Answer:
32
Step-by-step explanation:
Find the surface area of a triangular prism that has a height of 11 meters and the following triangular base. All
dimensions are in meters.
13.5
4
surface area =
m?
Answer:
3 is your answer took the test
Step-by-step explanation:
Answer:
S A = 146 m^2
Step-by-step explanation:
Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 10 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks at a rate of 8 cubic feet per minute?
Answer:
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Step-by-step explanation:
Given
Represent radius with r and height with h
[tex]h = 12ft[/tex]
[tex]r = 10ft[/tex]
[tex]Rate = \frac{8ft^3}{min}[/tex] when [tex]h = 10ft[/tex]
Express radius in terms of height
[tex]\frac{r}{h} = \frac{10}{12}[/tex]
[tex]\frac{r}{h} = \frac{5}{6}[/tex]
[tex]r = \frac{5}{6}h[/tex]
First, we need to determine the volume of the cone in terms of height.
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Substitute [tex]r = \frac{5}{6}h[/tex]
[tex]V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^3[/tex]
[tex]V = \frac{25}{108} \pi h^3[/tex]
Differentiate both sides w.r.t time (t)
[tex]\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}[/tex]
Solve for [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}[/tex]
At this point, [tex]h = 10[/tex] and [tex]\frac{dv}{dt} = \frac{8ft^3}{min}[/tex]
So, we have:
[tex]\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{864}{7500\pi}[/tex]
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Hence:
The rate is [tex]\frac{216}{1875\pi} ft/min[/tex]
Using implicit differentiation, it is found that the depth of water changes at a rate of -0.0764 feet per minute.
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
Applying implicit differentiation, we can find it's rate of change, thus:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
In this problem:
Height of 12 ft and radius of 10 ft, thus [tex]h = 12, r = 10[/tex].Radius does not change, thus [tex]\frac{dr}{dt} = 0[/tex].Water leaks at a rate of 8 cubic feet per minute, thus [tex]\frac{dV}{dt} = -8[/tex]Then:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
[tex]-8 = \frac{\pi (10)^2}{3}\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = -\frac{24}{100\pi}[/tex]
[tex]\frac{dh}{dt} = -0.0764[/tex]
The depth of water changes at a rate of -0.0764 feet per minute.
A similar problem is given at https://brainly.com/question/9543179
Match the number with its opposite.
Match Term Definition
9.2 A) 2.9
−2.9 B) −9.2
−1.4 C) −4.1
4.1 D) 1.4
Answer:
9.2 - B
-2.9 - A
-1.4 - D
4.1 - C
Step-by-step explanation:hope this helps
Lex be a random variable that represents the pH of arterial plasma (le, acidity of the blood). For healthy adults, the mean of the distribution is - 7.4.1 A new drug for arthritis has
been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with
sample standard deviations - 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
USE SALT
(a) what is the level of significance?
what is the value of the sample test sisse? (Round your answer to three decimal places)
Answer:
2.304
Step-by-step explanation:
PLEASE HELP
Logan bought a baseball bat on a trip. The baseball bat is 29 inches long.
Logan thinks he can bring the baseball bat home in his suitcase. Is he correct? Use your understanding of the Pythagorean Theorem to explain your answer.
Answer:
Use a^2 + b^2 = c^2 and substitute
18^2 + 24^2 = c^2
Solve what we know
324 + 576 = c^2
324 + 576 = 900
Square root 900 to get C
sqrt of 900 equals 30
So, yes he can fit the baseball bat in his suitcase
Please help I will put brainliest
Answer:
−64x12y12
Good Luck!!!
Answer:
[tex]-64x^{12} y^{12}[/tex]
Step-by-step explanation:
1. remove parentheses by multiplying factors.
2. use exponent rules to remove parentheses in terms with exponents.
3. combine like terms by adding coefficients.
4. combine the constants.
Evaluate 2x+6y when x= -4/5 and y= 1/3 Write your answer as a fraction or mixed number in simplest form.
2/5 is a answer
in this we can se the answer is 2/5
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
How many ounces are in 4 gallons?
Answer:
512
Step-by-step explanation
128 ounces in a gallon times that by 4. ====== ....... 512.
Ur welcome please heart this
10times larger than 40
Answer:400
Step-by-step explanation:10×40=400
Answer:400
Step-by-step explanation:
You are a school photographer taking individual and class pictures for 2 classes of 21 students each. On average, each individual picture takes 3 minutes and a class picture takes 10 minutes.About how long should it take you to get all of the pictures
Answer:
2h and 26 minutes
Step-by-step explanation:
21x2=42
42x3=126
2x10=20
126+20=146
146m=2h 26m
W/4 -4=3
Solve the eqution pls!
Answer:
W=28
Step-by-step explanation:
(W/4)-4=3
(W/4)=7
W=28
A 2 1/2 pound bag of grass seed covers 1/8 of an acre. How much grass seed is needed for 1 acre?
Answer:
it needs 234 grass seeds for the acre
Solve the inequality.
2(4+2x)25x+5
Answer:
[tex]100x^{2} +200x+5[/tex]
Step-by-step explanation:
Answer:
x ≤ 3
Step-by-step explanation:
Find the solution to the equation.
4(x + 7) = 38 i need it ASAP plzzz
Answer:
x = 2.5
or
x = 1/4
Step-by-step explanation:
watch the following steps:
4x + 28 = 38
4x = 38 - 28
4x = 10
x = 2.5
or
x = 1/4
Pls consider marking my answer as Brainliest! It would mean a lot!
Answer:
2.5, maybe
Step-by-step explanation:
distribute 4 into x and 7
subtract 28 from both sides (28-28, 38-28)
divide 4 and 10
2.5
it seems odd...
I need help ASAP please
A circle is 360 degrees so 360 = b + 96 + 209
360 = b + 305
b = 55 degrees.
Use the multiplier method to increase £72 by 12%
You must show your working.
Answer:
£80.62
Step-by-step explanation:
100+12%=112%
112/100= 1.12
1.12*£72 =£80.62
3. A store manager reports that the mean grocery bill at her store on a Saturday is between
$28.25 and $36.75. To do this, she considered a random sample of customers that Saturday.
What was the sample mean? (Remember that the sample mean is the center of the confidence
interval). What was the margin of error?
Answer:
Hope you understand, and never stop striving to learn!
Step-by-step explanation:
The sample mean is both values added together then divided by 2.
$46.63
The margin of error is the low value divided by the high value * 100% =76.8% (then you have to minus this from 100% so the margin of error is 23.2%)
FIRST RIGHT GETS BRAINLIEST
Answer:
-1 + 7 =-8
Step-by-step explanation:
Answer:
-6, -7
Step-by-step explanation:
-1 + -6 = -7
A food truck sells tacos $1.25 a piece. The truck operator earned $360.00 last night.
How many tacos did the food truck sell last night?
28.8 tacos
288 tacos
300 tacos
2.88 tacos
Answer:
288
Step-by-step explanation:
Each taco is 1.25 dollars and you are trying to figure out how many tacos he sold to do this we make an equation.
Step 1
1.25 x = 360
x =is the amount of tacos sold.
Step 2
1.25 x = 360
/1.25 /1.25
to get x on its own we need to cancel out the 1.25 so we dived because it was multiplied to the x. we did the same on the other side to balance the equation.
Step 3
x = 288
we now need to identify what x is, we can see it is 288. If we trade x for what it means it is then this is your answer the amount of tacos sold=288
i hope this helps ;)
For how many different positive integers n is each of n, n+2, and n+4 a prime number?
Answer:
3,5,7
Step-by-step explanation:
odd numbers is a multiple of three, at least one of them can't be prime
hope this helps there is 1 of them
3 + 8 + 6 + 6 + 6 = 58 + 6
How do we solve this
Answer:
93
Step-by-step explanation:
A, B, C, or D???? Please help! Thank you!
Answer:
Step-by-step explanation:
either the c or d
Name an equivalent ratio for One-half with a denominator of 8.
a. 4 Over 8
c. 5 Over 8
b. 1 Over 8
d. 3 Over 8
Answer:
it is A
Step-by-step explanation:
Taylor is driving on the freeway at 55 miles per hour. What question finds her distance
Answer:
distance(miles) = number of hours driven * 55
Step-by-step explanation:
The school store sells 4 pencils for $0.80. What is the unit cost of a pencil?
q(x) = –2x+1
r.(x)=x²+2
Find the value of q (r (3)).
Can someone please help?
match the simplified expressions to an equivalent expression
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 36 x2 x dx
We need to find the integration of (36x²)x.dx .
We know,
[tex]\int x^n.dx = \dfrac{x^{n+1}}{n+1} +c[/tex]
Now,
[tex]I=\int {36x^2x} \, dx \\\\I=36\int x^3.dx\\ \\I=36\times \dfrac{x^4}{4}+c\\\\I=9x^4+c[/tex]
Therefore, the integration of (36x²)x.dx is [tex]9x^4+c[/tex] .
Hence, this is the required solution.
Lines m and n are parallel. What is
Answer:
Line m and m is a straight line