ[/tex]
2.
(a)SAS = side,angle , side
Given ,side AB = side KJ
and ∠CAB= ∠LJK
All Pythagorean Triples are unique.
Since side AB = side KJ
Therefore , Side LJ =side CA
It satisfies SAS postulate ThereforeΔABC≅ΔKJL
(b)
HL Theorem: If hypotenuse and one leg of of a right triangle are congruent to the hypotenuse and one leg of of other right triangle , then the triangle congruent.
Since,
All Pythagorean Triples are unique.
Then hypotenuse of ΔABC=ΔLKJ ⇔BC = KL
5 1/2 of 2 1/3 is what number?
Answers
Answer:
19 1/4
Step-by-step explanation:
5 1/2 of 2 1/3
Change mixed fraction to improper fraction
11/2 of 7/2
Of means multiplication
11/2 x 7/2
77/4
19 1/4
find the value of x.
13,15,17,x,20,21; The median is 18.
Answers
Answer:
1
Step-by-step explanation:
13 15 17 x 20 21
Cross out all outer numbers
We are left with 17 and x
With double medians, you add those two together and then divide them by two.
With the median (total) being 18, we will first add 17+x then divide Y/2 = 18
The value of x is 1
570 times what gets 690
Answers
Answer:
1.21052631579 is the exact answer or 1.2 is if you round it
Step-by-step explanation:
This is the answer I got from dividing 690 by 570. Hope this helped
Answer:
1.21 to the nearest hundredth.
Step-by-step explanation:
570 * x = 690
x = 690/570
x = 1.210526316.
Simplify: (-7x^2y^4)(-2x^3y^4)
Answers
Answer: 14x^5y^8
Step-by-step explanation:
(-7x^2y^4)(-2x^3y^4)
-7x^2y^4*-2x^3y^4, next take out the constants
−(7×−2)x^2x^3y^4y^4, -(7*-2)=14, so now you just need to add the variables.
(x^2+x^3)+(y^4+y^4)=x^5y^8
14x^5y^8
Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)
- Cutiepatutie ☺❀❤
A building has the shape of a pyramid within a square base. The mid segment parallel to the ground of each triangular face of the pyramid has a length of 58 feet. Find the length of the base the pyramid.
Answers
Answer:
The length of the base the pyramid is 116 feet.
Step-by-step explanation:
See the diagram attached to this answer.
Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.
Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.
Hence, [tex]\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}[/tex]
⇒ AB = 2 × 58 = 116 feet.
The length of the base the pyramid is 116 feet. (Answer)
Final answer:
The length of the base of the pyramid in question, referenced as the Great Pyramid of Cheops, is historically known to be 230 meters on each side.
Explanation:
The student's question relates to finding the length of the base of a pyramid with a known mid-segment length in one of the triangular faces.
Based on the information provided, which references the Great Pyramid of Cheops (or the Great Pyramid of Giza), the original square base length of the pyramid was 230 meters on each side.
This measurement is crucial for answering questions related to the geometry and scale of pyramids in mathematical problems.
Which equation represents a proportional relationship?
y=2x2
y = 4x - 2
y= 1/2x +3
y=5x
Answers
Answer:
D: y = 5x
Step-by-step explanation:
According to Google, a proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if: y=kx. for some constant k , called the constant of proportionality. So the only one in that form would be the y = kx.
The constant k = 5
Write this decimal in number, thirty-nine thousandths
Answers
Answer:
0.039
Step-by-step explanation:
5. Katie makes and sells scarves. Her monthly profit is given by P(s) = -s2 + 25s - 100, where "s" is the selling price. For what range of prices can Katie sell the scarves, in order to make a profit? (For what values of "s" will -s2 + 25s - 100 be greater than 0?)
Answers
Answer: s > 5
Step-by-step explanation:
-s² + 25s - 100 > 0
Coefficient of s² is -1, multiply the equation through by -1.
-1 × (-s² + 25s - 100)
s² — 25s + 100
ax² + bx + c
Then you get the factors x and y that gives x + y = b and xy = c
b = -25 and c = 100, x = -20 and y = -5
-20 × -5 = 100 and -20 + -5 = -25
Then
s² — 20s — 5s + 100 > 0
Factorising,
s (s — 20) — 5(s — 20) > 0
(s — 5)(s — 20) > 0
(s — 5) > 0 and (s — 20) > 0
s>5 and s>20
s > 5
Hope this Helps?
If theta is an acute angle, solve the equation tangent theta equals four fifths
. Express your answer in degrees, rounded to one decimal place.
Answers
Answer:
[tex]\theta=38.7\degree[/tex]
Step-by-step explanation:
We want to solve [tex]\tan \theta=\frac{4}{5}[/tex] given that [tex]\theta[/tex] is acute.
We take tangent inverse of both sides to get:
[tex]\theta=\tan^{-1}(\frac{4}{5})[/tex]
Now set your calculator to degree mode and evaluate [tex]\tan^{-1}(\frac{4}{5})[/tex] to obtain:
[tex]\theta=38.6598\degree[/tex]
To one decimal place, we have;
[tex]\theta=38.7\degree[/tex]
To solve the equation 'tangent theta equals four fifths', we use the inverse tangent function, or arctan(4/5). Using a calculator in degree mode, the result is approximately 38.7 degrees.
Explanation:To solve the equation tangent theta equals four fifths, we need to find the angle whose tangent is 4/5. We can find this using the inverse tangent function (also known as arctan)
So, theta = arctan(4/5)
Use a calculator to find out the value of arctan(4/5). Make sure your calculator is in degree mode because the answer needs to be in degrees. The answer is approximately 38.7 degrees, rounded to one decimal place.
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What is the y-intercept of the function f(x)=4 -- 5x?
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