Answer:
256 cm³
Step-by-step explanation:
Here, V = (1/3)(area of base)(height), and the numbers here are
V = (1/3)(64 cm²)(12 cm) = 256 cm³
The slope of line l is 3/4 . Line m is perpendicular to line l.
What is the slope of line m?
A.
4 over 3
B.
-3 over 4
C.
- 4 over 3
D.
3 over 4
Final answer:
The slope of a line perpendicular to a line with slope 3/4 is -4/3. This follows from the principle that slopes of perpendicular lines are negative reciprocals of each other.
Explanation:
The question pertains to finding the slope of a line that is perpendicular to another line with a given slope. Given that the slope (m) of line l is 3/4, let's find the slope of line m which is perpendicular to l. In algebra, the slope of perpendicular lines are negative reciprocals of each other. This means that to find the slope of m, you take the negative reciprocal of 3/4, which is -4/3.
Thus, the correct answer is C. - 4 over 3.
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:
f(t) = −16t2 + 48t + 160
The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
Answer:
The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is -80 feet per second.
Step-by-step explanation:
The function that models the height of the ball is:
[tex]f(t)=-16t^2+48t=160[/tex]
At t=3, [tex]f(3)=-16(3)^2+48(3)+160=160[/tex]
At t=5, [tex]f(5)=-16(5)^2+48(5)+160=0[/tex]
The average rate of change is simply the slope of the secant line connecting.
[tex](3,f(3))[/tex] and [tex](5,f(5))[/tex].
The average rate of change
[tex]=\frac{f(3)-f(5)}{3-5}[/tex]
[tex]=\frac{160-0}{-2}[/tex]
[tex]=-80fts^{-1}[/tex]
The triangles are similar. What is the value of x? Enter your answer in the box. X=
Answer:
x =16
Step-by-step explanation:
You can use Theorem Pythagoras method to solve this question.
The formula is a^2 + b^2 =c^2
In this question a=x , b=12, and c= 20
to find a which means x you should use this formula : c^2 - b^2=20^2-12^2
= 400 - 144
=√256
=16
You also can use another method by using the second diagram.
In that diagram you have to know that 12÷3 is 4, 20÷5 is 4, hence x÷4 is 4
so , x=16.
I hope this two ways for answering this question will be helpful for you.
Answer:
x = 16
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] ( cross- multiply )
5x = 4 × 20 = 80 ( divide both sides by 5 )
x = 16
The expression 6(x − 5) means the -------- If x = 7, the value of the expression is -------
(Blank 1 )
1. Sum of 6 and the sum of X and 5.
2. Product of 6 and the sum of X and 5.
3. Product of 6 and the difference of X minus 5.
4. Sum of 6 and the difference of X minus 5.
(Blank 2 )
1. 3
2. 8
3. 12
4. 18
The expression 6(x − 5) means the product of 6 and the difference of x minus 5. If x = 7, the value of the expression is 12.
We can see that the number 6 to the left of the expression 6(x - 5), this means 6 times (x - 5), The reason we write it that way is because the multiplication symbol, ×, can be confused with the variable x, follow by (x - 5) which is the difference of x minus 5. All together is the product of 6 and the difference of x minus 5.
If x = 7, then:
6(7 - 5) = 6(2) = 12
Following are the solution to the given expression:
Given:
[tex]6(x-5) \\\\ x=7 [/tex]
To find:
value=?
Solution:
[tex]\to 6(x-5)\\\\ [/tex]
putting the x value into the above expression:
[tex]\to 6(7-5)\\\\ \to 6(2)\\\\ \to 12[/tex]
Therefore the final answer is "12".
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Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
A prism is rectangular shaped,. a pyramid is triangular shaped.
The ratio would be 1 to 3
The formula for the pyramid is V = 1/3Bh
The function y=ln(x+3)-6 has been shifted left three units and down 5 units .... (Please help my math project is due tommrow)
Answer:
y = ln( x + 6 ) - 11
h = 6
k = -11
h + k = -5
Step-by-step explanation:
Horizontal shift changes whats inside the brackets, in other words, changes just the x-value.If the shift is right, the number should be subtracted, if the shift is left, the number should be added.
Vertical shift changes the equation as a whole.if the shift is up, the number of should be added.If the shift is down, the number should be subtracted.
The changes given to us are 3 units left ( horizontal translation ) and 5 units down ( vertical translation )
If we rewrite the equation, we have:
y = ln( x + 3 + 3 ) - 6 - 5
y = ln( x + 6 ) - 11
plz help! i will give brainliest to the correct answer!
Answer:
It is B because this triangle Q and R are congruent
Step-by-step explanation:
Answer:
B. 68
Step-by-step explanation:
Because the side lengths PQ and PR both equal 5 and are congruent, the angles opposite them (angle Q and angle R) are also congruent to each other.
Angle Q is 68, so angle R is also 68.
Find the value of x. round the length to the nearest tenth.
HELP! Urgent!
Answer:
(10 yd) ............=x.....
Find the length of side c in the right triangle below. Round to the nearest tenth if necessary.
A) 4.9
B) 13
C) 14
D) 1669
Answer:
13
Step-by-step explanation:
You need to use the Pythagorean theorem. Which is a^2+b^2=c^2
so 5^2+12^2
which simplifies to 25+144=c^2
then it simplifies to 169=c^2
Now you take the square root
c=sqrt(169)
c=13
For this case we have that by definition, the Pythagorean theorem states that:
[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]
Where:
c: It is the hypotenuse
a, b: Are the legs
Substituting the values of the figure:
[tex]c = \sqrt {5 ^ 2 + 12 ^ 2}\\c = \sqrt {25 + 144}\\c = \sqrt {169}\\c = 13[/tex]
Thus, the value of the hypotenuse is 13.
Answer:
13
Option B
Complete the equation of the line through (-1,6) and (7,-2)
Use exact numbers.
See attachment for solution steps and answer.
The slope of the line through the points (-1,6) and (7,-2) is -1. Substitute this and one of the points into the point-slope form, 'y - y1 = m (x - x1)', to get the equation of the line. The final equation is y = -x + 5.
Explanation:To complete the equation of the line through points (-1,6) and (7,-2), we first need to find the slope (m) of the line using the formula m=(y2-y1)/(x2-x1). Here, (-1,6) is (x1,y1) and (7,-2) is (x2,y2). When we substitute these values in, we get m=(-2-6)/(7-(-1)), which simplifies to m=-8/8 or m=-1.
Now, you can use the point-slope form of a line, which is y - y1 = m (x - x1). You can use either of the points given, but let's use (-1,6). The equation then becomes y - 6 = -1(x - (-1)). To simplify, this becomes y - 6 = -x - 1. If you add 6 to both sides, the final equation of the line is y = -x + 5.
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Let m be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x2+y2=49, 0≤z≤1, and a hemispherical cap defined by x2+y2+(z−1)2=49, z≥1. for the vector field f=(zx+z2y+8y, z3yx+5x, z4x2), compute ∬m(∇×f)⋅ds in any way you like.
It seems that the boundary of [tex]M[/tex] is the circle [tex]x^2+y^2=49[/tex] in the plane [tex]z=0[/tex]. By Stokes' theorem,
[tex]\displaystyle\iint_M(\nabla\times\vec f)\cdot\mathrm d\vec S=\int_{\partial M}\vec f\cdot\mathrm d\vec r[/tex]
Parameterize [tex]\partial M[/tex] by
[tex]\vec r(t)=(7\cos t,7\sin t,0)[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral is
[tex]\displaystyle\int_{\partial M}\vec f(x(t),y(t),z(t))\cdot\mathrm d\vec r=\int_0^{2\pi}(56\sin t,35\cos t,0)\cdot(-7\sin t,7\cos t,0)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(245\cos^2t-392\sin^2t)\,\mathrm dt=\boxed{-147\pi}[/tex]
The question involves computing the double surface integral of the curl of the given vector field over a specified surface. The curl of the vector field is found first using a determinantal formula, and the surface integral is then evaluated over the capped cylindrical surface. These concepts are fundamental in vector calculus and have applications in fields such as physics and engineering.
Explanation:This question requires the application of vector calculus concepts, specifically surface integrals and the divergence theorem. Given the vector field f=(zx+z²y+8y, z³yx+5x, z⁴x²), your task is to compute the double surface integral of the curl of f over a capped cylindrical surface m, which is a union of a cylinder and a hemispherical cap.
To solve it, you will start by finding the curl of the vector field using the determinant of a special kind of 3x3 matrix, called the curl matrix, containing the unit vectors i, j, k, the coefficients of the derivatives in the Cartesian coordinate system, and the components of the vector field. Once you get an expression for the curl of f, you will set up and evaluate a double surface integral over the given region m to find the desired quantity.
The concept of surface integrals is prevalent in many fields including physics and engineering where it is used to calculate quantities like flux. The divergence theorem, also known as Gauss's theorem, connects the flux of a vector field through a closed surface to the divergence of this field in the volume enclosed by the surface.
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98 POINTS!!!!! The two cones are congruent.
Determine the unknown measures of the cones.
A = ___ units
B = ___ units
C = ___ units
D = ___ units3
Congruent means they are the same. Match the letter with the corresponding dimension on the other cone.
A = 6.2/2 = 3.1 units
B = 4.2 units
C = 5.2 units
D = 42 units^3
The unknown measures of the cones are A = 3.1, B = 4.2, C = 5.22 and D = 42 units³
What are congruent figures?
Two figures are said to be congruent if they have the same shape and the their corresponding sides are the same.
Given that both cones are congruent. Hence:
A = 6.2 / 2 = 3.1
B = 4.2
Using Pythagoras:
C² = A² + B²
C² = 3.1² + 4.2²
C = 5.22
D = 42 units³
The unknown measures of the cones are A = 3.1, B = 4.2, C = 5.22 and D = 42 units³
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HELP QUICK GIVING 50 POINTS!!!
The volume of a square prism is 64 cubic centimeters. What is the volume of a triangular pyramid with the same base area and height as the square prism? 64 cubic centimeters cubic centimeters 32 cubic centimeters
Answer:
64/3 cc or 64/3 cm³
Step-by-step explanation:
The formula for the volume of a triangular pyramid is
V = (1/3)(area of base)(height)
Here we have a square prism (actually, a cube), whose square base is 4 cm by 4 cm (4 cm is the cube root of 64 cc). The height of this cube is also 4 cm.
The volume of a triangular pyramid of base area (4 cm)² and height 4 cm is
V = (1/3)(base area)(height)
= (1/3)(16 cm²)(4 cm) = 64/3 cc
Answer:
64/3 cc or 64/3 cm³
Step-by-step explanation:
A fountain on a lake sprays water in a parabolic arch modeled by the equation y= -0.3x^2 +3x. A beam of light modeled by the equation -2x+5.5y=19.5 passes through the fountain to create a rainbow effect. f the beam cuts the water spray at points A and B, such that point B is higher than point A, what distance from the ground level is point A?
ANSWER
4.1 units to the nearest tenth.
EXPLANATION
The graph of the two functions are shown in the attachment.
The coordinates of point A is (1.6,4.1).
The coordinates of point B is (7.1,6.1)
The x-axis represents the ground level.
The distance of point A from the ground level is how far the y-coordinate of this point is from the x-axis.
Which is |4.1-0|=4.1
Mean, Median, mode, range Please help
There are no numbers here
True or false? The variable in the linear term of a quadratic trinomial is always raised to the first power
Answer:
True
Step-by-step explanation:
The first power of the variable is what makes it a linear term.
please help!!!!!!!!
9a^2b^4/3a^3b^-3
Answer:
3a5b
Step-by-step explanation:
Answer:
3a5b
Step-by-step explanation:
Identify m∠JKL, given that JK is a tangent line. HELP PLEASE!!
Answer:
The measure of angle JKL is m∠JKL=35°
Step-by-step explanation:
step 1
Find the measure of the arc KL
we know that
arc KL+arc KN+arc NL=360° ----> by complete circle
arc KL+150°+140°=360°
arc KL=360°-290°=70°
step 2
Find the measure of angle JKL
we know that
The inscribed angle is half that of the arc it comprises.
so
m∠JKL=(1/2)[arc KL]
substitute
m∠JKL=(1/2)[70°]=35°
By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
Answer:
The fraction will decrease [tex]33.33\%[/tex]
Step-by-step explanation:
Let
x/y ----> the fraction
we know that
100%-50^=50%=50/100=0.50
100%-25%=75%=75/100=0.75
substitute
[tex]\frac{x}{y}*\frac{0.50}{0.75} =\frac{2}{3}(\frac{x}{y})[/tex]
therefore
The percent that the fraction will decrease is equal to
[tex](1-\frac{2}{3})*100=33.33\%[/tex]
Does anyone know the answers to this test???OFFERING LOTS PF POINTS. Just Incase the picture isn’t loading it’s the parametric functions test Part 1 in pre calculus.
Answer:
The correct choice is C
Step-by-step explanation:
The given curve is described by the parametric equations:
[tex]x=4-t[/tex]
[tex]y=t^2-2[/tex]
Let us eliminate the parameter by making t the subject in the first equation and substitute into the second equation;
[tex]t=4-x[/tex]
We substitute this into the second equation to get:
[tex]y=(4-x)^2-2[/tex]
This is the equation of a parabola whose vertex is at (4,-2)
The correct choice is C
Find the height of the tree if it casts a 28 foot shadow and the 6 foot 3 inch man casts a 7 foot shadow.
Answer:
25 ft
Step-by-step explanation:
The tree's shadow is 4 times the length of the man's shadow, so we presume the tree is 4 times the height of the man: 4 × (6 ft 3 in) = (24 ft 12 in) = 25 ft.
Approximate the real zeros of f(x)=2x^4-x^3+x-2 to the nearest tenth. A. 2, 1 c. 0, -1 b. 1, 0 d. -2, -1 Please select the best answer from the choices provided A B C D
Answer:
A
Step-by-step explanation:
Answer:
answer is A
Step-by-step explanation:
in the diagram below, O is circumscribed about quadrilateral ABCD. what is the value of x?
Answer:
(D)[tex]x=104^{\circ}[/tex]
Step-by-step explanation:
Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.
To find: the value of x.
Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.
We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore
[tex]{\angle}ABC+{\angle}ADC=180^{\circ}[/tex]
Substituting the given values, we have
[tex]91^{\circ}+x-15^{\circ}=180^{\circ}[/tex]
[tex]x+76^{\circ}=180^{\circ}[/tex]
[tex]x=104^{\circ}[/tex]
thus, the value of x is [tex]104^{\circ}[/tex].
Hence, option D is correct.
Answer:
the answer is 104 i just took quiz 6.11.3
Step-by-step explanation:
The back to back stem and leaf plot below show exam scores from two different two different math classes. Which class has a greater mean score ? Which class has a greater median score?
Class A Class B
12 4 2
168 5 4
5779 6 16
66789 7 2566
12 8 00489
1 9 3567
Answer:
what
Step-by-step explanation:
Answer:
B. greater mean = class B greater median = class B
Step-by-step explanation:
Factor the expression. 9b2 – 25
Answer: (3b + 5)(3b - 5)
Because both terms, 9b² and 25, are perfect squares, you can factor by taking the square roots of both terms.
The square root of 9b² is 3b (3b × 3b = 9b²).
The square root of 25 is 5 (5 × 5 = 25).
9b² - 25 has a negative, so the factored expression would be
(3b + 5)(3b - 5). The signs (+ and -) alternate in this case because the expression, 9b² - 25, has no middle term.
You can check your work by using FOIL. See the attachment below.
F irst
O utside
I nside
L ast
Answer:
(3b + 5)(3b - 5)
Step-by-step explanation:
(3b + 5)(3b - 5)
A chemistry student mixes two solutions to study the properties of the resulting mixture. The temperature of the new solution is given by the function
T = 24t − 2t2 + 5, where T is the temperature in degrees Celsius and t is the time elapsed in seconds after the solutions are mixed. What is the time interval that the temperature of the solution will be at least 69°C?
[2, 6]
[3, 8]
[5, 8]
[4, 8]
Answer:
[4, 8]
Step-by-step explanation:
You want to find t such that ...
T ≥ 69
24t − 2t^2 + 5 ≥ 69
t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2
(t -4)(t -8) ≤ 0 . . . . . . . factor
The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...
t ∈ [4, 8]
11. a model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.02x^2+2.3x+6, where X is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land?
A) 57.5 meters
B) 115 meters
C) 117.55 meters
D) 235.1 meters
Need help with this please.
Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price a TV with a cash price of $600 at $59.00 per month for 12 months
A. the choices are
708.00
698.00
688.00
B. the choices are
88.00
108.00
98.00
C. the choices are
10
11
9
Answer:
a) 708.00
b) 108.00
c) 11
Step-by-step explanation:
a) The cost is $59 for each of 12 months, so the total cost is ...
12×$59 = $708
__
b) The "carrying charges" are the difference between what is paid and the cash price:
$708 -600 = $108
__
c) Saving at the rate of $59 per month, it will take ...
$600/($59/mo) ≈ 10.17 mo
to save the money. The amount saved will be $590, or $10 short of the required amount after 10 months, so it will take 11 months to save enough for the cash purchase.
Answer:
a) 708.00
b) 108.00
c) 11
Step-by-step explanation:
Hank is taking a walking tour of a park. The route he takes is shown on the map above. How far is the fountain from the entrance? Note: picture not drawn to scale.
A) 0.20 mi
B) 0.40 mi
C) 0.45 mi
D) 0.63 mi
Answer: B) 0.40 mi
Step-by-step explanation:
Using the Pythagorean Theorem.
A squared + B squared = C squared.
A = leg B = leg C = hypotenuse
A = 0.3 B = ? C = 0.7
0.3 squared x ? squared = 0.7 squared
Answer:
on usatestprep its 0.63
Step-by-step explanation:
Working together, it takes two computer 15 minutes to send out a company's email. If it takes the slower computer 45 minutes to do the job on its own, how long will it take the faster computer to do the job on its own?
It will take them 30 minutes
The faster computer will take approximately 22.5 minutes to do the job on its own.
Explanation:Let's assume that the faster computer can complete the job on its own in x minutes.
If the slower computer takes 45 minutes to complete the job on its own, it means that in 1 minute it completes 1/45th of the job.
Working together, the two computers can complete the entire job in 15 minutes. So in 1 minute, they can complete 1/15th of the job.
Therefore, 1/45 + 1/x = 1/15
Simplifying the equation, we get 1/x = 1/15 - 1/45
Substituting the numerator values with a common denominator, 1/x = (3/45) - (1/45) = 2/45
Now, solving for x, we get x = 45/2 = 22.5
So, it will take the faster computer approximately 22.5 minutes to do the job on its own.
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