Answer:
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
Step-by-step explanation:
From Geometry we understand that area of triangle is determined by the following expression:
[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (Eq. 1)
Where:
[tex]A[/tex] - Area of the triangle, measured in square centimeters.
[tex]b[/tex] - Base of the triangle, measured in centimeters.
[tex]h[/tex] - Height of the triangle, measured in centimeters.
By Differential Calculus we deduce an expression for the rate of change of the area in time:
[tex]\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}[/tex] (Eq. 2)
Where:
[tex]\frac{dA}{dt}[/tex] - Rate of change of area in time, measured in square centimeters per minute.
[tex]\frac{db}{dt}[/tex] - Rate of change of base in time, measured in centimeters per minute.
[tex]\frac{dh}{dt}[/tex] - Rate of change of height in time, measured in centimeters per minute.
Now we clear the rate of change of base in time within (Eq, 2):
[tex]\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}[/tex]
[tex]\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}[/tex] (Eq. 3)
The base of the triangle can be found clearing respective variable within (Eq. 1):
[tex]b = \frac{2\cdot A}{h}[/tex]
If we know that [tex]A = 130\,cm^{2}[/tex], [tex]h = 15\,cm[/tex], [tex]\frac{dh}{dt} = 2.5\,\frac{cm}{min}[/tex] and [tex]\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}[/tex], the rate of change of the base of the triangle in time is:
[tex]b = \frac{2\cdot (130\,cm^{2})}{15\,cm}[/tex]
[tex]b = 17.333\,cm[/tex]
[tex]\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)[/tex]
[tex]\frac{db}{dt} = -2.262\,\frac{cm}{min}[/tex]
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
Some one plz help this is a wuick question
the answer is c
3.3 x10 restu power minus 3
7. Given a right triangle as shown below, use a calculator to estimate the length of the
missing side to the nearest tenth of a centimeter
Answer:
D. 11.6 cm
Step-by-step explanation:
The missing length of the right angled triangle can be calculated using Pythagorean Theorem as shown below:
[tex] c^2 - b^2 = a^2 [/tex]
Where,
a = x cm
b = 11 cm
c = 16 cm
Thus:
[tex] 16^2 - 11^2 = x^2 [/tex]
[tex] 256 - 121 = x^2 [/tex]
[tex] 135 = x^2 [/tex]
[tex] \sqrt{135} = \sqrt{x^2} [/tex]
[tex] \sqrt{135} = x [/tex]
[tex] 11.61895 = x [/tex]
[tex] x = 11.6 cm [/tex] (nearest tenth)
Answer:
Step-by-step explanation:
11.16
i’ll mark brainlest:( i need help!
Answer: Choice A) [tex]3 \sqrt{26}[/tex]
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Work Shown:
[tex]\text{The two points are } (x_1,y_1) = (6,7) \text{ and } (x_2,y_2) = (3,-8)\\\\d = \text{Distance between } (x_1,y_1) \text{ and } (x_2,y_2)\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} = \text{Distance Formula}\\\\d = \sqrt{(6-3)^2+(7-(-8))^2}\\\\d = \sqrt{(6-3)^2+(7+8)^2}\\\\[/tex]
[tex]d = \sqrt{(3)^2+(15)^2}\\\\d = \sqrt{9+225}\\\\d = \sqrt{234}\\\\d = \sqrt{9*26}\\\\d = \sqrt{9}*\sqrt{26}\\\\d = 3\sqrt{26}\\\\[/tex]
When going from 234 to 9*26, the idea here is to factor where one factor is the largest perfect square possible. That way we can use the rule [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex] to break up the root and simplify.
1 bag of grape tomatoes coast $3 how many packages can you buy for $15
Answer:
5 package
Step-by-step explanation:
1 bag = $3
X bag = $15
1 * 15/3 = 5 bags
hence : 5 bag can be bought out of $15
Dylan mowed three lawns for $45. Determine the cost per lawn
Answer:
15 dollars per lawn
Step-by-step explanation:
45 divided by 3= 15
Answer:
He earned $45 dollars when he mowed 3 lawns.
So get 45 and divide it by 3.
That's 15.
So Dylan earned $15 per lawn.
Hope this helped!!
simplify the square root of -15 times the square root of -20
Step-by-step explanation:
-15√-20 = -15√(-1)*4*5 = -15√(i^2)*2^2*5 = -15i*2√5
= -30i√5
what is 2(3x+4)=x-7
Which fraction is not equivalent to 9/12
PLEASE SOMEBODY HELP ASAP
Answer:
15/20 I am studying with international schooling so you can ask me anything anytime
Answer:
16/24 is NOT equivalent to 9/12
Step-by-step explanation:
9/12 ÷ 3 = 3/4
3/4 × 2 = 6/8
3/4 × 5 = 15/20
3/4 × 8 = 24/32
Enter the coordinates where P' should be.
Answer:
2, -2
Step-by-step explanation:
i have already learned this
Answer:
(-2 , -2)
Step-by-step explanation:
The Area of a rectangle is 70 cm²
What could be the perimeter of the rectangle?
Type Out The Answer.
A) 7 cm
B) 9 cm
C) 12 cm
D) 26 cm
E) 34 cm
GOOD LUCK
Answer:
D
Step-by-step explanation:
Answer:
E.
Step-by-step explanation:
Area=7*10=70
Perimeter=7+7+10+10=34
Thirty-seven school buses arrived at the zoo, each carrying thirty-seven to forty-three students per bus.
Estimate the number of students visiting the museum.
A: 16,000
B: 160
C: 1,600
D: 160,000
Answer:
C 1,600
Step-by-step explanation:
because If you multiply 37*43 It will get you 1591 and it's asking for the estimated answer which is 1600
The sign of the product of –35 and –625 is
Answer:
positive
Step-by-step explanation:
positive
negative*negative=positive
-35*-625=21875
I need help with this ASAP !! I’m failing !!!
Answer:
c=130,b=50
Step-by-step explanation:
[tex]c = 180 - 50 = 130[/tex]
[tex]b = 180 - 130 = 50[/tex]
i think this is the answer
Intro:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
<b and 50° are vertical angles so that means they are congruent. So that means <b is 50.
<c and 50° are supplementary angles which means when you add them you should get 180. So if do 180 - 50 we will get 130. So that means <c is 130°.
multiply the complex number by this complex conjugate.
16. 8+i
17. 3 - 2i
18. -7- 5i
Two different box-filling machines are used to fill cereal boxes on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is 1 ounce. Experiments are conducted using both machines with sample sizes of 36 each. The sample averages for machines A and B are 4.5 ounces and 4.7 ounces respectively. Engineers are surprised that the two sample averages for the filling machines are so different. a. Use the CLT to determine the distribution of �$! − �$ ". b. What is �(�$! − �$ " ≥ 0.2)?
Answer:
0.1981
Step-by-step explanation:
See attachment for calculation
Jada is putting a border around her rectangular garden. The garden is 12.63 meters long and 3.28 wide. Jada estimates the perimeter of her garden by rounding the length and width to the nearest whole number. What equation shows
Answer:
12.63 rounded to 13 and 3.28 rounded to 3 the perimeter is 32
Choose the true statement.
Answer:
-8 < 8
Step-by-step explanation:
-8 is less than 0 so it is definitely less than 8
Hope this helped :)
The mean mass of the 15 players in a rugby team is 85.2kg the mean mass of the team plus a substitute is 85.4kg what is the mass of the substitute ?
Answer:
88.4 kg
Step-by-step explanation:
Since we are given the mean we will need to multiply the mean by how many players there are on the team to find the total mass. (The second mean will be multiplied by 16 because it is the number of players on the team plus the substitute)
85.2 x 15 = 1,278
85.4 x 16 = 1,366.4
Subtract the first mass from the second because this will remove the mass of the 15 other players.
1366.4 - 1278 = 88.4
88.4 kg is the mass of the substitute.
The ratio of the number of boys to the number of girls I just school is 5 to 8 if there are 208 students in the school how many girls can you expect
Answer:
128 girls
Step-by-step explanation:
boys : girls = 5 : 8
Number of boys = 5x
Number of girls = 8x
Total students = 208
5x + 8x = 208
13x = 208
x = 208/13
x = 16
Number of girls = 8x = 8 * 16 = 16 * 8
= 128
Answer:
12
Step-by-step explanation:
Find the equation of the line khan academy slope intercept equation from the graph
PLEASE HELP!!!
find the slope of the graphed line
Answer:
rise over run
Step-by-step explanation:
In this case it is undefined
On a lunch counter, there are 3 oranges, 5 apples, and 2 bananas. If 3 pieces of fruit are selected, find the probability that 1 orange, 1 apple, and 1 banana are selected (does not have to be in that order).
Answer:
[tex]Probability = \frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]Oranges = 3[/tex]
[tex]Apples = 5[/tex]
[tex]Banana = 2[/tex]
[tex]Total = 10[/tex]
Required
Determine the probability of 1 orange, 1 apple and 1 banana
Since, order is not important:
[tex]Probability = P(Orange) * P(Apple) * P(Banana)[/tex]
[tex]Probability = \frac{3}{10} * \frac{5}{9} * \frac{2}{8}[/tex]
The difference in the numerator is as a result of picking the fruit without replacement
[tex]Probability = \frac{30}{720}[/tex]
[tex]Probability = \frac{1}{24}[/tex]
Probability is simply how likely something is to happen.
The probability of 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]
On lunch counter,
Number of oranges = 3
Number of apples = 5
Number of bananas = 2
If 3 piece of fruit is selected then, probability of 1 orange, 1 apple and 1 banana
[tex]=\frac{3}{10}*\frac{5}{9} *\frac{2}{8} \\\\=\frac{30}{720}\\\\=\frac{1}{24}[/tex]
Therefore, the probability of selecting 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]
Learn more:
https://brainly.com/question/15589719
this is an simplified or not?
[tex] \frac{3}{x - 5?} [/tex]
can u solve this please? 18x-2 = 17x +2
Answer:
Step-by-step explanation:
18x-2 = 17x +2
⇒18x-17x - 2 = 2
⇒x - 2 = 2
∴ x = 4
Answer:
x=4
Step-by-step explanation:
18x-2=17x+2
step 1: isolate the x by subtracting 17x from both sides
18x-2-17x=17x+2-17x
x-2=2
then add 2 to both sides
x-2+2 = 2+2
x=4
What value of a will make the following equation true?
Answer:
a=16
Step-by-step explanation:
Answer:
A=4
Step-by-step explanation:
6th grade math I mark as brainliest
Answer:
4 1/6
Step-by-step explanation:
If you divide 25 (Miles) by 6 (Days) then you get:
4.1666666666666666666666666666667.
But, when you make it a fraction you get 4 1/6.
Answer:
4 1/6
Step-by-step explanation:
25/6
Hope this helps! Good Luck!
I need help on it pls
Answer:
6
Step-by-step explanation:
26+32=58 and if there is 58 kids then they would need 6 vans but one van is holding 8 kids
Answer:
6 vans / in the first 5 10 kids in each and in the 6th van only 8 kids.
Step-by-step explanation:
1.) 26+32=58
2.) 58 divided by 10=5 8/10=6vans
brainliest pls B) hope i help
You have 8 donuts and you want to give 1/4 of them to a friend. How many donuts would your friend get?
Answer: pretty sure the friend would get 2 donuts
Step-by-step explanation:
4950/6 + 112 x 1.75 = ? x 2
Answer:
1021
Step-by-step explanation:
Answer:
1021 is the answer to this question
Which point represents the opposite of –2?
A number line going from negative 5 to positive 5. Point A is at negative 2, point B is between negative 1 and 0, point C is between 0 and 1, and point D is at 2.
A
B
C
D
Answer:
D
Step-by-step explanation:
I did this already