Answer:
1.) 14.09 m/s
2.) 6.9 m/s
Step-by-step explanation:
Given that the boat is pointing North and can typically move at a speed of 12.8 m/s in calm waters. The boat travels through water where there is a 5.9 m/s current flowing to the East.
The speed of the boat relative to a stationary observer on land will be achieved by using pythagorean theorem
V^2 = 12.8^2 + 5.9^2
V^2 = 198.65
Square root both sides
V = 14.09 m/s
2.) If the boat turns to face directly West.
Since the boat can move at speed 12.8 m/s in a calm water, the speed of the boat if it face west will be
12.8 - 5.9 = 6.9 m/s
Therefore, the boat is moving relative to land at 6.9m/s
Jasmin, Quinn, and Maddy are rock climbing. Jasmin is 42 ½ feet below Quinn. Maddy is 67 ¾ feet above Jasmin. What is Maddy's position compared to Quinn?
Answer:
[tex]25\frac{1}{4}[/tex] feet
Step-by-step explanation:
Given
[tex]Maddy = 67\frac{3}{4}[/tex] above Jasmin
[tex]Jasmin = 42\frac{1}{2}[/tex] below Quinn
Required
Determine Maddy's position relative to Quinn's
From the given parameter, one can easily deduce that Quinn is in between Maddy and Jasmin (See attachment)
Using the attachment as a point of reference;
[tex]z = 67\frac{3}{4}[/tex]
[tex]x = 42\frac{1}{2}[/tex]
The relationship between x, y and z is
[tex]z = y + x[/tex]
Make y the subject of formula
[tex]y = z - x[/tex]
Substitute the values of z and x
[tex]y = 67\frac{3}{4} - 42\frac{1}{2}[/tex]
Convert to improper fractions
[tex]y = \frac{271}{4} - \frac{85}{2}[/tex]
Take LCM
[tex]y = \frac{271 - 170}{4}[/tex]
[tex]y = \frac{101}{4}[/tex]
[tex]y = 25\frac{1}{4}[/tex]
Hence; Maddy's position relative to Quinn's is [tex]25\frac{1}{4}[/tex] feet
The 100 residents are asked if they like to watch basketball and or football. The results are that 98 like to watch basketball, 12 like to watch football, and 2 dislike both. How many like to watch football?
Answer:
12 people like to watch football
Step-by-step explanation:
The results are that 98 like to watch basketball, 12 like to watch football, and 2 dislike both.
Total number of residents = 100
Basketball (B) = 98
Football(F) = 12
Number of residents that like basketball and football = ( B ∩ F)
2 dislike both
n ( B ∪ F) - People that dislike it = n(B) + n ( F ) - n ( B ∩ F)
100 - 2 = 98 + 12 - n ( B ∩ F)
98 = 110 - n ( B ∩ F)
n ( B ∩ F) = 110 - 98
= 12
Therefore, 12 people like both Football and Basketball
How many like to watch football?
From the above question, we can see that the total number of people that like to watch football = 12 people
I’m really confused on how to do this
Answer:
Substitute x with six in the equation and solve as normal.
Step-by-step explanation:
The format here is a bit weird, but it basically means x is six.
What Do You Want To Learn About In Math This Year
Answer:
math
Step-by-step explanation:
Find p(4) and p(-2) for each function.
p(x) = x² – 3x + 8
Answer:
p(x)=x2 - 3x + 8
p(4) =(4)2 - 3(4) + 8
= 16 - 12 + 8
= 4+8
= 12
p(-2)= (-2)2 - 3(-2) + 8
= 4+6+8
=18
9*9=??????????????????????
Answer:
18
Step-by-step explanation:
9+9=18 bam solved it
3. Your friend is having trouble deciding which shirt, tie, and pair of pants to wear to
his school's formal dance. He has 4 shirts, 3 pairs of pants, and 4 ties. How many
total possible outfits can be created?
64 outfits
16 outfits
48 outfits
12 outfits
Answer: 4 shirts x 3 pairs of pants x 4 ties = 4 x 3 x 4=48
so there are 48 possibilities (option 3)
3. What is the volume of the triangular
prism?
Answer:
C. 51,84
Step-by-step explanation:
the volume of the triangular prism is 1/2*3.2*5.4*6
Answer:
C
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular end, l is the length )
A = [tex]\frac{1}{2}[/tex] bh ( b is the base, h the perpendicular height )
Here b = 5.4 and h = 3.2 , thus
A = 0.5 × 5.4 × 3.2 = 8.64 cm² , then
V = 8.64 × 6 = 51.84 cm³ → C
What is the upper bound of the function f(x)=4x4−2x3+x−5?
Answer:
(no global maxima found)
Step-by-step explanation:
Find and classify the global extrema of the following function:
f(x) = 4 x^4 - 2 x^3 + x - 5
Hint: | Global extrema of f(x) can occur only at the critical points or the endpoints of the domain.
Find the critical points of f(x):
Compute the critical points of 4 x^4 - 2 x^3 + x - 5
Hint: | To find critical points, find where f'(x) is zero or where f'(x) does not exist. First, find the derivative of 4 x^4 - 2 x^3 + x - 5.
To find all critical points, first compute f'(x):
d/( dx)(4 x^4 - 2 x^3 + x - 5) = 16 x^3 - 6 x^2 + 1:
f'(x) = 16 x^3 - 6 x^2 + 1
Hint: | Find where f'(x) is zero by solving 16 x^3 - 6 x^2 + 1 = 0.
Solving 16 x^3 - 6 x^2 + 1 = 0 yields x≈-0.303504:
x = -0.303504
Hint: | Find where f'(x) = 16 x^3 - 6 x^2 + 1 does not exist.
f'(x) exists everywhere:
16 x^3 - 6 x^2 + 1 exists everywhere
Hint: | Collect results.
The only critical point of 4 x^4 - 2 x^3 + x - 5 is at x = -0.303504:
x = -0.303504
Hint: | Determine the endpoints of the domain of f(x).
The domain of 4 x^4 - 2 x^3 + x - 5 is R:
The endpoints of R are x = -∞ and ∞
Hint: | Evaluate f(x) at the critical points and at the endpoints of the domain, taking limits if necessary.
Evaluate 4 x^4 - 2 x^3 + x - 5 at x = -∞, -0.303504 and ∞:
The open endpoints of the domain are marked in gray
x | f(x)
-∞ | ∞
-0.303504 | -5.21365
∞ | ∞
Hint: | Determine the largest and smallest values that f achieves at these points.
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
The open endpoints of the domain are marked in gray
x | f(x) | extrema type
-∞ | ∞ | global max
-0.303504 | -5.21365 | global min
∞ | ∞ | global max
Hint: | Finally, remove the endpoints of the domain where f(x) is not defined.
Remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved:
x | f(x) | extrema type
-0.303504 | -5.21365 | global min
Hint: | Summarize the results.
f(x) = 4 x^4 - 2 x^3 + x - 5 has one global minimum:
Answer: f(x) has a global minimum at x = -0.303504
A seat on a Ferris wheel is level with the center of the wheel.The diameter of the wheel is 200 feet. Suppose the wheel rotated 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation
Answer: 86.6ft closer to the ground.
Step-by-step explanation:
The diameter of the wheel is 200ft
Then the radius, half of the diameter, is: r = 200ft/2 = 100ft.
Initially, the seat is at the same level that the center of the wheel.
And the distance between the center of the wheel and the bottom is the radius.
Then the initial position is at an angle of 0° from the x-axis. (where the (0,0) of this axis coincides with the center of the wheel=
Now, the wheel rotates 60°. (downwards, so we actually could use -60° measuring from the positive x-axis)
And thinking in this as a triangle rectangle, where the opposite angle is 60°, we can calculate the displacement in the vertical direction as:
y = sin(-60°)*R
y = sin(-60°)*100ft = -86.6ft
So the seat is 86.6ft closer to the ground.
The seat is [tex]86.6feet[/tex] closer to the ground
The seat will be closer by the height it drops when the Ferris wheel turns downwards by [tex]60^{\circ}[/tex].
The height, and the radius of the Ferris wheel form the opposite and the hypotenuse of a [tex]60^{\circ}[/tex] right-angled triangle. Since the diameter of the Ferris wheel is 200feet, the radius will be 100feet. So we have
[tex]sin60^{\circ}=\frac{opp}{hyp}=\frac{h}{100}\\\\h=100\times sin60^{\circ}\\=100\times 0.8660\\=86.6[/tex]
So the seat is [tex]86.6feet[/tex] closer to the ground
Learn more here: https://brainly.com/question/95152
In the quadratic formula,
−b±√b^2−4αc/2a, What is
6^2-4ac called? (1 point)
A.Numerator
B.Solution
C.Discriminant
D.Radical
Answer:
C
Step-by-step explanation:
Discriminant : tell us whether there are two solution,one solution, or no solution for the quadratic equation
Given that f(x) = 3x + 1 and g(x) = the quantity of 4x plus 2 divided by 3 , solve for g(f(0)). (5 points) 2 6 8 9
[tex]f(0)=3(0)+1[/tex]
[tex]f(0)=1[/tex]
[tex]g(1)=\frac{4(1)+2}{3}[/tex]
[tex]g(1)=\frac{4+2}{3}[/tex]
[tex]g(1)=\frac{6}{3}[/tex]
[tex]g(1)=2[/tex]
Hope this helps.
頑張って!
Find the midpoint: (-1, 9), (7, -1)
Answer: (3,4)
Step-by-step explanation:
To find the midpoint, you want to use the formula [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]. Since we are given the two points, we can plug them in and solve.
[tex]m=(\frac{-1+7}{2} ,\frac{9+(-1)}{2} )[/tex] [add numerator]
[tex]m=(\frac{6}{2} ,\frac{8}{2} )[/tex] [divide]
[tex]m=(3,4)[/tex]
Now, we know that the midpoint is (3,4).
I know it’s a lot but I need help didn’t get the material because I’m doing online classes and my WiFi is trash
Answer: not sure if that is a b but i beleive it is so
bh+hr=25
move all terms to the left side and set equal to 0. then set each factor equal to zero.
h= [tex]\frac{25}{b+r}[/tex]
isolate the variable by dividing each side by factors that dont
contain the variable.
r=[tex]\frac{25}{h}-b[/tex]
x=[tex]\frac{r-h}{y}[/tex]
isolate the variable by dividing each side by factors that dont
contain the variable.
h=-xy+r
solve for r by simplifieng both sides of the equation, then isolating the variable.
r=xy+h
Answer:
1A. h = 25/(b + r)
1B. r = 25/h - b
2A. h = r - xy
2B. r = xy + h
Step-by-step explanation:
1. bh + hr = 25
A. h(b + r) = 25
h = 25/(b + r)
B. h(b + r) = 25
b + r = 25/h
r = 25/h - b
2. x = (r - h)/y
A. xy = r - h
h + xy = r
h = r - xy
B. xy = r - h
r = xy + h
Solve for b. 13/b = 8/1 A. b=1.25 B. b=1.26 C. b=16.25 D. b=1.625
Answer: [tex]b=13/8[/tex]
Cross multiply
[tex](13)*(1)=8*b\\13=8b[/tex]
Flip the equation
[tex]8b=13[/tex]
Divide both sides by 8
[tex]8b/8=13/8\\b=13/8[/tex]
When a car's brakes are applied, it travels 7 feet less in each second than the previous second until it comes to a complete stop. A car goes 28 feet in the first second after the brakes are applied. How many feet does the car travel from the time the brakes are applied to the time the car stops?
Answer:
70feet
Step-by-step explanation:
during the
1st sec it travels 28 ft
2nd sec =28-7=21ft
3rd sec= 21-7=14ft
4th sec= 14-7= 7ft
last sec=7-7=0ft, at this point the car stops.
so altogether it travels 28+21+14+7+0= 70 feet
What are the next three numbers in the sequence? 80, 90, 85, 95, 90, 100, 95, 105, _____, _____, _____
Answer:
100, 110, 105
Step-by-step explanation:
Answer:
100,105,110
Step-by-step explanation:
-Is ZFDE a possible name for the figure below? Explain.
E
D
F
It’s number 14
Answer: Yes [tex]\angle FDE[/tex] is one possible angle name
Another name is [tex]\angle EDF[/tex]
When it comes to naming an angle this way, all we need to worry about is the vertex point. This is where the angle hinges (think of a door or a pair of scissors). In this case, the hinge or vertex point is at point D. The vertex is always the middle letter of any three-letter sequence. The order of the other two points does not matter.
This is why saying "angle FDE" is the same as "angle EDF".
BC = 12 and AB = 11. Find AC.
Answer:
AC = 23
Step-by-step explanation:
Assuming A, B, and C are on a line with B in the middle...
We know that AB + BC = AC. Travelling from A to C is the same as travelling from A to B, then B to C, as B is on the way between A and C.
Knowing this, we can set up this equation and add the 2 numbers we know:
AC = AB + BC
AC = 11 + 12
AC = 23
If 5y + 2 = 8/3, what is the value of 5y - 6?
A car travels 420 miles in 6 hours. What is the unit rate?
Answer:
70
Step-by-step explanation:
because 70 times 6 equals 420
Rewrite as a simplified fraction.
\large{2.1\overline{6} = ?}2.1
6
=?
Answer:
Note that
0.16666...is equivalent to 1/6
Step-by-step explanation:
We can use the sum of fractions to write out the decimal:
For this particular question, we can see that
0.16666...is the fraction 1/6, therefore
the given decimal
2.16666...=2+1/6=13/6
Factor 20x2 + 35x plz help
Answer:
Step-by-step explanation:
5x(4x + 7)
what is 2/4 as a % plz hurry important
Answer: 50%
To convert fractions into a percentage you Divide the Numerator and Denominator.
2÷4=0.5
Since the result came out as a decimal we convert it to a percentage.
As you can see 5 is in the tenth place so that means 0.5 as a percent is 50%
What is the solution to this equation? 6x+4=4x−2 Enter your answer in the box.
Answer:
-3
Step-by-step explanation:
6x take 4x equals 2x
So it'll be 2x+4=-2
Then you do - 2 take 4 which is - 6
So then it is 2x=-6
-6÷2=-3
Hope this helps you :)
Answer:
x=-3
Step-by-step explanation:
6x+4=4x-2
Subract the x on the right side on both sides
Equation should now be:
2x+4=-2
Now subtract the 4 from both sides
The equation is now:
2x=-6
Now all you have to do is divide the x on both sides
Your answer is now x=-3
A whale swims down 300 feet to feed what is the whales elevation now?
Answer:
-300
Step-by-step explanation:
if the whale is at the serface 0 and it goes 300ft down its -300
A 4-cup bottle of shampoo costs $18.36. What is the price per pint?
Answer:
$9.18
Step-by-step explanation:
4 cups = 2 pints. 18.36/2 = 9.18
What term describes the monomial 14xyz?
A. constant
B. linear
C. quadratic
D. cubic
Answer:
c
Step-by-step explanation:
just because sorry, I'm new but please don't rate this bad but I do know the awnser
look at image. reflection across the x-axis
Answer:
H stays G -2,-4 F -5,-3 are the new points
Step-by-step explanation:
1) x² 2(x+y) - y^2
2) x^4+ x^2y^2+ y^4
Answer: 1) Let's simplify step-by-step.
x22(x+y)−y2
Distribute:
=(x22)(x)+(x22)(y)+−y2
=x23+x22y+−y2
Answer:
=x23+x22y−y2
2)Let's simplify step-by-step.
x4+x2y2+y4
There are no like terms.
Answer:
=x4+x2y2+y4