find the length of the curve. r(t) = 6t i + 8t3/2 j + 6t2 k, 0 ≤ t ≤ 1
The length of the curve is given by the integral of the magnitude of the velocity vector, which is the derivative of the position vector. Taking the derivative of the position vector, we get the velocity vector as follows:
v(t) = 6i + 24t1/2j + 12tk
The magnitude of this vector is
√(6²+ 24²t + 12²t²)
= √(36 + 576t + 144t²).
To find the length of the curve, we need to integrate this magnitude from t=0 to t=1. This is given by the integral:
L = ∫0² √(36 + 576t + 144t²)dt
This evaluates to L = 18.75. Therefore, the length of the curve is 18.75.
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Find the missing side. Round the answers to TWO decimal places.
Answer:
ok so we need to use the pythagorean theorem
a^2+b^2=c^2
3^2+10^2=
the square root of 109
10.4403065089
10.44
Hope This Helps!!!
To solve -6x + 4 = -20, what steps would you perform? Subtract 4. Divide by -6.
Answer:
x = 4
Step-by-step explanation:
Original Equation:
-6x + 4 = -20
Subtract 4 from both sides.
-6x = -24
Divide both sides by -6
x = 4
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Answer:
To solve -6 x + 4 = -20, what steps would you perform?
Subtract
4.
Divide by
-6.
Step-by-step explanation:
what is the sum 3/x+9+5/x-9
Answer:
\(\frac{8}{x}\)
Step-by-step explanation:
what is the sum 3/x+9+5/x-9
\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\) (add \(\frac{3}{x}\) and \(\frac{5}{x}\))
\(\frac{8}{x} + 9 - 9 =\) (solve 9 - 9 = 0)
\(\frac{8}{x}\) ( your answer)
HELP! WILL MARK BRAINLIEST!
Answer:
thank for the free point
Give the probability distribution for the indicated random variable. HINT [See Example 3.] (Enter your probabilities as fractions.) A red die and a green die are rolled, and X is the larger of the two numbers facing up. x 1 2 3 4 5 6
Full question attached
Answer explanation attached
Answer:
bottom right histogram fits the distribution
Step-by-step explanation:
we have chosen the bottom right histogram from the options as this fits the distribution best. It can be observed that probability for each outcome from 1(left from the table) increases till 6(right from the table)
What is the slope of a line that is parallel to the line y = 3/4x + 2?
what is the variable "d" equal to in the equation 2d + 13
Answer:
d=-6.5
Step-by-step explanation:
2d+13=0
2d=-13
d= -13/2
d=-6.5
I really need help on this (:
The answer is the last one
What is f(-2)?
-3
-1
1
3
Can someone explain how to do this? Normally i’d know how to do it but I’m clueless. HELP!!!
The value of the missing sides assuming both triangles are similar will be 18 inches.
What is the similarity?Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
As per the given two triangle,
Suppose the length of missing side is x inches.
Suppoes both triangles are similar by AAA rule.
The ratio of corresponding sides will be same thus,
x/6 = 12/4
x = 3 x 6 = 18 inches
Hence "If both triangles are comparable, the value of the missing sides will be 18 inches".
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15√6 cm
12/54 cm
6√24 cm
Answer:
Step-by-step explanation:
15√6
12√54 = 12√(9×6) = 36√6
6√24 = 6√(4×6) = 12√6
15√6 + 36√6 + 12√6 = 63√6
Question : to the nearest thousandth of an inch what is the length of the diagonal D
The diagonal of rectangular prism with dimensions 7 in x 5 in x 12 in is 14.76 in
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.
A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
Given is a rectangular prism with dimensions 7 in x 5 in x 12 in, we need to find the diagonal of the rectangular prism,
Diagonal of a rectangular prism = √l²+w²+h²
L = length
W = width
H = height
Diagonal of a rectangular prism = √7²+5²+12²
= 14.76 in
Hence, the diagonal of rectangular prism with dimensions 7 in x 5 in x 12 in is 14.76 in
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Solve −3x=2x2−4
using the Quadratic Formula.
Answer:
-3x= 2×2-4
Step-by-step explanation:
-3x= 4-4
-3x= 0
divide both sides by the co-efficient of x
-3x/-3= 0÷-3
x= 0/-3x = 0
The solution of the quadratic equation 2x² + 3x − 4 = 0 will be 2.35 and negative 0.85.
What are the roots of the equation?Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
\(\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\)
The equation is given below.
−3x = 2x² − 4
Simplify the equation, then we have
2x² − 4 = −3x
2x² + 3x − 4 = 0
Then the roots of the equation are given as,
x = [3 ± √(3² - 4 · 2 · (-4))] / (2 · 2)
x = (3 ± 6.403) / 4
x = 2.35, -0.85
The solution of the quadratic equation 2x² + 3x − 4 = 0 will be 2.35 and negative 0.85.
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A hospital needs a supply of an expensive medicine. Company A has the most supply available, 1.7 milligrams, which is twice
the difference between the weight of Company B's supply and Company C's, and 0.9 milligram more than Company C's supply.How many milligrams can the hospital get from these three companies?
The hospital can get 4.15 milligrams from these three companies.
A linear equation is one in which the highest power of any variable is not more than 1. A linear equation in 2 variables can be solved by substitution method, if we have two simultaneous equations.
Here, we know that
Company A's supply of medicine = 1.7 mg
also, company A's supply = 2( B's supply - C's supply)
⇒ 1.7 = 2( B - C)
⇒ 1.7 = 2B - 2C .... (1)
Moreover, we are given that
A's supply = C's supply + 0.9
⇒ 1.7 = C + 0.9
⇒ 1.7 - 0.9 = C
⇒ 0.8 = C
Now, substituting the value of C in (1), we get,
1.7 = 2B - 2(0.8)
1.7 = 2B - 1.6
1.7 + 1.6 = 2B
⇒ B = 3.3/2
B = 1.65
Thus, the total supply from all three companies is (1.7 + 1.65 + 0.8) = 4.15 mg
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x = -9 and y = 2 plz help me plz
Answer: 9 and -2
Step-by-step explanation: because of the way it's writen.
Which expression is equivalent to 2(5)^4
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
Hey I'm not good at math! please help me!
100 Points. Algebra question, photo attached. Graph the function. Describe its key characteristics. Thank you!
Answer:
Domain = (-∞, ∞) Range = (-∞, ∞)
End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞
Inflection Point: (2,0)
Step-by-step explanation:
3. Are all molecules, compounds? Explain.
Answer:
Every combination of atoms is a molecule. A compound is a molecule made of atoms from different elements. All compounds are molecules, but not all molecules are compounds. Hydrogen gas (H2) is a molecule, but not a compound because it is made of only one element.
Step-by-step explanation:
Answer
Every combination of atoms is a molecule. A compound is a molecule made of atoms from different elements. All compounds are molecules, but not all molecules are compounds. For example : Hydrogen gas (H2) is a molecule, but not a compound because it is made of only one element.
Hope that helps :)
Find the area of the following figure: 12yd 8yd 4yd
2.1. Provide a general rule to describe the relationship between the dates of spread and number of people infected infected.
The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.
However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.
This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.
As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.
It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.
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PLEASE HELP ME, I GIVE 69 POINTS FOR CORRECT ANSWER
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
A: Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
B: Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
C: Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
D: Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
(PS: If you choose C, you're wrong.)
Answer:
D
Step-by-step explanation:
I hope this helps! If it does, please mark me Brainliest! Thanks in advance!
A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 9
Answer:
The probability is 1/6
Step-by-step explanation:
Since we are rolling a pair of die, the number of expected results is 36
Sum that can be greater than 9 include;
4,6
6,4
5,5
6,5
5,6
6,6
This shows 6 out of a possible 36
So the probability will be 6/36 = 1/6
If the figures below are similar with a scale factor of 6:5, find the value of x
Using Scale Factor, the value of x = 33.6.
A scale factor is what?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Scale factor = Dimension of the new shape / Dimension of the original shape is the fundamental formula used to calculate it.
The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.
Dimension of the large triangle divided by the little triangle is the formula to utilize.
Based on the accompanying figure,
The little triangle's corresponding side length is 28, whereas the giant triangle's side length is x.
Scale factor = 6/5 Scale factor = 6/5 = 28
x = 33.6
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Complete Question -
If the figures below are similar with a scale factor of 6:5, find the value of x
54 ÷ 6 x (12-4) + 2 =
Answer:
3
Step-by-step explanation:
1. 54÷6 =9
2. (12-4)=8
3. 9-8 = 1
4. 1+2 = 3
5. I hope this helps it's pretty simple oh and 3 is your anansw.Also you can you your calculator
Answer:
a=72\(\frac{2}{3}\)
Step-by-step explanation:
56/6*(12-4)+2=n
56/6*8+2-2=n-2
56/6*8/8=(n-2)/8
x=9\(\frac{1}{3}\)
x=(n-2)/8
y=74\(\frac{2}{3}\)
y=n-2=a
a=72\(\frac{2}{3}\)
Maria heard on the radio that the high temperature that day would be 64 degrees Fahrenheit. To determine the temperature in degrees Celsius, she used the formula C = StartFraction 5 Over 9 EndFraction (F minus 32), where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. Which describes a correct step in the process Maria should take to convert the temperature? Check all that apply.
Substitute 64 for F.
Substitute 64 for C.
Subtract 32 from F before multiplying by StartFraction 5 Over 9 EndFraction.
Multiply the value of F by StartFraction 5 Over 9 EndFraction before subtracting 32.
64 degrees Fahrenheit is approximately 3.6 degrees Celsius.
64 degrees Fahrenheit is approximately 17.8 degrees Celsius.
Answer:
Substitute 64 for F.
Subtract 32 from F before multiplying by StartFraction 5 Over 9 EndFraction.
64 degrees Fahrenheit is approximately 17.8 degrees Celsius.
Step-by-step explanation:
formula for conversion of F to C
C = 5/9(F-32)
C = 5/9(64-32) = 5/9(32) = 17.8 degrees C
Answer:
Substitute 64 for F.
Subtract 32 from F before multiplying by StartFraction 5 Over 9 EndFraction.
64 degrees Fahrenheit is approximately 17.8 degrees Celsius.
Step-by-step explanation:
uh hi how was your day or night?
Question 3 (10 points)
(01.07 MC)
The mass of the Eiffel Tower is about 9.16 ⋅ 106 kilograms. The mass of the Golden Gate Bridge is 8.05 ⋅ 108 kilograms. Approximately how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower? Show your work and write your answer in scientific notation. (10 points)
Answer:
7.96 × 10⁸ kg
Step-by-step explanation:
Step 1: Given data
Mass of the Eiffel Tower (mE): 9.16 × 10⁶ kgMass of the Golden Gate Bridge (mG): 8.05 × 10⁸ kgStep 2: Determine how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower
To determine this ratio, we need to do the following subtraction.
mG - mE = 8.05 × 10⁸ kg - 9.16 × 10⁶ kg = 7.96 × 10⁸ kg
The Golden Gate Bridge has approximately 7.96 × 10⁸ kg more than the Eiffel Tower.
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answer: where is the answer choices
Step-by-step explanation:
Find theValue of x
40°
70°
(5x+10)°
Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.
therefore,\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)
\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)
\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)
\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)
Value of x = 20°
Hey! there . Thanks for your question :)
Answer:
20° is the correct answer.Step-by-step explanation:
In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.
Solution :-
For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :
Step 1: Making equation :
\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)
Solving :
\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)
Step 2: Subtracting 10 on both sides :
\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)
We get ,
\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)
Step 3: Dividing both sides by 5 :
\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)
On cancelling , we get :
\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)
Therefore , value of x is '20°'Verification :-
For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :
40° + 70° = 5(20°) + 10°110° = 100° + 10°110° = 110°L.H.S = R.H.STherefore , our answer is correct .
Hope , it'll help you! :)#\( \underline{ \sf{ \bold{ Keep \: Learning }}}\)