Answer:
Final answer is approx x=4.26.
Step-by-step explanation:
Given equation is [tex]1.8^{-x+7} = 5[/tex]
Now we need to solve equation [tex]1.8^{-x+7} = 5[/tex] and round to the nearest hundredth.
[tex]1.8^{-x+7} = 5[/tex]
[tex]\log(1.8^{-x+7}) = \log(5)[/tex]
[tex](-x+7)\log(1.8) = \log(5)[/tex]
[tex](-x+7) = \frac{\log(5)}{\log(1.8)}[/tex]
[tex](-x+7) = \frac{0.698970004336}{0.255272505103}[/tex]
[tex]-x+7 = 2.73813274192[/tex]
[tex]-x = 2.73813274192-7[/tex]
[tex]-x =−4.26186725808[/tex]
[tex]x =4.26186725808[/tex]
Round to the nearest hundredth.
Hence final answer is approx x=4.26.
Solve each exponential equation by using properties of common logarithms. Do not round the expression until the final answer. When necessary, round answers to the nearest hundredth.
17x = 89
x ≈ 1.58
x ≈ 5.24
x ≈ 63
Answer:
Option 1 - [tex]x\approx 1.58[/tex]
Step-by-step explanation:
Given : Exponential equation [tex]17^x=89[/tex]
To find : Solve exponential equation by using properties of common logarithms?
Solution :
Step 1 - Write the exponential equation,
[tex]17^x=89[/tex]
Step 2 - Take logarithm both side,
[tex]\log 17^x=\log 89[/tex]
Step 3 - Apply logarithmic property, [tex]\log a^x=x\log a[/tex]
[tex]x\log 17=\log 89[/tex]
Step 4 - Divide both side by log 17,
[tex]x=\frac{\log 89}{\log 17}[/tex]
Step 5 - Solve,
[tex]x=1.584[/tex]
[tex]x\approx 1.58[/tex]
Therefore, Option 1 is correct.
At lunch, 8 friends share 6 sandwiches equally what fraction of a sandwich does each friend get?
Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yield of 85 and a sample standard deviation of 3. Fifteen batches were prepared using catalyst 2, and they resulted in an average yield of 89 with a standard deviation of 2. Assume that yield measurements are approximately normally distributed with the same standard deviation. (a) Is there evidence to support the claim that catalyst 2 produces higher mean yield than catalyst 1? Use (b) Find a 99% confidence interval on the difference in mean yields that can be used to test the claim in part (a). Round your answer to two decimal places (e.g. 98.76).
To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, a two-sample t-test can be performed. To find a 99% confidence interval on the difference in mean yields, a formula can be used.
Explanation:To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, we can perform a two-sample t-test.
Null Hypothesis: There is no difference in mean yields between catalyst 2 and catalyst 1.Alternative Hypothesis: The mean yield of catalyst 2 is higher than that of catalyst 1.Calculate the pooled standard deviation:Calculate the t-value using the formula: t = ((mean1 - mean2) - 0) / (pooled standard deviation * sqrt(1/n1 + 1/n2))Compare the t-value with the critical t-value from the t-distribution table to determine if there is enough evidence to reject the null hypothesis.(b) To find a 99% confidence interval on the difference in mean yields, we can use the formula: CI = (mean1 - mean2) ± (critical t-value * standard error), where standard error = sqrt((standard deviation1^2/n1) + (standard deviation2^2/n2)).
Learn more about Hypothesis testing here:https://brainly.com/question/34171008
#SPJ11
(a) Yes, there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1.
(b) The 99% confidence interval on the difference in mean yields is approximately (-6.52, -1.48).
(a) To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, we can conduct a hypothesis test.
- Null Hypothesis [tex](\(H_0\))[/tex]:
The mean yield produced by catalyst 2 is not higher than the mean yield produced by catalyst 1. [tex]\( \mu_1 \geq \mu_2 \)[/tex]
- Alternative Hypothesis [tex](\(H_1\))[/tex]:
The mean yield produced by catalyst 2 is higher than the mean yield produced by catalyst 1. [tex]\( \mu_1 < \mu_2 \)[/tex]
We'll use a two-sample t-test for independent samples since we are comparing the means of two independent groups.
Given:
- Sample mean [tex](\( \bar{x}_1 \))[/tex] for catalyst 1 = 85
- Sample mean [tex](\( \bar{x}_2 \))[/tex] for catalyst 2 = 89
- Sample standard deviation [tex](\( s_1 \))[/tex] for catalyst 1 = 3
- Sample standard deviation ([tex]\( s_2 \)[/tex]) for catalyst 2 = 2
- Sample size [tex](\( n_1 \))[/tex] for catalyst 1 = 12
- Sample size [tex](\( n_2 \))[/tex] for catalyst 2 = 15
- Degrees of freedom [tex](\( df \)) = \( n_1 + n_2 - 2 \)[/tex]
Let's calculate the t-statistic:
[tex]\[ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \][/tex]
[tex]\[ t = \frac{(85 - 89)}{\sqrt{\frac{3^2}{12} + \frac{2^2}{15}}} \][/tex]
[tex]\[ t \approx \frac{-4}{\sqrt{\frac{9}{12} + \frac{4}{15}}} \][/tex]
[tex]\[ t \approx \frac{-4}{\sqrt{0.75 + 0.2667}} \][/tex]
[tex]\[ t \approx \frac{-4}{\sqrt{1.0167}} \][/tex]
[tex]\[ t \approx \frac{-4}{1.0083} \][/tex]
[tex]\[ t \approx -3.97 \][/tex]
Now, we'll find the critical value for the t-distribution with the given degrees of freedom and a one-tailed test at a 99% confidence level.
Since it's a one-tailed test, we're interested in the critical value to the right of the distribution.
Using a t-table or a statistical software, the critical value for a one-tailed test with [tex]\( df = 12 + 15 - 2 = 25 \)[/tex] and [tex]\( \alpha = 0.01 \)[/tex] is approximately [tex]\( t_{\text{critical}} \approx 2.492 \)[/tex].
Since [tex]\( t = -3.97 < t_{\text{critical}} = 2.492 \)[/tex]we reject the null hypothesis.
Therefore, there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1.
(b) To find a 99% confidence interval on the difference in mean yields, we'll use the formula:
[tex]\[ \text{Confidence Interval} = (\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]
Substituting the given values:
[tex]\[ \text{Confidence Interval} = (85 - 89) \pm 2.492 \times \sqrt{\frac{3^2}{12} + \frac{2^2}{15}} \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times \sqrt{0.75 + 0.2667} \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times \sqrt{1.0167} \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times 1.0083 \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.5161 \][/tex]
[tex]\[ \text{Confidence Interval} = (-6.5161, -1.4839) \][/tex]
Rounded to two decimal places, the 99% confidence interval on the difference in mean yields is approximately (-6.52, -1.48).
Let’s say the area of the map is 21 square inches. You want to make an enlarged map of Central Park to take with you on your journey. Describe how you can determine the area of the enlarged map. plzzzzzzz answer quickly I have 20 minutes.
Answer:
find the perimeter and multiply it to a decent size to see what you would need to do to enlarge the map
Step-by-step explanation:
can i get brainliest i need 5
The area of the enlarged map is gotten by multiplying the square of the scale factor by 21 in²
What is scaling?Scaling is the increase or decrease in the size of a figure by a scale factor so as to create an image.
If a map is enlarged by a scale factor. To determine the area of the enlarged map, if the original map has an area of 21 in²:
Area of enlarged map = scale factor² * 21 in²
The area of the enlarged map is gotten by multiplying the square of the scale factor by 21 in²
Find out more on scaling at: https://brainly.com/question/25324744
The domain of f(x) is the set of all numbers greater than or equal to 0 and then less than or equal to 2
It means f(x) has a set of numbers from 0-2
i.e, 0,1,2
NEED HELP !!!!! WILL GIVE BRAINLIEST AND 99 PTS!!!!order from least to greatest. 0.81, 4/5, 90%
In order from least to greatest, it goes 4/5, 0.81, 90%
Answer:
4/5, 0.81, 90% is the answer from least to greatest.
Hope this helps :)
Identify the domain of the function shown in the graph.
For this case, we find the equation of the line, for this we look for points where the line passes:
[tex](x1, y1) = (- 2,0)\\(x2, y2) = (- 10, -4)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {-4-0} {- 10 - (- 2)} = \frac {-4} {- 10 + 2} = \frac {- 4} {- 8} = \frac {1} {2}[/tex]
Thus, the equation of the line is:
[tex]y = \frac {1} {2} x + b[/tex]
We substitute a point to find "b":
[tex]0 = \frac {1} {2} (- 2) + b\\0 = -1 + b\\b = 1[/tex]
Finally:
[tex]y = \frac {1} {2} x + 1[/tex]
Now, the domain is given by all the values for which the function is defined.
It is observed that "x" can take any value, that is, it is defined for all real numbers.
Answer:
Option A
can i have some help please uwu?
use the iterative rule to find the 8th term in the sequence
an= 25-3n
a8=___
thankyou! ~bangtanboys7
hope im right but i think it 1 sorry if im wrong
Plug in 1, 2, 3, ... up to 8 into our sequence an.
You really just need to plug in 8, but plug in lower numbers to see the sequence emerge.
For example:
a1 means n equals 1, so a1 = 25 - (3 * 1) = 25 - 3 = 22
a2 means n equals 2, so a2 = 25 - (3 * 2) = 25 - 6 = 19
...
a8 means n equals 8, so a8 = 25 - (3 * 8) = 25 - 24 = 1
I hope this helps you understand the problem.
EDIT: You can also graph your iterative rule an on a graph. The values on the x axis correspond to the value of n and the y-axis would then correspond to the value of the sequence. Notice that a8 = 1, as shown in the attached picture.
(1 point) Suppose F⃗ (x,y)=−yi⃗ +xj⃗ F→(x,y)=−yi→+xj→ and CC is the line segment from point P=(4,0)P=(4,0) to Q=(0,5)Q=(0,5). (a) Find a vector parametric equation r⃗ (t)r→(t) for the line segment CC so that points PP and QQ correspond to t=0t=0 and t=1t=1, respectively. r⃗ (t)=r→(t)= <4,0>+t<-4,5> (b) Using the parametrization in part (a), the line integral of F⃗ F→ along CC is ∫CF⃗ ⋅dr⃗ =∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt=∫ba∫CF→⋅dr→=∫abF→(r→(t))⋅r→′(t)dt=∫ab 20 dtdt with limits of integration a=a= 0 and b=b= 1 (c) Evaluate the line integral in part (b). 20 (d) What is the line integral of F⃗ F→ around the clockwise-oriented triangle with corners at the origin, PP, and QQ
The vector parametric equation for the line segment CC is <4,0> + t<-4,5>. The line integral of F⃗ along CC is 20. The line integral of F⃗ around the clockwise-oriented triangle with corners at the origin, P, and Q cannot be determined without additional information.
Explanation:(a) To find a vector parametric equation for the line segment CC, we can use the points P=(4,0) and Q=(0,5). We can represent the line segment CC as r(t) = <4,0> + t<-4,5>, where t is the parameter. This equation represents the line segment from P to Q, with t=0 corresponding to P and t=1 corresponding to Q.
(b) Using the parametrization in part (a), we can evaluate the line integral of F⃗ along CC. The line integral is given by ∫CF⃗ ⋅ dr⃗ = ∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt. In this case, the line integral is ∫01-5yi⃗ +4xj⃗⋅-4i⃗ +5j⃗ dt
(c) Evaluating the line integral from part (b), we get 20.
(d) The line integral of F⃗ around the clockwise-oriented triangle with corners at the origin, P, and Q can be found using the Green's theorem. We can calculate it by subtracting the line integral along CP from the line integral along CQ. However, we would need more information to determine the path from C to the origin.
manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth. Predict the number of computers with defects in a shipment of 15,000 computers. Round your answer to the nearest whole number.
Answer:
0.01.
113.
Step-by-step explanation:
Probability of a defect = 9/1200
= 0.0075
= 0.01 to the nearest hundredth.
Prediction of number of defects in 15,000 computers
= 15,000 * 0.0075
= 113.
The probability of choosing defective computers is 0.01 and the number of predictions is 113.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect.
The probability will be calculated as,
Probability of a defect = 9/1200
= 0.0075
= 0.01 to the nearest hundredth.
Prediction of the number of defects in 15,000 computers
= 15,000 * 0.0075
= 113.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ5
Which equation is equivalent to 5√X+8=35? A. 3√x+8=175 B. X+8=343 C. X+8=21 D. X=351
Answer with explanation:
The equation whose equivalent equation we have to find is:
5 √X +8=35
Two equations are said to be equivalent,if they have same solution .
There is another definition of equivalent equation.Two equation are said to be equivalent ,also, if their solution are not same, but these equations appear Identical that is congruent but not Similar.
Option A: Equation ,3√X +8=175 is equivalent to 5√X+8=35.
Answer:
A
Step-by-step explanation
Please help me asap!!!
Answer:
C x=17
Step-by-step explanation:
The top and bottom sides have to be equal for the quadrilateral to be a parallelogram
2x-9 = x+8
Subtract x from each side
2x-9-x = x+8-x
x-9 = 8
Add 9 to each side
x-9+9=8+9
x=17
➷ Opposite lengths in a parallelogram are equal
Therefore:
2x - 9 = x + 8
Add 9 to both sides:
2x = x + 17
Subtract x from both sides:
x = 17
Your answer is option c.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
33/8 x 12/5 = ? Jdnnhdwjebcbraoq
Answer:
9.9
Step-by-step explanation:
First, you divide the 33 by 8 because that's the first part that goes together.
33/8=4.125
Second, divide 12 by 5.
12/5=2.4
Then, you multiply the 4.125 and the 2.4 together.
4.125 x 2.4 = 9.9
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷To multiply a fraction, you can just multiply the top and multiply the bottom.
Top: 33 * 12 = 396
Bottom: 8 * 5 = 40
Fraction: 396/40
Simplify: 28 2/7
Or in decimal form: 9.9
Final answer:
33/8 * 12/5 = 28 2/7
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
Find the circumferences of both circles to the nearest hundredth.
Answer:
28.27 inches for inner and 36.12 inches for outer
Step-by-step explanation:
2[tex]\pi[/tex]r
and 2 pi r with 4.5 +2.5 inches as the radius.
You're done :-)
On a number line, what is the distance between ?17 and 9? A) -26 B) -8 C) 8 D) 26 Submit
Answer:
c) 8
Step-by-step explanation:
its C. because 17-9=8.
if y varies directly with x, find the constant of variation with x = 4 and y = - 24
A: -6
B: 4
C: -96
D: 6
Answer:
A: -6
Step-by-step explanation:
A direct variation is y =kx
We know x =4 and y = -24
Substituting in
-24 = 4k
Dividing by 4
-24/4 = 4k/4
-6 =k
The constant of variation is -6
A shirt's sale price is marked $14.40, which is 60% off the original price. How many dollars was the original price of the shirt?
Answer:
The original price of the shirt is $36.
Step-by-step explanation:
Let us call p_o the original price of the shirt, then we know that $14.40 is 60% off [tex]p_o[/tex]; or $14.40 is 100% - 60% = 40% of [tex]p_o[/tex]. In other words,
[tex]\dfrac{40\%}{100\%}*p_o= \$ 14.40.[/tex]
This equation simplifies to
[tex]0.4p_o= \$14.40[/tex] (we evaluated 40/100 )
We divide both sides by 0.4 and get:
[tex]p_o= \dfrac{\$14.40}{0.4}[/tex]
[tex]\boxed{p_o = \$36.}[/tex]
The original rice of the shirt is $36.
Answer:
$36
Step-by-step explanation:
If the shirt is 60% off, it is currently .4 of the original price. Thus the original price was: $36
Hope this helped! :)
Use the x-intercept method to find all real solutions of the equation.
x^3-8x^2+9x+18=0
Answer:
a. [tex]x=-1,3,\:or\:6[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-8x^2+9x+18=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.
The corresponding function is
[tex]f(x)=x^3-8x^2+9x+18[/tex]
The solution to [tex]x^3-8x^2+9x+18=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(3,0) and (6,0).
Therefore the real solutions are:
[tex]x=-1,3,\:or\:6[/tex]
Answer:
Use a graphing utility or a graphing calculator.
x = -1, 3, 6. (3 real solutions).
Step-by-step explanation:
The points of intersection on the x axis are the 3 solutions to the equation.
Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 48°
Step-by-step explanation: The Answer is 48° this is because a triangle is equal to 180° and to find the missing side, add the two sides you do know and subtract them from 180 and you will get 48°
Have an awesome day,
Eric
Angle AOB and angle AOC are complementary angles. What is the measure of angle AOB if the measure of angle AOC is 37°?
A. 53°
B. 63°
C. 323°
D. 143°
90-37=53 complementary angles are 90 degrees
Answer:
Option A, 53°
Step-by-step explanation:
If the two angles are complimentary to each other then sum of these angles is equal to 90°.
∠AOB + ∠AOC = 90°
If ∠AOC = 37°
Then ∠AOB = 90° - ∠AOC
= 90° - 37°
= 53°
Option A 53° is the answer.
Please help me with thesw question i will give 10 points
A is the answer to that question
How much would it cost to ship a package weighing 3.2 lbs at a cost of $2.69 per pound. Explain how you arrived at your answer.
Answer:
$8.608
Step-by-step explanation:
We are given that it costs $2.69 per pound to ship a package and we are to find how much would it cost to ship a package weighing 3.2 lbs.
To find this, we simply need to multiply the unit cost per pound with the weight of the package that is to be shipped.
Total cost to ship 3.2 lbs package = [tex] 3.2 \times 2.69 [/tex] = $8.608
The quadrilateral is inscribed in a circle with opposite angles measuring 3x + 2 and 3x – 32. Find the value of x.
Question 5 options:
35
22
25
30
Answer:
[tex]x=35\°[/tex]
Step-by-step explanation:
we know that
In a quadrilateral inscribed in a circle , the opposite angles are supplementary
so
In this problem
[tex](3x+2)\°+(3x-32)\°=180\°[/tex]
Solve for x
[tex]6x-30\°=180\°[/tex]
[tex]6x=210\°[/tex]
[tex]x=210\°/6=35\°[/tex]
Answer:
A. 35
Step-by-step explanation:
I did this question earlier and A. 35 was the answer that was right for me. Hope this helps!
Identify the area of the kite. Please help!!
Answer:
[tex]\large\boxed{A=480\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a kite:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁, d₂ - diagonal
Look at the picture.
Use the Pythagorean theorem.
[tex]x^2+5^2=13^2[/tex]
[tex]x^2+25=169[/tex] subtract 25 from both sides
[tex]x^2=144\to x=\sqrt{144}\\\\x=12\ m[/tex]
Therefore d₁ = (2)(12 m) = 24 m.
[tex]y^2+12^2=37^2[/tex]
[tex]y^2+144=1369[/tex] subtract 144 from both sides
[tex]y^2=1225\to y=\sqrt{1225}\\\\y=35\ m[/tex]
Therefore d₂ = 5 + 35 = 40 m.
Substitute:
[tex]A=\dfrac{(24)(40)}{2}=(24)(20)=480\ m^2[/tex]
Jon makes a map of his neighborhood for a presentation. The scale of his map is 1 inch:125 feet. How many feet do 4 inches
represent on the map? Answer-500 feet ( I just need help on the problem below)
From the problem above Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map? Show your work.
Answer:
Part A) [tex]500\ ft[/tex]
Part B) [tex]2\ in[/tex]
Step-by-step explanation:
we know that
The scale of the map is [tex]\frac{1}{125} \frac{in}{ft}[/tex]
That means
1 in on the map represent 125 ft in the real
Part A) How many feet do 4 inches
using proportion
[tex]\frac{1}{125} \frac{in}{ft}=\frac{4}{x} \frac{in}{ft}\\ \\x=125*4\\ \\x=500\ ft[/tex]
Part B) Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map?
using proportion
[tex]\frac{1}{125} \frac{in}{ft}=\frac{x}{250} \frac{in}{ft}\\ \\x=250/125\\ \\x=2\ in[/tex]
Jon's home is 2 inches from Max's on the map, according to the scale of 1 inch:125 feet, considering Jon lives 250 feet from Max.
Explanation:To find out how many inches separate Jon's home from Max's on the map, we need to apply the given scale of the map which is 1 inch:125 feet. Since Jon lives 250 feet away from Max, we can set up a proportion to solve for the distance on the map as follows:
1 inch / 125 feet = x inches / 250 feet
Cross-multiply to solve for x:
125x = 1 * 250
125x = 250
Now, divide both sides by 125 to isolate x:
x = 250 / 125
x = 2
So, Jon's home is 2 inches from Max's on the map.
WHAT ARE THE SPECIFIC RULES FOR PROVING SIMILARITY IN TRIANGLES? EXPLAIN.
Answer:
AAA (Or even just two angles work too, since the last has to be the same no matter what) ASA and SSS
Step-by-step explanation:
I believe this is the same as before? As far as I know these are the main rules for proving similarity. (AAS and A** do not exist (Brainly won't let me say the two Ss), make sure no trick questions get you ;p)
I'm not sure if what you needed earlier was the relationships between angles to find them? Like to find Exterior Angles subtract <C from 180 = <EA?
Identify the area of the trapezoid. Please help!
Answer:
[tex]\large\boxed{A=46x\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
b₁, b₂ - bases
h - height
We have
b₁ = 12m , b₂ = 6.4 m, h = 5x m.
Substitute:
[tex]A=\dfrac{12+6.4}{2}\cdot5x=\dfrac{18.4}{2}\cdot5x=9.2\cdot5x=46x[/tex]
The correct option is a) [tex]\large\boxed{A=46x\ m^2}[/tex]
The formula of an area of a trapezoid:
[tex]A=(b_1+b_2)/(2)\cdot h[/tex]
b₁, b₂ - bases
h - height
We have
b₁ = 12m , b₂ = 6.4 m, h = 5x m.
Substitute:
[tex]A=(12+6.4)/(2)\cdot5x=(18.4)/(2)\cdot5x=9.2\cdot5x=46x[/tex]
What is the width of a rectangular room with an are 90 square feet and a length of 9 feet
[tex]A=lw\Rightarrow w=\frac{A}{l}=\frac{90}{9}=10\: ft[/tex]
Answer:
10 ft
Step-by-step explanation:
Area of a rectangular room is
A = l*w
We know the area and the length
90 = 9*w
Divide by 9
90/9 = 9w/9
10 =w
The width is 10 feet
Approximate the change in the lateral surface area (excluding the area of the base) of a right circular cone of fixed height of h=6 m when its radius decreases from r= 10m to r= 9.9 m
Answer:
The change in the lateral surface area is approximate [tex]6.32\ m^{2}[/tex]
Step-by-step explanation:
we know that
The lateral surface area of the cone is equal to
[tex]LA=\pi r l[/tex]
where
r is the radius of the base
l is the slant height
Part 1
we have
[tex]r=10\ m, h=6\ m[/tex]
Calculate the slant height l (applying the Pythagoras Theorem)
[tex]l^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]l^{2}=10^{2}+6^{2}[/tex]
[tex]l^{2}=136[/tex]
[tex]l=\sqrt{136}\ m[/tex]
Find the lateral area of the cone
[tex]LA=\pi (10)(\sqrt{136})[/tex]
[tex]LA=10\pi \sqrt{136}\ m^{2}[/tex]
Part 2
we have
[tex]r=9.9\ m, h=6\ m[/tex]
Calculate the slant height l (applying the Pythagoras Theorem)
[tex]l^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]l^{2}=9.9^{2}+6^{2}[/tex]
[tex]l^{2}=134.01[/tex]
[tex]l=\sqrt{134.01}\ m[/tex]
Find the lateral area of the cone
[tex]LA=\pi (9.9)(\sqrt{134.01})[/tex]
[tex]LA=9.9\pi \sqrt{134.01}\ m^{2}[/tex]
Part 3
Find the change in the lateral surface area
[tex]10\pi \sqrt{136}-9.9\pi \sqrt{134.01}[/tex]
assume [tex]\pi =3.14[/tex]
[tex]10(3.14)\sqrt{136}-9.9(3.14)\sqrt{134.01}=6.32\ m^{2}[/tex]
To approximate the change in the lateral surface area of a right circular cone with a fixed height of 6m, we can use the formula √A = 2πrL, where A is the cross-sectional area, r is the radius, and L is the slant height. By calculating the slant height for both radii and using the formula, we find that the change in the lateral surface area is 15.36m².
Explanation:To approximate the change in the lateral surface area of a cone, we can use the formula √A = 2πrL, where A is the cross-sectional area, r is the radius, and L is the slant height. In this case, the height (h) is fixed at 6m. So, we need to find the slant height for both radii, using the formula L = √(r² + h²).
Step 1: Find the slant height for the first radius, r1 = 10m:
L1 = √(10² + 6²) = √136 = 11.66m
Step 2: Find the slant height for the second radius, r2 = 9.9m:
L2 = √(9.9² + 6²) = √135.20 = 11.61m
Step 3: Calculate the change in the lateral surface area, using the formula √A1 - √A2:
√A1 = 2π x 10m x 11.66m = 732.94m²
√A2 = 2π x 9.9m x 11.61m = 717.58m²
Change in Lateral Surface Area = √A1 - √A2 = 732.94m² - 717.58m² = 15.36m²
Learn more about Approximating change in lateral surface area of a cone here:https://brainly.com/question/12392369
#SPJ3
Find the area of a triangle when A=22 B=105 and B=14
Answer:
a.30.4 units²
Step-by-step explanation:
Using the triangle attached, we can find the angle at C which is 180-(22+105)=53°
Then we use the sine rule to find the value of side c.
14/sin105=c/sin53
c=(14/sin105)× sin53
c=11.575
We can now use the sine formula to find the area of the triangle. A=(1/2)absin∅
A= (1/2)×14×11.575sin22
A=30.4
Answer:
30.4
Step-by-step explanation:
Correct on edg2020