Answer: Try D
Step-by-step explanation:
What is the volume of the cylinder below?
The answer is D. 36pi units^3
Hope this helps!
The formula for cylinder volume is: pi*r^2*h
For this case we have that the volume of the cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
h: It is the height of the cylinder
A: It is the radius of the cylinder
We have to, according to the given data:[tex]h = 4\\r = 3[/tex]
Substituting:
[tex]V = \pi * (3) ^ 2 * 4\\V = \pi * 9 * 4\\V = 36 \ pi[/tex]
[tex]36 \pi \ units ^ 3[/tex]
ANswer:
Option D
[tex]36 \pi \ units ^ 3[/tex]
Help please simplify: 4(3b)
Answer: 12b
Step-by-step explanation: you multiply 4 by 3 but keep the b
Answer:
C ---> 12b
Step-by-step explanation:
First you would distribute the 4 to the 3b which will give you 12b.
4(3b)
4*3=12
12b
Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y, z) = (x + y2) i + xz j + (y + z) k, r(t) = t2 i + t3 j − 2t k, 0 ≤ t ≤ 2 $$ correct: your answer is correct.
[tex]\vec r(t)=t^2\,\vec\imath+t^3\,\vec\jmath-2t\,\vec k[/tex]
[tex]\mathrm d\vec r=(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]
[tex]\vec f(x,y,z)=(x+y^2)\,\vec\imath+xz\,\vec\jmath+(y+z)\,\vec k[/tex]
[tex]\vec f(x(t),y(t),z(t))=(t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k[/tex]
The line integral is
[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^2\bigg((t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k\bigg)\cdot(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2(2t^7-6t^5+4t)\,\mathrm dt=\boxed{8}[/tex]
Given:
[tex]\to \bold{\int_{c} \ F \cdot dx}[/tex]
Where
[tex]\to \bold{F(x,y,z)=(x+y^2)i+xzj+(y+z)K}[/tex] and C is given by the vector function [tex]\bold{r(t)}[/tex].
[tex]\to \bold{r(t)=t^2i+t^3j-2tk,\ \ 0\leq t\leq 2}\\\\\to \bold{dx=(2ti+3t^2j-2k)dt}\\\\[/tex]
therefore
[tex]\to \bold{x=t^2}\\\\ \to \bold{y=t^3}\\\\ \to \bold{z=2t}\\\\\to \bold{F(r)=(t^2+(t^3)^2)i+t^2(-2t)j+(t^3-2t)k}\\\\[/tex]
[tex]\bold{=(t^2+t^6)i-2t^3j+(t^3-2t)k}\\\\[/tex]
[tex]\bold{\therefore}\\\\\bold{F(r).dx=((t^2+t^6)i-2t^3j+(t^3-2t)k).(2ti+3t^2j-2k)}\\\\[/tex]
[tex]=\bold{((t^2+t^6)2t-2t^3(3t^2)+(t^3-2t)(-2)]dt}\\\\=\bold{(2t^3+2t^7-6t^5-2t^3+4t)dt}\\\\=\bold{(2t^7-6t^5+4t)dt}\\\\[/tex]
Calculating the line integral:
[tex]\bold{\int_{c}\ F .dx=\int^{2}_{t=0} (2t^7-6t^5+4t)dt}\\\\[/tex]
[tex]=\bold{[\frac{t^8}{4}-t^6+2t^2]^{2}_{0}}\\\\=\bold{\frac{2^8}{4}-2^6+2(2)^2}\\\\=\bold{\frac{256}{4}-64+2(4)}\\\\=\bold{64-64+8}\\\\=\bold{8}[/tex]
Therefore the final answer "8".
Learn more:
line integral: brainly.com/question/16571684
Use the divergence theorem to find the outward flux of the vector field F(xyz)= 4x^2 i + 4y^2 j + 3z^2 k across the boundary of the rectangular prism: 0
[tex]\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z[/tex]
Let [tex]S[/tex] be the surface of the rectangular prism bounded by the planes [tex]x=0[/tex], [tex]x=a[/tex], [tex]y=0[/tex], [tex]y=b[/tex], [tex]z=0[/tex], and [tex]z=c[/tex]. By the divergence theorem, the integral of [tex]\vec F[/tex] over [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over the interior of [tex]S[/tex] (call it [tex]R[/tex]):
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}[/tex]
Answer:
[tex]\displaystyle \iiint_D {\nabla \cdot \textbf{F}} \, dV = \boxed{6875}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Partial Derivatives
Vector Calculus (Line Integrals)
Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]
Div and Curl:
[tex]\displaystyle \text{div \bf{F}} = \nabla \cdot \textbf{F}[/tex][tex]\displaystyle \text{curl \bf{F}} = \nabla \times \textbf{F}[/tex]Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]
Step-by-step explanation:
*Note:
Your question is incomplete, but I have defined the missing portions of the question below.
Step 1: Define
Identify given.
[tex]\displaystyle \textbf{F} (x, y, z) = 4x^2 \hat{\i} + 4y^2 \hat{\j} + 3z^2 \hat{\text{k}}[/tex]
[tex]\displaystyle \text{Region (Boundary de} \text{fined by rectangular prism):} \left\{ \begin{array}{ccc} 0 \leq x \leq 5 \\ 0 \leq y \leq 5 \\ 0 \leq z \leq 5 \end{array}[/tex]
Step 2: Find Flux Pt. 1
[Vector Field] Find div F:Step 3: Find Flux Pt. 2
[Flux] Define:We can evaluate the Flux integral (Divergence Theorem integral) using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 \int\limits^5_0 {4x^2 + x \big( 8y + 6z \big) \bigg| \limits^{x = 5}_{x = 0}} \, dy \, dz \\& = \int\limits^5_0 \int\limits^5_0 {\big( 40y + 30z + 100 \big)} \, dy \, dz \\& = \int\limits^5_0 {20y^2 + y \big( 30z + 100 \big) \bigg| \limits^{y = 5}_{y = 0}} \, dz \\\end{aligned}[/tex]
[tex]\displaystyle\begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 {\big( 150z + 1000 \big)} \, dz \\& = \big( 75z^2 + 1000z \big) \bigg| \limits^{z = 5}_{z = 0} \\& = \boxed{6875} \\\end{aligned}[/tex]
∴ [tex]\displaystyle \Phi = \boxed{6875}[/tex]
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Topic: Multivariable Calculus
Unit: Stokes' Theorem and Divergence Theorem
Julio and his family ordered 6 pizzas for dinner. His parents ate 3/7 of one pizza, Julio's brothers ate 2 3/4 pizzas and his sisters ate 2 1/2 pizzas. How much pizza was left for Julio to eat?
approximately 0.3 or 3/10 pizza was left for Julio to eat.
mind you some numbers were rounded. if you want the exact number then it's 9/28 which is equal to 0.32.
hope this helps
After accounting for the amounts of pizza eaten by Julio's family (parents, brothers, and sisters), you find that there was approximately 0.36 pizzas left for Julio to eat.
Explanation:This question deals with some basic arithmetic and fractions. Start by counting how many pizzas Julio's family ate altogether. His parents ate 3/7 of one pizza, his brothers ate 2 3/4 pizzas, and his sisters ate 2 1/2 pizzas.
To add these amounts together, you might find it easiest to convert all the fractions to sevenths. The brothers ate 2 4/7 pizzas (as 4/7 is equivalent to 1/2) and the sisters ate 2 3.5/7 pizzas (as 3.5/7 is equivalent to 1/2). Add these to the 3/7 pizza the parents ate, you find the family ate a total of approximately 5.64 pizzas.
Since Julio's family ordered 6 pizzas in total, you then subtract the total amount eaten by the family from 6, which is approximately 0.36 pizzas. Therefore, Julio was left with 0.36 pizzas to eat.
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At each point (x,y) on the curve the slope is 2x+3 the curve passes through the point (-3,0)
Answer:
The equation of the curve is y = x² + 3x
Step-by-step explanation:
I get your drift, but wish you had stated specifically that you wanted to find the equation of this curve.
Slope of tangent line to curve is dy/dx = 2x + 3.
Integrating that with respect to x yields y = x² + 3x + C.
The point (-3, 0) must satisfy this equation:
0 = (-3)² + 3(-3) + C, so C = 0.
The equation of the curve is y = x² + 3x
The equation of the curve where the slope at any point is 2x + 3 and it passes through the point (-3, 0) is y = x² + 3x.
The student's question involves finding the equation of a curve given that at each point (x, y) on the curve, the slope is 2x + 3, and the curve passes through the point (-3, 0). This is a problem that involves differential equations, as it asks us to find a function y(x) whose derivative with respect to x is given.
To find the equation of the curve, we integrate the slope function. Since the slope at any point is 2x + 3, we have:
∂y/∂x = 2x + 3
Integrating both sides with respect to x gives:
y = x² + 3x + C
To find the constant of integration C, we use the fact that the curve passes through (-3, 0). Substituting these values into the equation gives:
0 = (-3)² + 3(-3) + C
0 = 9 - 9 + C
Thus, C = 0, and the equation of the curve is:
y = x² + 3x.
Given the scale drawing of a one bedroom apartment, what is the actual area of the bedroom?
A) 27 ft2
B) 54 ft2
C) 96 ft2
D) 108 ft2
Answer: Option D.
Step-by-step explanation:
You can observe that the dimensions of the bedroom in the scale drawing are:
[tex]length=2"\\width=1.5"[/tex]
You know that [tex]\frac{1}{2}"=3feet[/tex]
Then you need to convert these dimensions to the actual dimensions. So, you get:
[tex]actual\ lenght=\frac{(2")(3ft)}{\frac{1}{2}" }=12ft\\\\actual\ width=\frac{(1.5")(3ft)}{\frac{1}{2}" }=9ft[/tex]
Therefore, you can calculate the actual area of the bedroom. This is:
[tex]Area=(actual\ lenght)(actual\ width)\\Area=(12ft)(9ft)\\Area=108ft^2[/tex]
Answer:
Option D.
Step-by-step explanation:
From the given figure it is clear that
Length of the bedroom in scale drawing = 2''
Width of the bedroom in scale drawing = 1.5''
It is given that
Scale [tex]\frac{1}{2}''=3feet[/tex]
[tex]1''=6feet[/tex]
Using this conversion we get
[tex]2''=12feet[/tex]
[tex]1.5''=9feet[/tex]
Actual length of the bedroom = 12 feet
Actual width of the bedroom = 9 feet
Area of a rectangle is
[tex]Area=length\times width[/tex]
Actual area of the bedroom is
[tex]Area=12\times 9[/tex]
[tex]Area=108[/tex]
The actual area of the bedroom is 108 ft2.
Therefore, the correct option is D.
Two friends leave there houses and go towards each others, one friend runs 8 miles a hour, the other runs 7 miles an hour, there houses are 20 miles apart they both leave at 6:00 pm, what time do they meet each other?
hi there the answer is 7:30 see the picture
Which of the following would you do if you were to write the expression 3 * 3 * 3 *3 * 3 * 3 *3 * 3 * 3 *3 * 3 * 3 using an exponent?
Check al that apply.
A. You would write 12^3
B. You would use 12 as the base and 3 as the exponent.
C. You would write 3^12
D. You would use 3 as the base and 12 as the exponent.
Answer:
C and D
Step-by-step explanation:
3 is the base because its the number being multiplied repeatedly while the exponent would be the number of times its being multiplied.
Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per week. This week, her goal is to make at least $75.
Answer:
i have provided some pictures to help you i cant post the graphs though cuz they dont allow me to but if you need them i can send link pictures :)
i also love you're Naruto profile picture uwu
Jeanne can use a system of inequalities to make at least $75.
How Jeanne can make at least $75?Let X represent babysitting hours = $6 per hour.
Y represent tutoring hours = $10 per hour.
If she will work more 7.5hours or more than 7.5 hours she can make $75 easily.
$10 per hour × 7 hours = $70
& $6 per hour × 1 hour = $6
so, $70 + $6 = $76.
In the above way she can make easily $75.
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18, 19, 20, 20, 23, 26, 260
What is the better measure of center for these data? Mean or median? Why? Explain your answer.
Answer:
Median
Step-by-step explanation:
This set of data has an extreme outlier, which will throw off the mean. The median, on the other hand, does not change or changes minimally whether or not the outlier is there.
By default, the mean is always better, but if an outlier, such as this one, is too large, the median is better.
WILL MARK BRAINLIEST PLEASE HELP ASAP. The value of n is a distance of 1.5 units from -2 on a number line.
Answer:
see explanation
Step-by-step explanation:
There are 2 possible positions for n, that is
- 2 - 1.5 = - 3.5
OR
- 2 + 1.5 = - 0.5
Both are 1.5 units distance from - 2
The possible values of n are -0.5 and -3.5
Step-by-step explanation:
Analyze two cases
1) n-(-2)=1.5
Solve for n
n+2=1.5
n=1.5-2
n=-0.5
2) -2-n=1.5
n=-2-1.5
n=-3.5
A pepperoni pizza cost $7.50 and a cheese pizza costs $6.00. If Cindy purchases five cheese pizzas and four pepperoni pizzas for a birthday party and pays with a $65.00 cash, how much change will she receive?
Answer:
She will receive [tex]\$5[/tex]
Step-by-step explanation:
step 1
Find the total cost
The total cost is equal to
[tex]5(\$6.00)+4(\$7.50)=\$60[/tex]
step 2
Find the difference
[tex]\$65-\$60=\$5[/tex]
Answer:
$5
Step-by-step explanation:
65-6x5-4x7.5=5
The range of F(x) = logb x is the set of all real numbers. True or false
The range of F(x) = logb x is the set of all real numbers.
TRUE
The range of F(x) = logb x is the set of all real numbers since the correct option is True.
How to find a Domain?The domain of this function is R+ or a positive real number For range if b>1 function will be an increasing function and the graph will be asymptotic to the negative y-axis. which implies if x goes to infinity f(x) goes to infinity and vice versa if 0<b<1 function will be a decreasing and graph will be asymptotic to the positive y-axis. which implies if x goes to infinity f(x) goes to 0 and vice-versa the range of the above function is all real numbers.
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A person invests $1,150 in an account that earns 5% annual interest compounded continuously. Find when the value of the investment reaches $2,000. If necessary round to the nearest tenth.
The investment will reach a value of $2,000 in approximately_____years.
Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
[tex]A(t)=Pe^{rt}[/tex]
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
[tex]2000=1150e^{{.05t}[/tex]
We will simplify this first a bit by dividing 2000 by 1150 to get
[tex]1.739130435=e^{.05t}[/tex]
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.
Estimate the percent of each number. 47% of 77
To estimate 47% of 77, multiply 77 by 0.47. The estimated value is approximately 36.19.
Explanation:To estimate the percent of a number, we multiply the number by the percentage as a decimal. In this case, to estimate 47% of 77, we multiply 77 by 0.47. This gives us an estimated value of 36.19. Therefore, 47% of 77 is approximately 36.19.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Cynthia decides she is going to purchase a used passenger car. Her grandparents agree to pay for 50% of the passenger car. To get an idea of prices Cynthia looks at listings in a local used automobile publication and on a local internet site.
Which answer best describes the sample and population?
Answer:
its going to have to be option c
Step-by-step explanation:
because it shows all the listings of cars next to her
Answer: D) sample: local listings and internet sites
population: all used passenger cars
Step-by-step explanation:
A sample is a subset of items from a larger population.
A population includes all of the elements from a set of data.
Cynthia wants to buy a used passenger car.
All available used cars is the POPULATION
Cynthia looks at local listings and on internet sites.
This is a subset of all available used cars so this is the SAMPLE
Furthermore, she may not find what she is looking for and may expand her subset to include used car lots, etc.
Solve for Y (please help me solve!)
Answer:
b = 10
Step-by-step explanation:
a) Solve by inspection. b=10 makes both fractions equal to 1.
Both the numerator and denominator of the fraction on the right are 2 greater than those of the fraction on the left. The fractions will be equal when numerator and denominator are equal.
__
b) Multiply by 60 and solve in the usual way.
6b = 5(b+2)
b = 10 . . . . . . . . . . subtract 5b
__
c) Expand the fraction on the right, subtract the variable term.
b/10 = b/12 + 2/12
b(1/10 - 1/12) = 1/6
b/60 = 1/6 . . . . simplify
b = 60/6 = 10 . . . . multiply by 60
_____
Comment on the question
There is no "y", so you cannot solve for y. This is another example of poor quality control (editing) of math curriculum materials. It is my sincere wish that you not have to put up with that. Math is tough enough without this added confusion.
Answer:
b=10
Step-by-step explanation:
The pillars in front of Mr. Jefferson's home are shaped like cylinders with a height of 24 ft and a radius of 8 in. What is the lateral area of each pillar
Answer:
The lateral area is [tex]4,608\pi\ in^{2}[/tex] or [tex]32\pi\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a cylinder (pillar) is equal to
[tex]LA=2\pi rh[/tex]
Remember that
1 ft=12 in
Find the lateral area in square inches
we have
[tex]r=8\ in[/tex]
[tex]h=24\ ft[/tex] ----> convert to inches
[tex]h=24*12=288\ in[/tex]
substitute the values
[tex]LA=2\pi (8)(288)[/tex]
[tex]LA=4,608\pi\ in^{2}[/tex]
Find the lateral area in square feet
we have
[tex]h=24\ ft[/tex]
[tex]r=8\ in[/tex] -----> convert to feet
[tex]r=8/12=(2/3)\ ft[/tex]
substitute the values
[tex]LA=2\pi (2/3)(24)[/tex]
[tex]LA=32\pi\ ft^{2}[/tex]
Identify the volume of the composite figure. HELP PLEASE!!
Answer:
Vol. of the composite figure is 189 m³
Step-by-step explanation:
Find the volume of the larger figure by mult. together its 3 dimensions:
V = (9 m)(8 m)(3 m) = 216 m³.
Next, find the volume of the "notch," which is (3 m)³, or 27 m³.
Finally, subtract the "notch" volume from the 216 m³ volume found earlier:
216 m³ - 27 m³ = 189 m³
What is the volume of the cylinder below?
For this case we have that, by definition, the volume of the cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
h: It's the height
A: It's the radio
We have to:
[tex]h = 15\\r = 12[/tex]
Substituting:
[tex]V = \pi * (12) ^ 2 * 15\\V = \pi * 144 * 15\\V = 2160 \pi \ units ^ 3[/tex]
Answer:
Option B
Answer: 2160
Step-by-step explanation:
apex
Classify each conic section and write its equations in standard form. Show work.
[tex]4x^2+2y^2-8x+16y-52=0[/tex]
Answer:
The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1
Step-by-step explanation:
* Lets revise how to identify the type of the conic
- Rewrite the equation in the general form,
Ax² + Bxy + Cy² + Dx + Ey + F = 0
- Identify the values of A and C from the general form.
- If A and C are nonzero, have the same sign, and are not equal
to each other, then the graph is an ellipse.
- If A and C are equal and nonzero and have the same sign, then
the graph is a circle
- If A and C are nonzero and have opposite signs, and are not equal
then the graph is a hyperbola.
- If either A or C is zero, then the graph is a parabola
* Now lets solve the problem
The equation is 4x² + 2y² - 8x + 16y - 52 = 0
∴ A = 4 and C = 2 ⇒ same sign and different values
∴ The equation is ellipse
* The standard form of the ellipse is
(x - h)²/a² + (y - k)²/b² = 1
- Lets try to make this form from the general form
- Group terms that contain the same variable, and move the
constant to the opposite side of the equation
∴ (4x² - 8x) + (2y² + 16y) = 52
- Factorize the coefficients of the squared terms
∴ 4(x² - 2x) + 2(y² + 8y) = 52
- Complete the square for x and y
# To make completing square
- Divide the coefficient of x (or y) by 2 and then square the answer
- Add and subtract this square number and form the bracket of
the completing the square
# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1
∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4
- Rewrite as perfect squares ⇒ 4(x -1)² - 4
# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16
∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32
- Rewrite as perfect squares ⇒ 2(y + 4)² - 32
∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52
∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52
∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88
∴ (x - 1)²/22 + (y + 4)²/44 = 1
A wall with an area of (3x2 + 4x + 1) square units has a rectangular window that has a width of (x + 2) units and a length of (x + 1) units. The wall also has a built-in shelving unit that occupies an area of (x2 + 5x + 6) square units of wall space. If the wall is to be covered with wallpaper, how much wallpaper will be required?
Answer:
the total available area = (3x^2 + 4x + 1) - (2x^2 + 8x + 8) = x^2 - 4x - 7
Step-by-step explanation:
The question seems to ask available area and not how much wallpaper is required. Let's calculate the area of the rectangular window. Area of a rectangle = Length * Breath Area = (x + 2) * (x + 1) = x^2 + 3x + 2 The wall also has a built- in shelving unit that occupies an area of (x^2 + 5x + 6). So total area occupied by the rectangular wall and shelf is (x^2 + 3x + 2) + (x^2 + 5x + 6) = 2x^2 + 8x + 8. If the wall is to be covered with wallpaper
Sorry for the wait
If the angle of elevation of the escalator is 10° 21’ 36° find th length of the escalator (picture provided)
Answer:
The length of the escalator ≈ 1088.8 ft ⇒ answer (b)
Step-by-step explanation:
* Lets explain the problem
- Consider the escalator and the vertical raise formed a right
angle triangle
- The length of the escalator is the hypotenuse
- The vertical rise is on leg of the right triangle
- The angle of elevation is the angle between the hypotenuse
and the horizontal
* Now lets solve the problem
∵ Angle of elevation = 10° 21' 36"
∵ Vertical distance = 195.8 feet
* The vertical is opposite to the angle of elevation
∴ sin angel of elevation= the vertical/the length of the escalator
∴ sin(10° 21' 36") = 195.8/the length of the escalator
- By using cross multiplication
∴ The length of the escalator = 195.8/sin(10° 21' 36") = 1088.8 feet
* The length of the escalator = 1088.8 ft
Vector v has a direction of (-3,21). find the direction angle for v
Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees
Direction of a vectorThe direction of a vector is the degree at which the vector is moving with respect to the horizontal.
Given the coordinate point (-3, 21), the direction is expressed as:
theta = arctan(y/x)
Substitute
theta = arctan(21/-3)
theta =arctan(-7)
theta = -81.7 degrees
Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees
Learn more on direction of vector here: https://brainly.com/question/3184914
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The equation of a parabola is given.
y=34x2−6x+15
What are the coordinates of the vertex of the parabola?
Enter your answer in the boxes.
(
,
)
ANSWER
[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]
EXPLANATION
The given parabola has equation;
[tex]y = 34 {x}^{2} - 6x + 15[/tex]
Comparing this equation to
[tex]y = a{x}^{2} + bx + c[/tex]
we have
a=34, b=-6 and c=15
The x-coordinate of the vertex is given by:
[tex]x = \frac{ - b}{2a} [/tex]
[tex]x = \frac{ - - 6}{2(34)} [/tex]
[tex]x = \frac{ 6}{2(34)} [/tex]
[tex]x = \frac{ 3}{34} [/tex]
The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:
[tex]y = 34( { \frac{3}{34} })^{2} - 6( \frac{3}{34}) + 15[/tex]
[tex]y = { \frac{9}{34} } - \frac{18}{34}+ 15[/tex]
[tex]y = \frac{501}{34} [/tex]
The vertex is
[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]
Answer: (4,3)
He meant 3/4 not 34
graph the line with slope 1/2 passing through the point (4,4)
Using the point slope formula (y-y1=m(x-x1)) it is found to be y=1/2x+2.
What graph shows the solution set of the inequality x^2+10x+16/x-3 >0
[tex]x < - 10.434462 \\ x > 0[/tex]
Answer:
D
Step-by-step explanation:
Write the equation of a horizontal line that passes through the point (–2, 2).
x = –2
y = –2
y = 2
x = 2
Answer:
option C
y = 2
Step-by-step explanation:
Given in the question,
a co-ordinate = (-2,2)
x = -2
y = 2
Equation of the straight line
y = mx + c
here m = gradient of the line
c = y - intercept
we know that gradient of the horizontal line = 0
plug value in the equation above
y = (0)x + 2
y = 2
Find the distance..
Please help!!!
Answer:
d = 7.071068
Step-by-step explanation: