The height of the rectangular pyramid is 7 ft.
How to get the height of the rectangular pyramid?
First, we know that the volume of a rectangular pyramid is given by:
[tex]V = B*H/3[/tex]
Where B is the base, H is the height.
First, we know that the volume is 56 ft³, and the base is 24ft², then we can replace these two in the volume equation to get:
[tex]56 ft^3 = 24ft^2*H/3[/tex]
Solving that for H, we get:
[tex]H = 3*(56ft^3/24ft^2) = 7ft[/tex]
The height of the rectangular pyramid is 7 ft.
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Evaluate the double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d
The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
What is the double integral 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d?Generally, the equation for is mathematically given as
The area denoted by the letter D that is bordered by y=0, y=x2, and x=7
The equation for the X-axis is y=0.
y=x² ---> (y-0) = (x-0)²
Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.
The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.
[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]
Integrating we have
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
If x equals zero, then we know that u equals zero as well.
When x equals seven, we know that u=72=49.
Therefore, by changing x2=u into our integral, it becomes from
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
[tex]7/2 \int^49_0 sin u dx[/tex]
Hence
=7/2(-cos49+1)
In conclusion,
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
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Factors to zero inverse operations
The zeros of the given equation are -5 and -7
Zeros of a quadratic equationQuadratic equations are equations that has a leading degree of 2. Given the factors of a quadratic equation as expressed below;
(-3x - 15)(x+7) = 0
The expressions -3x -15 and x + 7 are the factors of the equation. Equating both factors to zero
-3x - 15 = 0
Add 15 to both sides of the equation
-3x -15 + 15 = 0 + 15
-3x = 15
Divide both sides of the equation by -3
-3x/-3 = 15/-3
x = -5
Similarly;
x + 7 = 0
x = -7
Hence the zeros of the given equation are -5 and -7
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The cross-sectional areas of a triangular prism and a right cylinder are congruent. the triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. which conclusion can be made from the given information?
The conclusion can be made from the given information
The volume of the triangular prism is equal to the volume of the cylinder
Given that there are two figures
1. A right triangular prism
2. Right cylinder
The area of the cross-section of the prism is equal to the Area of a cross-section of the cylinder.
Let this value be A.
Also given that the Height of prism = Height of cylinder = 6
The volume of a prism is will be :
[tex]V _{prism} = cross section area \times height[/tex]
[tex]V _{prism} = A \times 6 = 6A[/tex] (1)
The Cross section of the cylinder is a circle.
hence the Area of the circle will be:
Area of cross-section, A = [tex]\pi \times r^2[/tex]
so, the Volume of the cylinder will be :
[tex]V _{cylinder} = \pi \times r^2 \times h[/tex]
[tex]V _{cylinder} = A \times h = A \times 6 = 6A[/tex] (2)
From equations (1) and (2) we can say that
The volume of the triangular prism is equal to the volume of the cylinder.
What is a triangular prism?A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry.If the sides of a right triangular prism are not rectangular, the prism is oblique. Right triangle prisms with square sides and equilateral bases are known as uniform triangle prisms.It is, in essence, a polyhedron with two parallel sides and three surface normals that are all in the same plane (which is not necessarily parallel to the base planes).There are parallelograms in these three faces. The identical triangle appears in every cross-section running parallel to the base faces.To learn more about triangular prism with the given link
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Solve the given differential equation by undetermined coefficients. y'' 4y = 7 sin(2x)
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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A function has a slope of 3, and one solution is given in the table. identify the missing outputs. x: 5 6 7 8 9 y: -50
The remaining value will increase by the value of the slope. Hence the remaining missing values are -47, -44, -41, -38 and -35
Slope and tablesThe slope of a line is the ratio of the rise to run of a line. It is also defined as the rate of change of coordinate y with respect to x. Mathematically;
slope = change in y/change in x
If the slope of the table given is 3, then using the coordinate points (5, -50)and (6, y)
Substitute
3 = y-(-50)/6-5
3 = y+50/1
y+50 = 3
y = -47
The remaining value will increase by the value of the slope. Hence the remaining missing values are -44, -41, -38 and -35
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My car uses 8.5L of petrol per 100km travelled. If petrol costs $2.05 per litre, how much will the petrol cost for my trip?
the petrol cost for the trip is:
C = 2.125*$2.05 = $4.36
How to get the cost of the trip?After a search online, I've found that the trip is of 25km.
Here we know that the car uses 8.5L per 100km, then in 25 km, the car will use one-fourth of 8.5L, that is:
8.5L/4 = 2.125L
So the volume of petrol that the car uses for the trio is 2.125 liters of petrol.
And each liter costs $2.05, then the petrol cost for the trip is given by the product between the total volume of petrol consumed and the cost per liter.
C = 2.125*$2.05 = $4.36
Thus, we conclude that the petrol cost for the trip is 4.36 dollars.
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An experiment consists of drawing 1 card from a standard 52 card deck. let e be the event that the card drawn is a red card. find p(e)
The probability of drawing a red card from a standard deck of cards is 1/2.
Given that there is a standard deck of cards.
We are required to find the probability of drawing a rd card from a standard deck of cards.
Probability is the calculation of chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Probability=Number of items/Total items.
Total number of cards=52
Number of red cards =26
Number of black cards=26
Probability of drawing a red card =Number of red cards/ Total cards.
=26/52
=1/2
Hence the probability of drawing a red card from a standard deck of cards is 1/2.
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If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?
The value of the functions f(x) and g(x) will be √(4x + 3) and √2. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
If (f g)(x) = h(x) such that h(x) = √(8x + 6). Then we have
(f g)(x) = h(x)
f(x) · g(x) = h(x)
Then put the value of h(x), then we have
f(x) · g(x) = √(8x + 6)
f(x) · g(x) = √2(4x + 3)
f(x) · g(x) = √(4x + 3) × √2
Thus, the value of the functions f(x) and g(x) will be √(4x + 3) and √2.
Then the correct option is B.
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Solve the system of equations by graphing.
2x^2 + 8y^2 = 50
x^2 + y^2 = 13
The solutions for the given system are (3,2), (3,-2), (-3,2) and (-3,-2).
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The solution of these equations represents the points at which the parabolas intersect.
2x²+8y²=50 (1)
x² + y²= 13 (2)
Multiplying the equation 2 by -2, you have:
2x²+8y²=50 (1)
-2x² -2 y²= -26(2)
Sum both equations, you have: 6y²= 24. Now, you can find y.
6y²= 24
y²=4
y=±2
If y=2, from equation 2, you have
x² + y²= 13
x² + 2²= 13
x² + 4= 13
x² =13-4
x² =9
x=±3
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A circle is circumscribed around a rectangle with sides lengths 6 and 8 what is the area of the circle?
A. 16[tex]\pi[/tex]
B. 20[tex]\pi[/tex]
C. 24[tex]\pi[/tex]
D. 25[tex]\pi[/tex]
E. 30[tex]\pi[/tex]
Answer:
D. 25pi
Step-by-step explanation:
"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)
6^2 + 8^2 = d^2
36 + 64 = d^2
100 = d^2
d = 10
This is the diameter of the circle. The radius would then be 5.
Area of a circle is:
A = pi•r^2
= pi•5^2
= 25pi
12. Diameter,
A = 72Pie
(Circle)
Answer:
6.98
Step-by-step explanation:
I think that you are looking for the diameter and you are given the area of a circle.
a =[tex]\pi r^{2}[/tex] You are given pi, so [tex]r^{2}[/tex] = 72.
That means that r = [tex]\sqrt{72}[/tex] or a rounded answer of 8.49 rounded to the hundreds place. The diameter is equal to 2 radius, so the diameter rounded is 16.98
The difference of two numbers is 3/4. The sum of the two numbers is 9 1/4. Find the number
If the infinite curve y = e^−2x, x ≥ 0, is rotated about the x-axis. Find the area of the resulting surface.
The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
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If a true-false test with 10 questions is given what is the probability of scoring?
Answer:50%
Step-by-step explanation: It doesn't matter how many questions there are because for each question, you have a 50% chance of getting it right. So, the probability is 50%.
divide $800 between kofi and kweku so that kofi gets three times what kweku gets
Answer:
600 and 200
Step-by-step explanation:
kofi : kweku is 3 :1
so Kofi gets 3 out of ( 3 +1) = 3/4 of 800 = 3/4 * 800 = 600
kweku get s the rest 800- 600 = 200
5. Elias has 1/2 of a candy bar. He shares 1/4 of it with his best friend. How much of the candy bar did his best friend receive?
Answer:
1/8
Step-by-step explanation:
say the bar has 20 pieces. he has 10 pieces. and he gave away 1/4 of those 10
1/4 x 10 = 2.5
20 / 2.5 = 8
So his friend recieved 1/8
you could also just do 1/2 x 1/4 which is 1/8
Answer:
1/8 of the candy bar.
Step-by-step explanation:
Elias has 1/2 of a candy bar.
He gave 1/4 of 1/2 to his friend.
[tex]\sf Friend's s\ share = \dfrac{1}{4} \ of \ \dfrac{1}{2}[/tex]
[tex]\sf =\dfrac{1}{4}*\dfrac{1}{2}\\\\=\dfrac{1}{8}[/tex]
What are the solutions of the equation (x 2)2 12(x 2) – 14 = 0? use u substitution and the quadratic formula to solve.
The solutions of the given equation is x = -8 + 5√2 and x = -8 - 5√2.
The quadratic formula is used to find the roots of a quadratic equation. This formula helps to evaluate the solution of quadratic equations replacing the factorization method. If a quadratic equation does not contain real roots, then the quadratic formula helps to find the imaginary roots of that equation. The quadratic formula is also known as Shreedhara Acharya’s formula
(x + 2)² + 12(x + 2) – 14 = 0
Replacing x + 2 with u we get,
u² + 12u - 14
using quadratic formula we get
u = (-12 ±√(12² - 4x1 x-14))/2
u =(-12 ±√200)/2
u = -6 ± 5√2
x +2 = u = -6 ± 5√2
x = u = -8 ± 5√2.
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Solve the compound inequality and graph the solution on a number line
5x + 9 ≤ 2 and x + 6 > 12
Answer:
First:
5x + 9 < 2
x= 9/5= 1,8 < 2
Second:
x + 6 < 12
x= 12/6= 2 < 12
please help!!! i just need this one
Answer:
[tex]p = x \\ r = 6\% \\ t = 2yrs[/tex]
[tex]p = 1600[/tex]
please see the attachment
Answer:
P = $1600
Step-by-step explanation:
We have to use the equation:
[tex]\boxed{I = Prt}[/tex] .
We know that:
• I = $192
• P = ?
• r = 6% = 0.06
• t = 2 years
Substituting these values into the equation:
[tex]192 = P \times 0.06 \times 2[/tex]
Solving for P:
[tex]P = \frac{192}{0.06 \times 2}[/tex]
[tex]P = \bf \$1600[/tex]
The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days: Sample No.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Temperature 40 45 49 47 52 45 51 46 44 48 51 50 56 44 48 50 49 50 46 46 49 49 51 50 Use the data above to calculate the descriptive statistics.
The descriptive statistics for the above data is given as follows:
X = 12.5
What is Descriptive Statistics?
A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.
For X (mean) = [tex]{\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}[/tex]
= 300/24
= 12.5
For sample variance = [tex]s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr][/tex]
= (1/(24-1) (4,900 - (300²/24)
= 50
Standard deviation s = √s²
= √50
= 7.0711
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An astronaut visited mars. his weight on earth was 180 pounds, and his weight on mars was only 72 pounds. he removed a rock with a weight of 16 pounds on mars. what is the weight of the rock on earth? a. 1.4 pounds c. 6.4 pounds b. 4 pounds d. 40 pounds
Answer: d. 40 pounds
Step-by-step explanation: let e equal the number of pounds weigh on Earth and m equal the number of pounds weighs on Mars.
so
72m=180e
1m= 72m/72
e= 180/72 = 2.5
1m=2.5e
16m=1 x16
e= 16 x 2.5
e= 40
so therefore, 16m=40e
I hope this helps
10 by 28 + - 32 by 49 rational number
pls answer it
thank you
By simplifying the fraction 10/28 ÷ 32/49 exists 35/64.
How to simplify fractions?The first stage of dividing fractions exists to estimate the reciprocal (reverse the numerator and denominator) of the second fraction. Subsequently, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if required.
To find the reciprocal of the divisor
Reciprocal of 32/49 = 49/32
Now, multiply it by the dividend, then we get
So, 1028 ÷ 3249 = 10/28 × 49/32
= (10 × 49)/(28 × 32) = 490/896
After decreasing the fraction, the answer exists at 35/64.
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I thought I just had to half the diameter and then put it into the volume formula for cylinders but ig I was wrong? Help please?
Answer:
10830.87 mm³
Step-by-step explanation:
Hello!
Volume of a cylinder: [tex]V = \pi r^2(h)[/tex]
[tex]\pi[/tex] = pir = radius (half diameter)h = heightThe radius for this cylinder is 9.525, after dividing 19.05 by 2.
Plug it into the volume formula to solve for the volume.
Find the Volume[tex]V = \pi r^2(h)[/tex][tex]V = \pi (9.525)^2(38)[/tex][tex]V = \pi (90.725625)(38)[/tex][tex]V = 3447.57375\pi[/tex][tex]V = 1083087236570...\approx10830.87[/tex]The volume is approximately 10830.87 cubic millimeters.
Laura completed the following steps to find a product.
Multiply: Three-sevenths times 8
Step 1: 8 times three-sevenths
Step 2: StartFraction (8 plus 3) over 7 EndFraction
Step 3: Eleven-sevenths
Step 4: 1 and four-sevenths
In which step did Laura make her first mistake?
Step 1
Step 2
Step 3
Step 4
The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying
Multiplication of fractions and integers
Fractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.
Given the following equation
Multiply 3/7 and 8
This is expressed mathematically as;
3/7 * 8
Step 1: Swap to have;
8 * 3/7
Step 2: Group the numerator
(8*2)/7
Step 3; Simplify
16/7
Step 4; Convert to mixed fraction
16/7= 2 2/7
The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying
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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y29=1
The Jacobian for this transformation is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}[/tex]
with determinant [tex]|J| = 12[/tex], hence the area element becomes
[tex]dA = dx\,dy = 12 \, du\,dv[/tex]
Then the integral becomes
[tex]\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv[/tex]
where [tex]R'[/tex] is the unit circle,
[tex]\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1[/tex]
so that
[tex]\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv[/tex]
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
[tex]\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}[/tex]
Then
[tex]\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}[/tex]
Please help what is the answer?
Answer:
C
Step-by-step explanation:
[tex]-15x+60\leq 105 \\ \\ -15x \leq 45 \\ \\ x \geq -3[/tex]
[tex]14x+11 \leq -31 \\ \\ 14x \leq -42 \\ \\ x \leq -3[/tex]
The intersection is x = 3.
pls help questions 5-7
Answer: 0.032, 18, 4224, 7.58
Step-by-step explanation:
5. 5 L = 5000 mL = 5000 [tex]cm^{3}[/tex]
5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L
6. There is (13 - 11) x 20 x 10 = 400 [tex]cm^{3}[/tex] left unoccupied in the box
400/23 = 17.4 so it takes 18 balls to overflow the water
7. 1 mL = 1 [tex]cm^{3}[/tex]
(a) 22 x 12 x 16 = 4224 [tex]cm^{3}[/tex] = 4224 mL
(b) 2 L = 2000 mL = 2000 [tex]cm^{3}[/tex]
22 x 12 = 264
2000/264 = 7.58 cm
What is the probability distribution of X when X~B(1,1/25)?
P(X= 0) = 0.96
P(X= 1) = 0.04
P(X= 0) = 0.75
P(X= 1) = 0.25
P(X= 0) = 0.04
P(X= 1) = 0.96
P(X= 0) = 0.25
P(X= 1) = 0.75
The probability distribution of X when X~B(1,1/25) is (Option A)
P(X= 0) = 0.96P(X= 1) = 0.04See the explanation below.
What is the explanation to the above solution?Given X~B(n,p)
P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)
Thus, X~B [1, 1/25]
1/25 = 0.04
hence, p(x=0)
= C⁰₁ * 0.04⁰ (1 - 0.04)¹
= 0.96
P (x=1)
= C¹₁ 0.04¹ (1-0.04)⁰
= 0.04
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How do I get my answer
What is 0.08 written as a fraction in simplest form?
Answer:
[tex]\frac{2}{25}[/tex]
Step-by-step explanation:
Each "place" in the decimal, can be represented with a base 10 in the numerator.
For example the "tenths" place can be represented as: [tex]\frac{a}{10^1}[/tex] where a=decimal.
The hundredths place can be represented as: [tex]\frac{a}{10^2}[/tex]
The thousandths place can be represented as: [tex]\frac{a}{10^3}[/tex]
and so on...
In this case, we have a decimal in the hundredths place which can be represented as: [tex]\frac{8}{10^2} = \frac{8}{100}[/tex]. Now to simplify this fraction, you simply divide both sides by 4 (greatest common factor of 8 and 100), or in other words multiply it by 0.25/0.25 which is just 1, so the value is the same. [tex]\frac{8}{100} * \frac{0.25}{0.25} = \frac{2}{25}[/tex]
