Answer:
45 degrees
Step-by-step explanation:
sin x=cos(90-x)
sin(45)=cos(90-45)=cos(45)
Answer:
The answer is 45.
sin45=cos45= 1/√2.
hope it helps u ...
find the area of the triangle. ? square units
Answer:
54 square units
Step-by-step explanation:
The formula for the area of a triangle is:
[tex]\frac{1}{2}[/tex] x base x height
The base is 12
The height is 9
So 1/2 x 12 x 9 = 54 square units
Please help. I’ll mark you as brainliest if correct!
These are 2 math problems .
Answer:
-4 503/12 ≈ 41.91667Step-by-step explanation:
To find the average rate of change, find the change in function value, and divide that by the length of the interval.
1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4
The average rate of change of g(x) on [-1, 1] is -4.
__
2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5
= (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5
= 503/12 = 41 11/12
The average rate of change of g(x) on [-2, 3] is 41 11/12.
if you start with (2,6) and move 2 units right and 3 units down what will you end up with?
For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.
Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.
The answer would be (4,3)
sider F and C below. F(x, y, z) = yz i + xz j + (xy + 4z) k C is the line segment from (1, 0, −2) to (6, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = xyz+2z2+c (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
Answer:
a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]
b) The value of the integral is 18
Step-by-step explanation:
a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that
[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]
From here, we have that
[tex] yz = \frac{\partial f}{\partial x}[/tex]
if we integrate both sides with respect to x, we get that
[tex] f(x,y,z) = xyz+ g(y,z)[/tex]
where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is
[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]
This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form
[tex] f(x,y,z) = xyz+g(z)[/tex]
If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get
[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]
This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]
So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]
b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is
[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answer:
8 and 64
Step-by-step explanation:
[tex]2^3[/tex] and [tex]4^3[/tex]
[tex]2^3=8[/tex]
[tex]4^3=64[/tex]
Find the number of possible outcomes if the numbers 1 through 7 are written on different pieces of paper and placed in a hat. Two of these numbered pieces of paper are selected without replacement, and a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.
Answer:
The number of the possible outcomes are:
12,13,14,15,16,17
21,23,24,25,26,27
31,32,34,35,36,37
41,42,43,45,46,47
51,52,53,54,56,57
61,62,63,64,65,67
71,72,73,74,75,76
The total number of possible outcomes = 42
Step-by-step explanation:
Given that :
the numbers 1 through 7 are written on different pieces of paper; &
Two of these numbered pieces of paper are selected without replacement;
Also,
a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.
Then:
if the first number drawn is 1 , then the possible outcomes will be :
12,13,14,15,16,17
If the first number drawn is 2; then the possible outcomes will be:
21,23,24,25,26,27
If the first number drawn is 3; then the possible outcomes will be:
31,32,34,35,36,37
If the first number drawn is 4; then the possible outcomes will be:
41,42,43,45,46,47
If the first number drawn is 5; then the possible outcomes will be:
51,52,53,54,56,57
If the first number drawn is 6; then the possible outcomes will be:
61,62,63,64,65,67
If the first number drawn is 7; then the possible outcomes will be:
71,72,73,74,75,76
The number of the possible outcomes are:
12,13,14,15,16,17
21,23,24,25,26,27
31,32,34,35,36,37
41,42,43,45,46,47
51,52,53,54,56,57
61,62,63,64,65,67
71,72,73,74,75,76
The total number of possible outcomes = 7 × 6 = 42
Let uequalsleft angle 4 comma negative 3 right angle, vequalsleft angle negative 2 comma 5 right angle, and wequalsleft angle 0 comma negative 6 right angle. Express 7 Bold u minus 5 Bold v plus Bold w in the form left angle a comma b right angle.
Answer:
[tex]<38,52>[/tex]
Step-by-step explanation:
[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]
We are required to express 7u-5v+w in the form <a,b>.
[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]
Use the substitution and to rewrite the equations in the system in terms of the variables and . Solve the system in terms of u and v . Then back substitute to determine the solution set to the original system in terms of x and y.
-3/x+4/y=11
1/x-2/y=-5
Answer:
x = -1 and y = 1/2
Step-by-step explanation:
Let u = 1/x, and v = 1/y
Then the pair of equations
-3/x + 4/y = 11
1/x - 2/y = -5
Can be written as
-3u + 4v = 11 .................................(1)
u - 2v = -5......................................(2)
From (2)
u = 2v - 5 .......................................(3)
Substituting (3) into (1)
-3(2v - 5) + 4v = 11
-6v + 15 + 4v = 11
-6v + 4v = 11 - 15
-2v = -4
v = 4/2 = 2
Substituting this value of v in (3)
u = 2v - 5
u = 2(2) - 5
= 4 - 5
= -1
That is
u = -1, v = 2
Since u = 1/x, and v = 1/y, we have
1/x = -1
=> x = -1
And
1/y = 2
=> y = 1/2
Therefore
x = -1 and y = 1/2
A 500.0 g piece of aluminum at 100° C is placed in 300ml of water. While in the water, the
aluminum then cools to 30°C. Calculate the amount of heat lost by the aluminum. The
specific heat of water is 4.18 J/g °C and the specific heat of aluminum is 0.90 J/g °C
Answer:
The amount of heat lost by the aluminum is 31,500 J
Step-by-step explanation:
Given;
mass of aluminum, m = 500 g
initial temperature of the aluminum, θ₁ = 100° C
final temperature of the aluminum, θ₂ = 30°C
specific heat capacity of water, C = 4.18 J/g °C
specific heat capacity of aluminum , C = 0.90 J/g
Heat lost by the aluminum is equal to heat gained by the water.
The amount of heat lost by the aluminum, is calculated as;
Q = MCΔθ
Q = 500 x 0.9 (100 - 30)
Q = 500 x 0.9 x 70
Q = 31,500 J
Therefore, the amount of heat lost by the aluminum is 31,500 J
Find the equations for a conical helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane). Include a plot of your conical helix.
Answer:
The equation are
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
z = z
Step-by-step explanation:
From the question we are told that
The radius of the conical helix is [tex]r= 8[/tex]
The height of the conical helix is [tex]h = 12[/tex]
The angular frequency is [tex]w = 2[/tex]
The plot of the conical helix is shown on the first uploaded image
Generally the parametric equation of a conical helix is mathematically represented as
for x -axis
[tex]x =\frac{ h-z }{h} r cos (wz)[/tex]
substituting values
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
for y-axis
[tex]y = \frac{h-z }{h} rsin (wz)[/tex]
substituting values
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
for z-axis
z = z
2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project
Answer:
It will take them approximately 51.43 minutes to complete the project together
Step-by-step explanation:
This is what is called a "shared job" problem.
The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.
So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project
Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.
We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).
Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.
In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:
[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]
So it will take them approximately 51.43 minutes to complete the project together.
What is the formula to find the area of parallelogram
Step-by-step explanation:
area of parallelogram= height * length of base
Please answer this correctly
Answer:
pic wont load
Step-by-step explanation:
Answer:
The quarter circle's area is 38.47 yard²
Step-by-step explanation:
The area of a full circle is pi * r ²
The area of a quarter circle is 1/4 * pi * r ²
Given:
Use 3.14 for pi
Round to the nearest hundredths.
Perimeter of quarter circle is 24.99 yards
For r you must leave it as 'r' because we do not know it for now...
1. Circumference of a full circle = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * r )
1/2 * 3.14 * r
1.57 * r
3 Since r = 'r'
We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.
4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch
1.57 * r + 2 * r = 24.99
( 1.57 + 2 ) * r = 24.99
3.57 * r = 24.99
Divide left and right of the = sign by 3.57
3.57 / 3.57 * r = 24.99 / 3.57
1 * r = 24.99 / 3.57
r = 7
The area of a quarter circle is 1/4 * pi * r ²
1/4 * pi * 7²
1/4 * 49 * pi
49/4 * pi
49/4 * 3.14
38.465
Round to the nearest hundredths gives 38.47 yard²
The quarter circle's area is 38.47 yard²
A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
HELP WITH THIS PLEASE
Answer:
a = 35º
b = 140º
c = 40º
d = 140º
e = 58º
Step-by-step explanation:
Angle A is supplementary to the angle that is 145º, and supplementary angles always add up to 180º. Therefore, 180 - 145 = 35, the measure of angle a. Angle B is supplementary to the 40º angle, so its measure is 140. Angle C is opposite the 40º angle, and opposite angles are congruent, so its measure would also be 40º. Angle D is also 140º because it is opposite of angle B. Angle E is supplementary to the angle that measures 122º, so 180 - 122 = 58. Hope this helped!
find the square root of 12 to the nearest hundredth
Answer:
\sqrt(12) hope this helped.
A commuter train travels 65 kilometers in 27 minutes. What is it’s speed in kilometers per hour?
Answer:
Per hour: 2.40740740741
Step-by-step explanation:
you have to divided 65 and 27 so
65/27
which is 2.40740740741
When estimating a job to bid, a contractor’s estimator first determines the actual cost of labor using the function L(h) = 28.75h, where h is the number of estimated hours it will take to complete the job. Next, the estimator adds the labor burden, which accounts for taxes and insurance, using the function B(L) = 1.78L. Finally, the estimator calculates the selling price, including the markup for overhead and profit, using the function M(B) = 1.43B. Which composite function can be used to find the selling price for the labor portion of a bid based on the estimated number of hours?
Answer:
M(h) = 73.18025h
Step-by-step explanation:
The composite function is ...
M(B(L(h))) = M(B(28.75h)) = M(1.78(28.75h)) = M(51.175h)
= 1.43(51.175h) = 73.18025h
The composite function is ...
M(h) = M(B(L(h))) = 73.18025h
Answer:
a
Step-by-step explanation:
YOU KNOW THE DRILL 2.0
Answer:
#1
Step-by-step explanation:
The four yellow boxes represent x so together they are 4 * x or 4x. The blue boxes seem to represent -1 and since there are three of them together they are -1 * 3 = -3. 4x + (-3) = 4x - 3.
A triangular plate with base 3 m and height 5 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
The hydro-static force [tex]F=245000N[/tex]
Step-by-step explanation:
given data
base = 3 m
height = 5 m
density of water = 1000 kg/m3
Acceleration due to gravity = 9.8
The area if the strip needs to be calculated using similar triangular formula as well as the hydrostatic force
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
Colgate claims that 90% of dentists recommend Colgate toothpaste. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answer:
the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;
P(X) = 0.0043
P(X) = 0.43%
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 90% = 0.9
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.9 = 0.1
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.9)^8 × (0.1)^2
P(X) = 0.0043
P(X) = 0.43%
The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.
Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.
Probability of dentist, who recommend Colgate toothpaste = 0.9
Probability of dentist, who does not recommend Colgate toothpaste,
= 1 - 0.9 = 0.1
When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend Colgate toothpaste and 2 recommend other tooth paste.
Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,
[tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]
Learn more:
https://brainly.com/question/20046335
which is the equation of a circle with center (-3, -5) and radius of 4
Answer: -8
Step-by-step explanation:
Find the area of the triangle
Answer:
54
Step-by-step explanation:
A = (9*12)/2
A = 9*6
A = 54
Answer:54
Step-by-step explanation:
multiply 9 and 12 then divide by 2 because a triangle is half of a square
The volume of the box shown in the diagram is 40π3 cubic units. Find the length of ‘x’.
Answer:
4: 4[tex]\pi^2[/tex]
Step-by-step explanation:
2[tex]\pi[/tex] x 5 x [tex]x[/tex] = 10[tex]\pi x[/tex]
10[tex]\pi x[/tex] = 40[tex]\pi ^3}[/tex]
x = 4[tex]\pi^2[/tex]
Answer:
4π units
Step-by-step explanation:
v=lwh
40π^3=2π×5×h
40π^3=10π^2×h
h=40π^3/10π^2
h=4π units
mark brianliest if my answer suit your question please.
A car travels 300 miles in 10 hours at a constant rate. If the distance traveled by the car can be represented as a function of
the time spent driving, what is the value of the constant of variation, K?
O 1/30 mph
30 mph
60 mph
3000 mph
Answer:
30 mph
Step-by-step explanation:
Distance travelled=300 miles
Time travelled=10hours
At a constant rate,k
Let distance travelled=d
Time travelled=t
Then,
d=kt
300=k*10
300=10k
k=300/10
=30
k=30mph
30 miles per hour
30 MPH ............................................................................................................
The radius of a circle is 10.7 m. Find the circumference
to the nearest tenth.
Answer:
2 x [tex]\pi[/tex] x 10.7 = 67.2
Step-by-step explanation:
Step-by-step explanation:
c=2πr
c=2×π×10.7m
c=67.2m
so about 67
NEED ASAP!!!!
Which equation represents the grafted function
Answer:
sorry i meant c
Step-by-step explanation:
Write down the 1st term in the sequence given by: T(n) = n² + 3
Answer:
4
Step-by-step explanation:
T(n) = n² + 3
T(1) = 1² + 3 = 1 + 3 = 4
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
P(greater than 1.25 minutes) = 0.8611 (Approx)
Step-by-step explanation:
Given:
Waiting time = 0 - 9 minutes
Find:
Probability that selected passenger has a waiting time greater than 1.25 minutes.
Computation:
⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =
⇒ P(greater than 1.25 minutes) = [9-1.25] / 9
⇒ P(greater than 1.25 minutes) = [7.75] / 9
⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)
