Answer:
dx/dt = 4 mph
Step-by-step explanation:
The two trains, with the station ( origin of the coordinates system) all, form a right triangle when we considered the distance between the two trains.
In that triangle:
distance between trains D = 24 miles
leg (1 ) distance of train going west to origin y = 15 miles
leg (2) distance of train going south x = ??
When d = 24 and y = 15
D² = y² + x² ⇒ x² = D² - y²
x = √ (24)² - (15)²
x = √351
x = 18,73 miles
Now according to Pythagoras theorem
D² = x² + y²
Taking derivatives (respect to time) on both sides of the equation we get
2*D*dD/dt = 2*y*dy/dt + 2*x*dx/dt
In this expression we are looking for dx/dt, all the rest of variables are known
2*24*25 = 2* 15*35 + 2*(18,73)* dx/dt
(1200 - 1050 )/37,46 = dx/dt
dx/dt = 4 mph
5 1
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4 3
What is the anwser
The temperature at 6 a.m. was −12°F. At 11 a.m. the temperature was 0°F. Which of the following shows the temperature change from 6 a.m. to 11 am?
Answer:
+12 degrees
Step-by-step explanation:
You never showed a picture, but im pretty sure this is correct
I hope this helped, please mark Brainliest, thank you!
Find the distance between -3/4 and 1 3/4 on a number line. Write your answer as a fraction or mixed number in simplest form.
A fraction is a way to describe a part of a whole. The distance between -3/4 and 1 3/4 on a number line is 1 unit.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
What is a Mixed Fraction?A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,
2 1/2
= (2×2 + 1)/2
= 5/2
= 2.5
The distance between -3/4 and 1 3/4 on a number line is,
Distance = 1 3/4 - 3/4
= 7/4 - 3/4
= (7-3)/4
= 4/4 units
= 1 units
Hence, the distance between -3/4 and 1 3/4 on a number line is 1 unit.
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what ratio is lesa than 7/15
Answer:
2/5=6/15 and that is less so....
Step-by-step explanation:
Brainliest will be given to the correct answer!
The formula for the area of a trapezoid is A = 1/2h (b1 + b2), where h is the height of the trapezoid, and b1 and b2 are the lengths of the bases.
Part A: Solve the formula for h. What is the height of a trapezoid that has an area of 91 cm2 and bases of 12 cm and 16 cm?
Part B: What method would you use to solve the formula for b1? What is the formula when solved for b1?
Part C: What is the length of the other base if one base of a trapezoid is 30 cm, the height of the trapezoid is 8.6 cm, and the area is 215 cm2?
Part D: If both bases of a trapezoid have the same length, can you find their lengths given the area and height of the trapezoid? Explain.
Answer:
A) The height of the trapezoid is 6.5 centimeters.
B) We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex]. [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex]
C) The length of the other base of the trapezoid is 20 centimeters.
D) We can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. [tex]b = \frac{A}{h}[/tex]
Step-by-step explanation:
A) The formula for the area of a trapezoid is:
[tex]A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})[/tex] (Eq. 1)
Where:
[tex]h[/tex] - Height of the trapezoid, measured in centimeters.
[tex]b_{1}[/tex], [tex]b_{2}[/tex] - Lengths fo the bases, measured in centimeters.
[tex]A[/tex] - Area of the trapezoid, measured in square centimeters.
We proceed to clear the height of the trapezoid:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.
3) [tex]2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}][/tex] Compatibility with multiplication/Commutative and associative properties.
4) [tex]h = \frac{2\cdot A}{b_{1}+b_{2}}[/tex] Existence of multiplicative inverse/Modulative property/Definition of division/Result
If we know that [tex]A = 91\,cm^{2}[/tex], [tex]b_{1} = 16\,cm[/tex] and [tex]b_{2} = 12\,cm[/tex], then height of the trapezoid is:
[tex]h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}[/tex]
[tex]h = 6.5\,cm[/tex]
The height of the trapezoid is 6.5 centimeters.
B) We should follow this procedure to solve the formula for [tex]b_{1}[/tex]:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.
3) [tex]2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})[/tex] Compatibility with multiplication/Commutative and associative properties.
4) [tex]2\cdot A \cdot h^{-1} = b_{1}+b_{2}[/tex] Existence of multiplicative inverse/Modulative property
5) [tex]\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}[/tex] Definition of division/Compatibility with addition/Commutative and associative properties
6) [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex] Existence of additive inverse/Definition of subtraction/Modulative property/Result.
We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].
C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ([tex]A= 215\,cm^{2}[/tex], [tex]h = 8.6\,cm[/tex] and [tex]b_{2} = 30\,cm[/tex])
[tex]b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm[/tex]
[tex]b_{1} = 20\,cm[/tex]
The length of the other base of the trapezoid is 20 centimeters.
D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. Now we present the procedure to clear [tex]b[/tex] below:
1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.
2) [tex]b_{1} = b_{2}[/tex] Given.
3) [tex]A = \frac{1}{2}\cdot h \cdot (2\cdot b)[/tex] 2) in 1)
4) [tex]A = 2^{-1}\cdot h\cdot (2\cdot b)[/tex] Definition of division.
5) [tex]A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b[/tex] Commutative and associative properties/Compatibility with multiplication.
6) [tex]b = A \cdot h^{-1}[/tex] Existence of multiplicative inverse/Modulative property.
7) [tex]b = \frac{A}{h}[/tex] Definition of division/Result.
In the expression 3x²y + 4x – 5x’y, are the terms 3x’y
and –5x+y like terms? Explain by providing support for
your answer.
Answer:
Yes. 3x²y and -5x²y are like terms because the variables x and y have the same exponents.
Help me plz
8th grade math
Answer
I would say the 3rd one.
Step-by-step explanation:
I do not really remember this but I am in 8th grade math to (Algebra)
7. Which statements about the values of 2.044
and 20.44 are true?
Answer:
20.44>2.044
Step-by-step explanation:
20% of 45
Help. Plzzzzzzzzzz
The expression 3x^2 + x +1 is the height of the building. The expression 2x - 2 is the distance from the floor of the cafeteria to the top of the building. What is the expression for the height from the ground to the floor of the cafeteria?
Answer:
3x²-x+3
Step-by-step explanation:
Given
Height of the building = 3x^2 + x +1
distance from the floor of the cafeteria to the top of the building = 2x -2
To get the expression for the height from the ground to the floor of the cafeteria, we will use the formula:
Height of the building = (distance from the floor of the cafeteria to the top of the building ) + (he height from the ground to the floor of the cafeteria)
substitute the given parameter into the formula:
3x^2 + x +1 = 2x -2 + P
P = 3x^2 + x +1 - (2X-2)
P = 3x^2 + x +1 - 2x+2
collect like terms:
P = 3x^2 + x-2x+2+1
P = 3x²-x+3
Hence the expression for the height from the ground to the floor of the cafeteria is 3x²-x+3
Write the word sentence as an inequality. Then solve the inequality. 3/4 is greater than or equal to a number k divided by -8
Answer:
[tex]\frac{3}{4} \geq \frac{k}{-8}[/tex] k ≥ -6Step-by-step explanation:
Re-arrange: [tex]\frac{3}{4} \geq \frac{k}{-8}[/tex] Multiply each side by -8 to cancel out the -8 under k. It should now look like this: k ≥ -6I hope this helps!
please help me and respond with legitimate answers!
Answer:
They are all obtuse scalene triangles I think
What is the value of x?
20
35
60
70
Answer:
20°
Step-by-step explanation:
Step 1:
x + 40° = 3x Vertical ∠'s
Step 2:
40° = 2x Subtract x on both sides
Step 3:
x = 40° ÷ 2 Divide
Answer:
x = 20°
Hope This Helps :)
Sketch the region enclosed by the given curves.
y = tan(9x), y = 2 sin(9x), −π/27 ≤ x ≤ π/27
Find its area.
Answer:
Area (A) [tex]\simeq[/tex] 0.0682
Step-by-step explanation:
The sketch for the region enclosed by the given curves can be found in the image attached below.
From the image below;
The two curves intersect in the area of tan 9x = 2 sin 9x
Recall that:
[tex]\dfrac{sin \ 9x }{cos \ 9x } = 2 \ sin \ 9x[/tex]
[tex]cos \ 9 x= \dfrac{1}{2}[/tex]
making x the subject; then:
[tex]x = \dfrac{1}{9} cos ^{-1}(\dfrac{1}{2})[/tex]
[tex]x = \dfrac{1}{9}(\dfrac{\pi}{3})[/tex]
[tex]x = \dfrac{\pi}{27}[/tex]
The subdivision of the domain is in two intervals [tex][-\dfrac{\pi}{27}, 0], [0, \dfrac{\pi}{27}][/tex]
where;
[tex]x \ \ \varepsilon \ \ [ -\dfrac{\pi}{27},0]; tan \ 9x > 2 sin \ 9x[/tex]
[tex]x \ \ \varepsilon \ \ [ 0,\dfrac{\pi}{27}]; tan \ 9x < 2 \ sin \ 9x[/tex]
Area (A) = [tex]\int ^0_{-\pi/27}}} ( tan \ 9x - 2 \ sin \ 9x ) \ dx + \int ^{\pi/27}_{0}(2 \ sin \ 9x - tan \ 9x \ ) \ dx[/tex]
[tex]= \begin {bmatrix} \dfrac{1}{9} In \ sec 9x + \dfrac{2}{9} \ cos \ 9x \end {bmatrix}^0_{-\pi/27} + \begin {bmatrix} -\dfrac{2}{7} cos 9x - \dfrac{1}{9} \ In \ sec \ 9x \end {bmatrix}^{-\pi/27} _0[/tex]
[tex]= \dfrac{1}{9}(1-In 2) + \dfrac{1}{9}(1-In 2)\\[/tex]
[tex]= \dfrac{2}{9}(1 - In 2)[/tex]
Area (A) = 0.06818
Area (A) [tex]\simeq[/tex] 0.0682
You are putting in a walkway around a tomato garden that has
dimensions of 14 feet x 8 feet. The width of the walkway needs to be
the same around each side of the garden. The total area of the
garden and the walkway needs to be 315 square feet.
Answer:
The garden is 14ft by 8ft.
The width of the walkway needs to be the same around each side of the garden, let's suppose that the width is X.
Then the area of the garden plus the walkway will be:
(14ft + X) by (8ft + X).
And we want that the total area of the garden and the walkway must be equal to 315 ft^2. Then we must solve the equation:
(14ft + X)*(8ft + X) = 315ft^2
Let's solve this for X.
112ft^2 + 14ft*X + 8ft*X + X^2 = 315ft^2
Let's move al the terms to the same side:
X^2 + (14ft + 8ft)*X + 112ft^2 - 315ft^2 = 0
X^2 + 22ft*X - 203ft^2 = 0.
Now to solve this we can use Bhaskara's equation:
[tex]X = \frac{-22ft +- \sqrt{(22ft)^2 - 4*1*(203ft^)} }{2} = \frac{-22ft +-36ft}{2}[/tex]
Then we have two solutions:
X = (-22ft - 36ft)/2 = -29ft
This solution is negative, and X represents a width, so must be positive, then we can discard this solution.
X = (-22ft + 36ft)/2 = 7ft
Then we can conclude that the width of the walkway must be 7ft.
There are 400 boys at Oak Middle school and 12% play football. What is a reasonable number of boys that play football?
Answer:
About 48 students play football
Step-by-step explanation:
400 times 12% is 48
What is the area of the figure below ?
Answer: 99 sq meters
Step-by-step explanation:
break the figure up into smaller boxes. the far left is 48 m^2, the middle box is 15 m^2, and the right box is 36 m^2
what is a thesis statement?
Answer:
es discurso que da un una persona sobre un hecho o circunstancia concreta, en éste, se especifican todos los detalles sobre estos, por lo que la mayor parte del tiempo está planificado. El uso de esta palabra está dirigido, principalmente, al campo jurídico.
10) Mrs. Jimenez bought some jeans to sell at her store. The wholesale
price for the jeans was $65 and she marked up the price by 25%. What
was the retail price of the jeans?
O $65.25
Answer:
The retail price of the jeans was $81.25.
Second Choice: $81.25.
Step-by-step explanation:
Mrs. Jimenez paid $65 for some jeans.
She intended to sell them at her store by marking their price up by 25%.
We have to add 25% to $65:
25 * $65 / 100 = $16.25
$65 + $16.25 = $81.25
The retail price of the jeans was $81.25.
Second Choice: $81.25.
Answer:
B
Step-by-step explanation:
the next model of a sports car will cost 6.8% less than the current model. the current model costs $42,000. how much will the price decrease in dollars? what will be the price of the next model?
Answer:
see below
Step-by-step explanation:
the current model costs $42,000.
next model = 6.8% less than $42,000
find;
1. how much will the price decrease in dollars?
2. what will be the price of the next model?
solution:
1. the price decrease = $42,000 x 0.068
= $2,8562. price of next model = $42,000 - $2,856
= $39,144Noah bought two boxes of fruit bars to share with his football team they are 12 bars in each box and 16 people on the team if the bars are shared equally how many fruit bars will each person get
Answer:
1.5
Step-by-step explanation:
this is because 24 divided by 16 equals 1.5
Answer:
7 bars
Step-by-step explanation:
and a bake sale there were 72 raising cookies sold if the ratio of raging cookies sold to oatmeal cookie show was 9 to 1 what is the combined amount of raisin in oatmeal cookie sold
80
9 to 1 is equivalent to 72 to 8 and 72+8=80
Which equation expresses d in terms of t and a?
Answer:
Option D
Step-by-step explanation:
I got it right
What is the coefficient of determination for this data set?
Answer:
0.91
explanation:
What is the answer to this equation? -108=8x
Does the graph represent y as a linear function of x ?
Answer: yes because without the x the y does not have a corresonding oint
Help me plz
It’s 8th grade math
And ion know what the answer is..
Answer:
B slope = 1 and y intercept is 3
Step-by-step explanation:
The y intercept is where the line crosses the y axis (x is zero).
The slope can be figured by how far the line rises and runs to the next intersection of lines. In this case it goes up 1 and to the right 1. The slope would be 1/1 or 1
Answer:
Slope =1 ; Y-intercept=3
Step-by-step explanation:
The y intercept would be the point on the vertical line that touches the graph which in this case is three.
then to get to the next point that's on the line would have to move over 1 once to the right and one time up. so the slope is 1 over 1 which would equal 1.
who is lionel messi
Answer:
He is a soccer player
Step-by-step explanation:
Lionel Andrés Messi is an Argentine professional footballer who plays as a forward and captains both Spanish club Barcelona and the Argentina national team.
Answer:
an Argentine professional footballer (soccer) who plays as a forward and captains both Spanish club Barcelona and the Argentina national team.
Step-by-step explanation:
Find the slope will mark brainliest
Step-by-step explanation:
Hey there!
The given equation is;
[tex]y = \frac{1}{2} x - \frac{1}{3} [/tex]
Comparing the equation with y = mx+c, we get;
Slope(m)= 1/2.
Hope it helps...
Triangle ABC with vertices A(2, 7), B(6,5),
and C(4, 1): 90° counterclockwise on a graph
Answer:
Step-by-step explanation:
Hope it helps!!
Triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).
Given that, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
90° counterclockwise rotation: (x, y) becomes (-y, x)
A(2, 7) → A'(-7, 2)
B(6, 5) → B'(-5, 6)
C(4, 1) → C'(-1, 4)
Therefore, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).
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